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Journal articles on the topic 'Generalized method of moments estimation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kuersteiner, Guido M., and Laszlo Matyas. "Generalized Method of Moments Estimation." Journal of the American Statistical Association 95, no. 451 (September 2000): 1014. http://dx.doi.org/10.2307/2669498.

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2

Andrews, Donald W. K. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation." Econometrica 67, no. 3 (May 1999): 543–63. http://dx.doi.org/10.1111/1468-0262.00036.

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3

Wooldridge, Jeffrey M. "Applications of Generalized Method of Moments Estimation." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 87–100. http://dx.doi.org/10.1257/jep.15.4.87.

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I describe how the method of moments approach to estimation, including the more recent generalized method of moments (GMM) theory, can be applied to problems using cross section, time series, and panel data. Method of moments estimators can be attractive because in many circumstances they are robust to failures of auxiliary distributional assumptions that are not needed to identify key parameters. I conclude that while sophisticated GMM estimators are indispensable for complicated estimation problems, it seems unlikely that GMM will provide convincing improvements over ordinary least squares and two-stage least squares--by far the most common method of moments estimators used in econometrics--in settings faced most often by empirical researchers.

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4

Hu, Yi, Xiaohua Xia, Ying Deng, and Dongmei Guo. "Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/324904.

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Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.

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5

Wilhelm, Daniel. "OPTIMAL BANDWIDTH SELECTION FOR ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION." Econometric Theory 31, no. 5 (October 2, 2014): 1054–77. http://dx.doi.org/10.1017/s026646661400067x.

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A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

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6

Chatelain, Jean-Bernard. "Improving consistent moment selection procedures for generalized method of moments estimation." Economics Letters 95, no. 3 (June 2007): 380–85. http://dx.doi.org/10.1016/j.econlet.2006.11.011.

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7

Nghiem, Linh H., Michael C. Byrd, and Cornelis J. Potgieter. "Estimation in linear errors-in-variables models with unknown error distribution." Biometrika 107, no. 4 (May 21, 2020): 841–56. http://dx.doi.org/10.1093/biomet/asaa025.

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Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

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8

Hall, Alastair R., Atsushi Inoue, Kalidas Jana, and Changmock Shin. "Information in generalized method of moments estimation and entropy-based moment selection." Journal of Econometrics 138, no. 2 (June 2007): 488–512. http://dx.doi.org/10.1016/j.jeconom.2006.05.006.

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9

Lynch, Anthony W., and Jessica A. Wachter. "Using Samples of Unequal Length in Generalized Method of Moments Estimation." Journal of Financial and Quantitative Analysis 48, no. 1 (February 2013): 277–307. http://dx.doi.org/10.1017/s0022109013000070.

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AbstractThis paper describes estimation methods, based on the generalized method of moments (GMM), applicable in settings where time series have different starting or ending dates. We introduce two estimators that are more efficient asymptotically than standard GMM. We apply these to estimating predictive regressions in international data and show that the use of the full sample affects inference for assets with data available over the full period as well as for assets with data available for a subset of the period. Monte Carlo experiments demonstrate that reductions hold for small-sample standard errors as well as asymptotic ones.

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10

Seo, Myung Hwan, Sueyoul Kim, and Young-Joo Kim. "Estimation of dynamic panel threshold model using Stata." Stata Journal: Promoting communications on statistics and Stata 19, no. 3 (September 2019): 685–97. http://dx.doi.org/10.1177/1536867x19874243.

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In this article, we develop a command, xthenreg, that implements the first-differenced generalized method of moments estimation of the dynamic panel threshold model that Seo and Shin (2016, Journal of Econometrics 195: 169–186) proposed. Furthermore, we derive the asymptotic variance formula for a kink-constrained generalized method of moments estimator of the dynamic threshold model and provide an estimation algorithm. We also propose a fast bootstrap algorithm to implement the bootstrap for the linearity test. We illustrate the use of xthenreg through a Monte Carlo simulation and an economic application.

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11

Alshkaki, Rafid. "A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data." Statistics, Optimization & Information Computing 8, no. 2 (May 28, 2020): 521–48. http://dx.doi.org/10.19139/soic-2310-5070-869.

