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1

Optimal unbiased estimation of variance components. Berlin: Springer-Verlag, 1986.

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2

Malley, James D. Optimal Unbiased Estimation of Variance Components. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4615-7554-2.

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3

Estrella, Arturo. Consistent covariance matrix estimation in probit models with autocorrelated errors. [New York, N.Y.]: Federal Reserve Bank of New York, 1998.

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4

Cashin, Paul. An unbiased appraisal of purchasing power parity. [Washington, D.C.]: International Monetary Fund, Research Department, 2001.

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5

Rahiala, Markku. On the identification and estimation of multiple input transfer function models with autocorrelated errors. Helsinki: Research Institute of the Finnish Economy, 1985.

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6

S, Nikulin M., ed. Unbiased estimators and their applications. Dordrecht: Kluwer Academic Publishers, 1993.

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7

Choi, Chi-Young. Unbiased estimation of the half-life to ppp convergence in panel data. Cambridge, MA: National Bureau of Economic Research, 2004.

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8

Optimal Unbiased Estimation of Variance Components. Springer, 2012.

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9

Malley, J. D. Optimal unbiased estimation of variance components. Springer, 1986.

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10

Amina Ali Abd El-Fattah Saleh. Nonlinear unbiased estimators that dominate the intra-block estimator. 1986.

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11

Geological Survey (U.S.), ed. KRIGING: An interactive program to determine the best linear unbiased estimation. [Reston, Va.?]: U.S. Dept. of the Interior, Geological Survey, 1985.

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12

Voinov, V. G., and M. S. Nikulin. Unbiased Estimators and their Applications: Volume 2: Multivariate Case (Mathematics and Its Applications). Springer, 1996.

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13

Mas, André, and Besnik Pumo. Linear Processes for Functional Data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.3.

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This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressive processes as well as two issues related to the general estimation problem, namely: identifiability and the inverse problem. Finally, it examines convergence results for the autocorrelation operator and the predictor, extensions for the autoregressive Hilbertian (ARH) model, and some numerical aspects of prediction when the data are curves observed at discrete points.
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14

McCleary, Richard, David McDowall, and Bradley J. Bartos. Noise Modeling. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190661557.003.0003.

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Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov (KS) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function (ACF). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function (PACF). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.
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15

Karakoç, Ekrem. Cross-National Test of the Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198826927.003.0003.

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The previous chapter posed the primary research question and offered a new theory that encompassed two interrelated arguments. This chapter produces three hypotheses derived from the new theory offered in Chapter 2. Chapter 3 tests these arguments in a large-N study using multivariate statistical analysis. The first section discusses the operationalization of our main dependent and independent variables. It will also briefly outline a set of control variables and what the literature predicts regarding their effect on spending and inequality. These factors range from economic factors (globalization, inflation, female labor participation, economic development), political factors (partisanship, electoral systems, election cycle), and demographic factors. To correct for problems associated with the nature of panel data models, such as endogeneity, heteroskedasticity, and autocorrelation, it uses the Arellano-Bond estimation, which uses the Generalized Method of Moments. The rest of the chapter presents the results and offers its interpretation and conclusion.
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