Preliminary test Liu estimators based on the conflicting W,LR and LM tests in a regression model with multivariate Student-<Emphasis Type="Italic">t</Emphasis> error

In this paper, the problem of estimation of the regression coefficients in a multiple regression model with multivariate Student-t error is considered under the multicollinearity situation when it is suspected that the regression coefficients may be restricted to a linear manifold. The preliminary test Liu estimators (PTLE) based on the Wald, Likelihood ratio (LR) and Lagrangian multiplier (LM) tests are given. The bias and mean square error (MSE) of the proposed estimators are derived and conditions of superiority of these estimators are provided. In particular, we show that in the neighborhood of the null hypothesis, the PTLE based on the LM test has the best performance followed by the estimators based on LR and W tests, while the situation is reversed when the parameter moves away from the manifold of the restriction. Furthermore, the optimum choice of the level of significance is also discussed.     

Restricted maximum likelihood estimation under Eisenhart model Ill

For a balanced two-way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non-negativity requirements of the variance components by L ee and K apadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non-negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.     

The finite-sample effects of VAR dimensions on OLS bias,OLS variance,and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.     

Bias Reduction in Dynamic Panel Data Models by Common Recursive Mean Adjustment*

The within‐group estimator (same as the least squares dummy variable estimator) of the dominant root in dynamic panel regression is known to be biased downwards. This article studies recursive mean adjustment (RMA) as a strategy to reduce this bias for AR(p) processes that may exhibit cross‐sectional dependence. Asymptotic properties for N,T→∞ jointly are developed. When ( log ²T)(N/T)→ζ, where ζ is a non‐zero constant, the estimator exhibits nearly negligible inconsistency. Simulation experiments demonstrate that the RMA estimator performs well in terms of reducing bias, variance and mean square error both when error terms are cross‐sectionally independent and when they are not. RMA dominates comparable estimators when T is small and/or when the underlying process is persistent.     

基于EMB多重插补法的线性模型系数估计量的模拟研究

基于EMB多重插补法的线性模型系数估计量,分析其统计性质,并与PMM多重插补法以及DA插补法进行比较。模拟结果显示,随着无回答率增加,系数估计量的偏差绝对值、均方误差呈递增趋势,估计方差的递增趋势相对更显著。在完全随机无回答机制或随机无回答机制下,建议插补重数为15。在依赖被解释变量的非随机无回答机制下,建议插补重数可适当增大。在依赖其他变量的非随机无回答机制下,估计量的均方误差和估计方差的差异大,使用EMB多重插补法要谨慎。     

Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances

In this paper we derive the exact risk (under quadratic loss) of pre-test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances. The pre-test in question is one of the validity of a set of exact linear restrictions on the model's coefficient vector. We demonstrate how the known results for the model with normal disturbances can be extended to this broader case. We also show that the critical value of unity results in a minimum of the risk of the pre-test estimator of the error variance. To illustrate the results we assume multivariate Student-t regression disturbances and numerically evaluate the derived expressions.     

Choosing instrumental variables in conditional moment restriction models

Properties of GMM estimators are sensitive to the choice of instrument. Using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and/or variance in small samples. In this paper we develop and implement asymptotic mean square error (MSE) based criteria for instrument selection in estimation of conditional moment restriction models. The models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity. We develop moment selection criteria for the familiar two-step optimal GMM estimator (GMM), a bias corrected version, and generalized empirical likelihood estimators (GEL), that include the continuous updating estimator (CUE) as a special case. We also find that the CUE has lower higher-order variance than the bias-corrected GMM estimator, and that the higher-order efficiency of other GEL estimators depends on conditional kurtosis of the moments.     

Mean squared error efficient estimators of the variance components

Summary Pseudo Bayesian estimators for the variance components based on Jeffrey’s Rule are derived for the mixed balanced incomplete block design and are compared with the usual analysis of variance estimators in terms of mean squared error (MSE) efficiency. Numerical results show that Pseudo-Bayesian estimators are more efficient in numerical results.     

Estimation of bias and standard error of an improved estimator of normal mean

This paper considers an improved estimator of normal mean which is obtained by considering a feasible version of minimum mean squared error estimator. The exact expression for the bias and the mean squared error are fairly complicated and do not provide any guidelines as how to estimate the standard error of improved estimator. As is well known that any estimator without a formula for standard error has little practical utility. We therefore derive unbiased estimators for the bias and mean squared error of the improved estimator. Incidently, they turn out to be minimum variance unbiased estimators. Further, this exercise yields a simple formula for estimating the standard error. Based on the criterion of estimated standard error, the efficiency of the improved estimator with respect to the traditional unbiased estimator (i.e., sample mean) is examined numerically. The relationship with asymptotic standard error is also studied.     

基于PMM多重插补法的线性模型系数估计量的模拟研究

在利用含无回答的经济数据建立线性回归模型,选择PMM多重插补法给出无回答的插补值。模拟结果显示,在任意无回答机制下,随着插补重数增大,系数估计量的偏差和均方误差减小不显著。对于任意无回答率,建议插补重数为5。在完全随机无回答机制下,随着无回答率增加,系数估计量的偏差或均方误差增大往往不显著。然而,在随机无回答机制下或在非随机无回答机制下,随着无回答率增加,系数估计量的偏差和均方误差增大往往显著。