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In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.

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12

Abouammoh, Abdulrahman, and Mohamed Kayid. "A New Flexible Generalized Lindley Model: Properties, Estimation and Applications." Symmetry 12, no. 10 (October 14, 2020): 1678. http://dx.doi.org/10.3390/sym12101678.

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A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.

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13

Frazier, David, and Eric Renault. "Indirect Inference: Which Moments to Match?" Econometrics 7, no. 1 (March 19, 2019): 14. http://dx.doi.org/10.3390/econometrics7010014.

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The standard approach to indirect inference estimation considers that the auxiliary parameters, which carry the identifying information about the structural parameters of interest, are obtained from some recently identified vector of estimating equations. In contrast to this standard interpretation, we demonstrate that the case of overidentified auxiliary parameters is both possible, and, indeed, more commonly encountered than one may initially realize. We then revisit the “moment matching” and “parameter matching” versions of indirect inference in this context and devise efficient estimation strategies in this more general framework. Perhaps surprisingly, we demonstrate that if one were to consider the naive choice of an efficient Generalized Method of Moments (GMM)-based estimator for the auxiliary parameters, the resulting indirect inference estimators would be inefficient. In this general context, we demonstrate that efficient indirect inference estimation actually requires a two-step estimation procedure, whereby the goal of the first step is to obtain an efficient version of the auxiliary model. These two-step estimators are presented both within the context of moment matching and parameter matching.

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14

Mamuangbon, Supitcha, Kamon Budsaba, and Andrei Volodin. "The Performance of Estimators for Generalization of Crack Distribution." WSEAS TRANSACTIONS ON MATHEMATICS 20 (April 2, 2021): 106–11. http://dx.doi.org/10.37394/23206.2021.20.11.

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In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.

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15

Mat Jan, Nur Amalina, Ani Shabri, and Ruhaidah Samsudin. "Handling non-stationary flood frequency analysis using TL-moments approach for estimation parameter." Journal of Water and Climate Change 11, no. 4 (August 16, 2019): 966–79. http://dx.doi.org/10.2166/wcc.2019.055.

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Abstract Non-stationary flood frequency analysis (NFFA) plays an important role in addressing the issue of the stationary assumption (independent and identically distributed flood series) that is no longer valid in infrastructure-designed methods. This confirms the necessity of developing new statistical models in order to identify the change of probability functions over time and obtain a consistent flood estimation method in NFFA. The method of Trimmed L-moments (TL-moments) with time covariate is confronted with the L-moment method for the stationary and non-stationary generalized extreme value (GEV) models. The aims of the study are to investigate the behavior of the proposed TL-moments method in the presence of NFFA and applying the method along with GEV distribution. Comparisons of the methods are made by Monte Carlo simulations and bootstrap-based method. The simulation study showed the better performance of most levels of TL-moments method, which is TL(η,0), (η = 2, 3, 4) than the L-moment method for all models (GEV1, GEV2, and GEV3). The TL-moment method provides more efficient quantile estimates than other methods in flood quantiles estimated at higher return periods. Thus, the TL-moments method can produce better estimation results since the L-moment eliminates lowest value and gives more weight to the largest value which provides important information.

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16

Gourieroux, C., and A. Monfort. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form." Econometric Theory 5, no. 1 (April 1989): 63–82. http://dx.doi.org/10.1017/s0266466600012263.

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A general framework for asymptotic tests is proposed. The framework contains as particular cases tests based on various estimation techniques: maximum likelihood methods, pseudo-maximum likelihood (PML) methods and quasi-generalized PML methods,m-estimation methods, moments or generalized moments method, and asymptotic least squares. Moreover the null hypothesis has a general mixed form, including the usual implicit and explicit form.

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17

Arellano, Manuel. "Sargan's Intrumental Variables Estimation and the Generalized Method of Moments." Journal of Business & Economic Statistics 20, no. 4 (October 2002): 450–59. http://dx.doi.org/10.1198/073500102288618595.

