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Books on the topic 'Maximum likelihood method - MMV'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Aït-Sahalia, Yacine. Maximum likelihood estimation of stochastic volatility models. Cambridge, MA: National Bureau of Economic Research, 2004.

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2

Kunitomo, Naoto, Seisho Sato, and Daisuke Kurisu. Separating Information Maximum Likelihood Method for High-Frequency Financial Data. Tokyo: Springer Japan, 2018. http://dx.doi.org/10.1007/978-4-431-55930-6.

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3

S, Burrus C., ed. Maximum-likelihood deconvolution: A journey into model-based signal processing. New York: Springer-Verlag, 1990.

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4

Güimil, Fernando. Comparing the Maximum Likelihood Method and a Modified Moment Method to fit a Weibull distribution to aircraft engine failure time data. Monterey, Calif: Naval Postgraduate School, 1997.

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5

Morelli, Eugene A. Determining the accuracy of aerodynamic model parameters estimated from flight test data. Washington, D.C: American Institute of Aeronautics and Astronautics, 1995.

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6

Morelli, Eugene A. Determining the accuracy of aerodynamic model parameters estimated from flight test data. Washington, D.C: American Institute of Aeronautics and Astronautics, 1995.

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7

Morelli, Eugene A. Determining the accuracy of aerodynamic model parameters estimated from flight test data. Washington, D.C: American Institute of Aeronautics and Astronautics, 1995.

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8

Schwenzfeger, K. J. Comparison of ERS-1 scatterometer Monte Carlo performance simulations using a weighted nonlinear least-squares and a maximum likelihood estimation method. Neubiberg: Hochschule der Bundeswehr München, 1985.

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9

Kunitomo, Naoto, Seisho Sato, and Daisuke Kurisu. Separating Information Maximum Likelihood Method for High-Frequency Financial Data. Springer, 2018.

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10

Geological Survey (U.S.), ed. Adjusted maximum likelihood estimation of the moments of lognormal populations from type 1 censored samples. [Denver, Colo.?]: Dept. of the Interior, U.S. Geological Survey, 1988.

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11

Adjusted maximum likelihood estimation of the moments of lognormal populations from type 1 censored samples. [Denver, Colo.?]: Dept. of the Interior, U.S. Geological Survey, 1988.

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12

Geological Survey (U.S.), ed. Adjusted maximum likelihood estimation of the moments of lognormal populations from type 1 censored samples. [Denver, Colo.?]: Dept. of the Interior, U.S. Geological Survey, 1988.

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13

Cheng, Russell. Infinite Likelihood. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0008.

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This chapter examines methods that overcome a difficulty with infinite likelihoods. In shifted threshold distributions where the PDF has the form f(y) ∼ k(b,c)(y−a)c−1, if y tends to the threshold parameter a, then the log-likelihood tends to infinity if c < 1 and a also tends to y(1) the smallest observation. The maximum likelihood (ML) method fails in this case, yielding parameter estimates that are not consistent. A method is described overcoming this problem, called the maximum product of spacings method. This yields parameter estimates with the same consistency and asymptotic normality properties as ML estimators when these exist, and which yield, when c < 1 where ML fails, consistent estimates with that for a hyper-efficient. Confidence intervals for a are difficult to obtain theoretically when c < 2. A method is given using percentiles of the stable law distribution and this is numerically compared with bootstrap confidence intervals.

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14

Mendel, Jerry M. Maximum-Likelihood Deconvolution: A Journey into Model-Based Signal Processing (Signal Processing and Digital Filtering). Springer, 1989.

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15

Comparing the Maximum Likelihood Method and a Modified Moment Method to Fit a Weibull Distribution to Aircraft Engine Failure Time Data. Storming Media, 1997.

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16

Determination of stability and control derivatives for the NASA F/A-18 HARV from flight data using the maximum likelihood method: Progress report. Morgantown, WV: West Virginia University, 1995.

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17

United States. National Aeronautics and Space Administration., ed. Determination of stability and control derivatives for the NASA F/A-18 HARV from flight data using the maximum likelihood method: Progress report. Morgantown, WV: West Virginia University, 1995.

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18

Cheng, Russell. Box-Cox Transformations. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0010.

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This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.

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19

Cheng, Russell. Change-Point Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0011.

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This chapter investigates change-point (hazard rate) probability models for the random survival time in some population of interest. A parametric probability distribution is assumed with parameters to be estimated from a sample of observed survival times. If a change-point parameter, denoted by τ‎, is included to represent the time at which there is a discrete change in hazard rate, then the model is non-standard. The profile log-likelihood, with τ‎ as profiling parameter, has a discontinuous jump at every τ‎ equal to a sampled value, becoming unbounded as τ‎ tends to the largest observation. It is known that maximum likelihood estimation can still be used provided the range of τ‎ is restricted. It is shown that the alternative maximum product of spacings method is consistent without restriction on τ‎. Censored observations which commonly occur in survival-time data can be accounted for using Kaplan-Meier estimation. A real data numerical example is given.

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20

Cheng, Russell. Finite Mixture Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0017.

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Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampling. MAPIS is compared with ML and the MCMC methods. The MCMC methods produce multimodal posterior parameter distributions in overfitted models. This results in the posterior distribution of k being biased towards high k. It is shown that MAPIS does not suffer from this problem. A simple numerical example is discussed.

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21

Newman, Mark. Community structure. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0014.

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A discussion of community structure in networks and methods for its detection. The chapter begins with an introduction to the idea of community structure, followed by descriptions of a range of methods for finding communities, including modularity maximization, the InfoMap method, methods based on maximum-likelihood fits of models to network data, betweenness-based methods, and hierarchical clustering. Also discussed are methods for assessing algorithm performance, along with a summary of performance studies and their findings. The chapter concludes with a discussion of other types of large-scale structure in networks, such as overlapping and hierarchical communities, core-periphery structure, latent-space structure, and rank structure.

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22

Cheng, Russell. Introduction. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0001.

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This chapter provides an overview of the book. The book investigates non-standard parametric, mainly continuous univariate estimation problems. The basic difference between standard and non-standard problems is explained in this chapter. The book considers different non-standard problems that can arise. Though some of the problems are advanced, a strong emphasis is placed on providing statistical methods to analyse them that are simple to understand and implement. Maximum likelihood (ML) estimation is the main method used to estimate parameters when fitting parametric models. This chapter outlines the method, emphasizing how it can be implemented numerically. Parametric bootstrapping is used throughout the book to analyse the statistical behaviour of estimators. This chapter gives the rationale of the approach, explaining its simplicity and wide applicability. Also explained is the underlying model building theme of the book.

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23

Cheng, Russell. The Pearson and Johnson Systems. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0009.

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This chapter re-examines two of the best-known systems of parametric distributions: the Pearson and the Johnson. It is shown that, in the Pearson system, Pearson Types III and V are boundary embedded models of the main Types I, IV, and VI. A comprehensive way of finding the best type to fit is given using appropriate score statistics to guide a systematic search of all model types, including symmetric boundary models. Maximum likelihood estimation is used and details of its numerical implementation are given. Type IV can be a difficult model to fit. A method is discussed for this model that is reasonably robust, subject to certain restrictions on the parameter values. The same examination is made of the Johnson system where the lognormal, SL family is shown to be an embedded subsystem of both the main subsystems SB and SU. Two real data examples are given.

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