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18

Kitamura, Yuichi, and Michael Stutzer. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation." Econometrica 65, no. 4 (July 1997): 861. http://dx.doi.org/10.2307/2171942.

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19

Park, Suk K., Sung K. Ahn, and Sinsup Cho. "Generalized method of moments estimation for cointegrated vector autoregressive models." Computational Statistics & Data Analysis 55, no. 9 (September 2011): 2605–18. http://dx.doi.org/10.1016/j.csda.2011.03.010.

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20

Ahmad, Muhammad Idrees. "Estimation of Generalized Logistic Distribution for Financial Data." Journal of Engineering and Science Research 3, no. 2 (April 17, 2019): 34–37. http://dx.doi.org/10.26666/rmp.jesr.2018.2.5.

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Risk management of financial assets requires the knowledge of the form of the probability distribution to estimate the probability of extreme price changes. It is not only the shape of the distribution which is important but the methods of estimation also plays a fundamental role to compare the risk-reward tradeoff for different trading strategies with a reasonable adequacy. In the present study the generalized logistic distribution is considered to fit stock market returns of Muscat Securities Market. The extreme quantiles are estimated by the method of probability weighted moments and are compared with that of method of moments.

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21

Westgate, Philip M. "A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE–type marginal model for binary outcomes." Clinical Trials 16, no. 1 (October 8, 2018): 41–51. http://dx.doi.org/10.1177/1740774518803635.

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Background/aims Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. Methods We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Results Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation–based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Conclusion Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation–based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation–based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

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22

Khan, Said Arab, Ijaz Hussain, Tajammal Hussain, Muhammad Faisal, Yousaf Shad Muhammad, and Alaa Mohamd Shoukry. "Regional Frequency Analysis of Extremes Precipitation Using L-Moments and Partial L-Moments." Advances in Meteorology 2017 (2017): 1–20. http://dx.doi.org/10.1155/2017/6954902.

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Extremes precipitation may cause a series of social, environmental, and ecological problems. Estimation of frequency of extreme precipitations and its magnitude is vital for making decisions about hydraulic structures such as dams, spillways, and dikes. In this study, we focus on regional frequency analysis of extreme precipitation based on monthly precipitation records (1999–2012) at 17 stations of Northern areas and Khyber Pakhtunkhwa, Pakistan. We develop regional frequency methods based on L-moment and partial L-moments (L- and PL-moments). The L- and PL-moments are derived for generalized extreme value (GEV), generalized logistic (GLO), generalized normal (GNO), and generalized Pareto (GPA) distributions. The Z-statistics and L- and PL-moments ratio diagrams of GNO, GEV, and GPA distributions were identified to represent the statistical properties of extreme precipitation in Northern areas and Khyber Pakhtunkhwa, Pakistan. We also perform a Monte Carlo simulation study to examine the sampling properties of L- and PL-moments. The results show that PL-moments perform better than L-moments for estimating large return period events.

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23

Liu, Bin, Cindy Long Yu, Michael Joseph Price, and Yan Jiang. "Generalized Method of Moments Estimators for Multiple Treatment Effects Using Observational Data from Complex Surveys." Journal of Official Statistics 34, no. 3 (September 1, 2018): 753–84. http://dx.doi.org/10.2478/jos-2018-0035.

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Abstract In this article, we consider a generalized method moments (GMM) estimator to estimate treatment effects defined through estimation equations using an observational data set from a complex survey. We demonstrate that the proposed estimator, which incorporates both sampling probabilities and semiparametrically estimated self-selection probabilities, gives consistent estimates of treatment effects. The asymptotic normality of the proposed estimator is established in the finite population framework, and its variance estimation is discussed. In simulations, we evaluate our proposed estimator and its variance estimator based on the asymptotic distribution. We also apply the method to estimate the effects of different choices of health insurance types on healthcare spending using data from the Chinese General Social Survey. The results from our simulations and the empirical study show that ignoring the sampling design weights might lead to misleading conclusions.

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24

Wang, Ning, Xuegui Song, and Julian Cheng. "Generalized Method of Moments Estimation of the Nakagami-m Fading Parameter." IEEE Transactions on Wireless Communications 11, no. 9 (September 2012): 3316–25. http://dx.doi.org/10.1109/twc.2012.071612.111838.

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25

Lee, Jeonghwa. "Generalized Bernoulli process: simulation, estimation, and application." Dependence Modeling 9, no. 1 (January 1, 2021): 141–55. http://dx.doi.org/10.1515/demo-2021-0106.

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Abstract A generalized Bernoulli process (GBP) is a stationary process consisting of binary variables that can capture long-memory property. In this paper, we propose a simulation method for a sample path of GBP and an estimation method for the parameters in GBP. Method of moments estimation and maximum likelihood estimation are compared through empirical results from simulation. Application of GBP in earthquake data during the years of 1800-2020 in the region of conterminous U.S. is provided.

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Gallant, A. Ronald, and George Tauchen. "Which Moments to Match?" Econometric Theory 12, no. 4 (October 1996): 657–81. http://dx.doi.org/10.1017/s0266466600006976.

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We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution' of the observed data but is not required to nest it. If the auxiliary model nests the structural model then the estimator is as efficient as maximum likelihood. The estimator is advantageous when expectations under a structural model can be computed by simulation, by quadrature, or by analytic expressions but the likelihood cannot be computed easily.

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27

Erickson, Timothy, Robert Parham, and Toni M. Whited. "Fitting the Errors-in-variables Model Using High-order Cumulants and Moments." Stata Journal: Promoting communications on statistics and Stata 17, no. 1 (March 2017): 116–29. http://dx.doi.org/10.1177/1536867x1701700107.

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In this article, we consider a multiple mismeasured regressor errors-in-variables model. We present xtewreg, a command for using two-step generalized method of moments and minimum distance estimators that exploit overidentifying information contained in high-order cumulants or moments of the data. The command supports cumulant or moment estimation, internal support for the bootstrap with moment condition recentering, an arbitrary number of mismeasured regressors and perfectly measured regressors, and cumulants or moments up to an arbitrary degree. We also demonstrate how to use the estimators in the context of a corporate leverage regression.

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Guerrier, Stephane, Roberto Molinari, and Maria-Pia Victoria-Feser. "Estimation of Time Series Models via Robust Wavelet Variance." Austrian Journal of Statistics 43, no. 4 (June 13, 2014): 267–77. http://dx.doi.org/10.17713/ajs.v43i4.45.

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A robust approach to the estimation of time series models is proposed. Taking froma new estimation method called the Generalized Method of Wavelet Moments (GMWM)which is an indirect method based on the Wavelet Variance (WV), we replace the classicalestimator of the WV with a recently proposed robust M-estimator to obtain a robustversion of the GMWM. The simulation results show that the proposed approach can beconsidered as a valid robust approach to the estimation of time series and state-spacemodels.

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Girik Allo, Caecilia Bintang, Bambang Widjanarko Otok, and Purhadi. "Estimation Parameter of Generalized Poisson Regression Model Using Generalized Method of Moments and Its Application." IOP Conference Series: Materials Science and Engineering 546 (June 26, 2019): 052050. http://dx.doi.org/10.1088/1757-899x/546/5/052050.

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30

Andrews, Donald W. K. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary." Journal of Business & Economic Statistics 20, no. 4 (October 2002): 530–44. http://dx.doi.org/10.1198/073500102288618667.

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Barboza, Luis A., and Frederi G. Viens. "Parameter estimation of Gaussian stationary processes using the generalized method of moments." Electronic Journal of Statistics 11, no. 1 (2017): 401–39. http://dx.doi.org/10.1214/17-ejs1230.

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Baum, Christopher F., Mark E. Schaffer, and Steven Stillman. "Enhanced Routines for Instrumental Variables/Generalized Method of Moments Estimation and Testing." Stata Journal: Promoting communications on statistics and Stata 7, no. 4 (January 2007): 465–506. http://dx.doi.org/10.1177/1536867x0700700402.

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Baum, Christopher F., Mark E. Schaffer, and Steven Stillman. "Enhanced Routines for Instrumental Variables/Generalized Method of Moments Estimation and Testing." Stata Journal: Promoting communications on statistics and Stata 7, no. 4 (December 2007): 465–506. http://dx.doi.org/10.1177/1536867x0800700402.

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34

Jesus, Joao, and Richard E. Chandler. "Estimating functions and the generalized method of moments." Interface Focus 1, no. 6 (September 8, 2011): 871–85. http://dx.doi.org/10.1098/rsfs.2011.0057.

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Estimating functions provide a very general framework for statistical inference, and are particularly useful when one is either unable or unwilling to specify a likelihood function. This paper aims to provide an accessible review of estimating function theory that has potential for application to the analysis and modelling of a wide range of complex systems. Assumptions are given in terms that can be checked relatively easily in practice, and some of the more technical derivations are relegated to an online supplement for clarity of exposition. The special case of the generalized method of moments is considered in some detail. The main points are illustrated by considering the problem of inference for a class of stochastic rainfall models based on point processes, with simulations used to demonstrate the performance of the methods.

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35

Luong, Andrew. "Generalized Method of Moments and Generalized Estimating Functions Using Characteristic Function." Open Journal of Statistics 10, no. 03 (2020): 581–99. http://dx.doi.org/10.4236/ojs.2020.103035.

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36

Hahn, Jinyong. "A Note on Bootstrapping Generalized Method of Moments Estimators." Econometric Theory 12, no. 1 (March 1996): 187–97. http://dx.doi.org/10.1017/s0266466600006496.

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Recently, Arcones and Giné (1992, pp. 13–47, in R. LePage & L. Billard [eds.], Exploring the Limits of Bootstrap, New York: Wiley) established that the bootstrap distribution of the M-estimator converges weakly to the limit distribution of the estimator in probability. In contrast, Brown and Newey (1992, Bootstrapping for GMM, Seminar note) discovered that the bootstrap distribution of the GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

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Anwar, Masood, and Amna Bibi. "The Half-Logistic Generalized Weibull Distribution." Journal of Probability and Statistics 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/8767826.

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A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

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Rovigatti, Gabriele, and Vincenzo Mollisi. "Theory and Practice of Total-Factor Productivity Estimation: The Control Function Approach using Stata." Stata Journal: Promoting communications on statistics and Stata 18, no. 3 (September 2018): 618–62. http://dx.doi.org/10.1177/1536867x1801800307.

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Alongside instrumental-variables and fixed-effects approaches, the control function approach is the most widely used in production function estimation. Olley and Pakes (1996, Econometrica 64: 1263–1297), Levinsohn and Petrin (2003, Review of Economic Studies 70: 317–341), and Ackerberg, Caves, and Frazer (2015, Econometrica 83: 2411–2451) have all contributed to the field by proposing two-step estimation procedures, whereas Wooldridge (2009, Economics Letters 104: 112–114) showed how to perform a consistent estimation within a single-step generalized method of moments framework. In this article, we propose a new estimator based on Wooldridge's estimation procedure, using dynamic panel instruments à la Blundell and Bond (1998, Journal of Econometrics 87: 115–143), and we evaluate its performance by using Monte Carlo simulations. We also present the new command prodest for production function estimation, and we show its main features and strengths in a comparative analysis with other community-contributed commands. Finally, we provide evidence of the numerical challenges faced when using the Olley–Pakes and Levinsohn–Petrin estimators with the Ackerberg–Caves–Frazer correction in empirical applications, and we document how the generalized method of moments estimates vary depending on the optimizer or starting points used.

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39

Al-Marzouki, Sanaa, and Sharifah Alrajhi. "A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution." Journal of Computational and Theoretical Nanoscience 17, no. 11 (November 1, 2020): 4813–18. http://dx.doi.org/10.1166/jctn.2020.9332.

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We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

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Wang, Xiaoshan. "Modified generalized method of moments for a robust estimation of polytomous logistic model." PeerJ 2 (July 1, 2014): e467. http://dx.doi.org/10.7717/peerj.467.

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Colonnese, S., S. Rinauro, and G. Scarano. "Generalized Method of Moments Estimation of Location Parameters: Application to Blind Phase Acquisition." IEEE Transactions on Signal Processing 58, no. 9 (September 2010): 4735–49. http://dx.doi.org/10.1109/tsp.2010.2050316.

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Li, H., and G. Yin. "Generalized method of moments estimation for linear regression with clustered failure time data." Biometrika 96, no. 2 (April 21, 2009): 293–306. http://dx.doi.org/10.1093/biomet/asp005.

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Li, H., and G. Yin. "'Generalized method of moments estimation for linear regression with clustered failure time data'." Biometrika 96, no. 4 (November 24, 2009): 1024. http://dx.doi.org/10.1093/biomet/asp061.

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Wani, Fehim J. "On Methods of Estimation for Generalized Logarithmic Series Distribution and Its Application to Counts of Red Mites on Apple Leaves." Indian Journal of Pure & Applied Biosciences 9, no. 3 (June 30, 2021): 151–55. http://dx.doi.org/10.18782/2582-2845.8689.

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The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

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Aryuyuen, Sirinapa, and Issaraporn Thiamsorn. "Methods for Parameter Estimation of the Negative Binomial-Generalized Exponential Distribution." Applied Mechanics and Materials 866 (June 2017): 383–86. http://dx.doi.org/10.4028/www.scientific.net/amm.866.383.

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Abstract. We proposed several estimation methods for the parameters of the negative binomial-generalized exponential (NB-GE) distribution. In the simulation study, the maximum likelihood estimation (MLE) with nlm function seems to have the most efficiency to estimate the parameters and of the NB-GE distribution when it compares with method of the moments (MM) and MLE with optim function by using the average mean square error (AMSE) for a criteria. The AMSE values of each parameter estimation methods are decreasing when the sample size increasing. Moreover, the example dataset is illustrated. Based on the chi-square values for the fitting distribution via the MLE with nlm function is better than other estimation methods.

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Breitung, J., N. R. Chaganty, R. M. Daniel, M. G. Kenward, M. Lechner, P. Martus, R. T. Sabo, Y. G. Wang, and C. Zorn. "Discussion of “Generalized Estimating Equations: Notes on the Choice of the Working Correlation Matrix”." Methods of Information in Medicine 49, no. 05 (2010): 426–32. http://dx.doi.org/10.1055/s-0038-1625133.

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Summary Objective: To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens “Generalized Estimating Equations: Notes on the Choice of the Working Correlation Matrix”. Methods: Inviting an international group of experts to comment on this paper. Results: Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data. Applied statisticians commented on practical aspects in data analysis. Conclusions: In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data. This particularly applies to the situation when data are missing at random.

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Baum, Christopher F., Mark E. Schaffer, and Steven Stillman. "Instrumental Variables and GMM: Estimation and Testing." Stata Journal: Promoting communications on statistics and Stata 3, no. 1 (March 2003): 1–31. http://dx.doi.org/10.1177/1536867x0300300101.

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We discuss instrumental variables (IV) estimation in the broader context of the generalized method of moments (GMM), and describe an extended IV estimation routine that provides GMM estimates as well as additional diagnostic tests. Stand-alone test procedures for heteroskedasticity, overidentification, and endogeneity in the IV context are also described.

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Magazzini, Laura, Randolph Luca Bruno, and Marco Stampini. "Using information from singletons in fixed-effects estimation: xtfesing." Stata Journal: Promoting communications on statistics and Stata 20, no. 4 (December 2020): 965–75. http://dx.doi.org/10.1177/1536867x20976326.

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In this article, we describe the xtfesing command. The command implements a generalized method of moments estimator that allows exploiting singleton information in fixed-effects panel-data regression as in Bruno, Magazzini, and Stampini (2020, Economics Letters 186: Article 108519).

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Hosking, J. R. M., J. R. Wallis, and E. F. Wood. "Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted Moments." Technometrics 27, no. 3 (August 1985): 251–61. http://dx.doi.org/10.1080/00401706.1985.10488049.

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Liao, Zhipeng. "ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION." Econometric Theory 29, no. 5 (February 25, 2013): 857–904. http://dx.doi.org/10.1017/s0266466612000783.

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This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

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