Empirical distribution function under heteroscedasticity

Neglecting heteroscedasticity of error terms may imply the wrong identification of a regression model (see appendix). Employment of (heteroscedasticity resistent) White's estimator of covariance matrix of estimates of regression coefficients may lead to the correct decision about the significance of individual explanatory variables under heteroscedasticity. However, White's estimator of covariance matrix was established for least squares (LS)-regression analysis (in the case when error terms are normally distributed, LS- and maximum likelihood (ML)-analysis coincide and hence then White's estimate of covariance matrix is available for ML-regression analysis, tool). To establish White's-type estimate for another estimator of regression coefficients requires Bahadur representation of the estimator in question, under heteroscedasticity of error terms. The derivation of Bahadur representation for other (robust) estimators requires some tools. As the key too proved to be a tight approximation of the empirical distribution function (d.f.) of residuals by the theoretical d.f. of the error terms of the regression model. We need the approximation to be uniform in the argument of d.f. as well as in regression coefficients. The present paper offers this approximation for the situation when the error terms are heteroscedastic.     

Design effect of randomized systematic sampling

In statistical practice, systematic sampling (SYS) is used in many modifications due to its simple handling. In addition, SYS may provide efficiency gains if it is well adjusted to the structure of the population under study. However, if SYS is based on an inappropriate picture of the population a high decrease of efficiency, i.e. a high increase in variance may result by changing from simple random sampling to SYS. In the context of two-stage designs SYS so far seems often in use for subsampling within the primary units. As an alternative to this practice, we propose to randomize the order of the primary units, then to select systematically a number of primary units and, thereafter, to draw secondary units by simple random sampling without replacement within the primary units selected. This procedure is more efficient than simple random sampling with replacement from the whole population of all secondary units, i.e. the variance of an adequate estimator for a total is never increased by changing from simple random sampling to randomized SYS whatever be the values associated by a characteristic with the secondary units, while there are values for which the variance decreases for the change mentioned. This result should hold generally, even if our proof, so far, is not complete for general sample sizes.     

中国省际经济差距来源分析

在利用索洛模型对中国省区1985—2009年经济增长进行分解的基础上,结合空间标准差指标并采用基于VAR模型的脉冲响应函数分析了中国省际经济差距状况及来源。研究发现:总的来看,中国省区劳均产出与要素投入均呈现空间σ趋异倾向,而全要素生产率则在呈现空间σ收敛后趋于稳定。进一步利用VAR模型及脉冲响应函数分析发现,在较长时期内,要素投入总体上扩大了中国省际经济差距,而全要素生产率则有助于缩小省际经济差距,这主要是由要素投入的经济拉动滞后效应和技术的扩散效应所致。     

ON UMP INVARIANT F-TEST PROCEDURES IN A GENERAL LINEAR MODEL

A simple method of setting linear hypotheses for a split mean vector testable by F-tests in a general linear model, when the covariance matrix has a general form and is completely unknown, is provided by extending the method discussed in Ukita et al. The critical functions in these F-tests are constructed as UMP invariants, when the covariance matrix has a known structure. Further critical functions in F-tests of linear hypotheses for the other split mean vector in the model are shown to be UMP invariant if the same known structure of the covariance matrix is assumed.     

Basic structure of the asymptotic theory in dynamic nonlinear econometric models

This is the second of two papers that provide an expository discussion of the basic structure of the asymptotic theory of M-estimators in dynamic nonlinear models and a review of the literature. The first paper, Pötscher and Prucha(1991), deals with consistency. In the present paper we discuss asymptotic normality. As an important ingredient to the asymptotic normality proof in dynamic nonlinear models we consider central limit theorems for dependent random variables. We also discuss the estimation of the variance covariance matrix of m-estimators under heteroscedasticity and autocorrelation.     

Optimal blocked main effects plans

In this paper, we consider the construction of optimal blocked main effects designs where m two-level factors are to be studied in N runs which are partitioned into b blocks of equal size. For N ≡ 2±od4 sufficient conditions are derived for a design to be Φ _f optimal among all designs having main effects occurring equally often at their high and low levels within blocks and then this result is extended to the class of all designs for the case when the block size is two. Methods of constructing designs satisfying the sufficient conditions derived are also given.     

New Algorithms for Evaluating the Log-Likelihood Function Derivatives in the AI-REML Method

In this study, we propose several improvements of the Average Information Restricted Maximum Likelihood algorithms for estimating the variance components for genetic mapping of quantitative traits. The improved methods are applicable when two variance components are to be estimated. The improvements are related to the algebraic part of the methods and utilize the properties of the underlying matrix structures.

In contrast to previously developed algorithms, the explicit computation of a matrix inverse is replaced by the solution of a linear system of equations with multiple right-hand sides, based on a particular matrix decomposition. The computational costs of the proposed algorithms are analyzed and compared.     

On simulation of normal records

ABSTRACT

In the present paper, we discuss algorithms of record generation when records are taken from a normal population. We propose three new generation algorithms, compare their efficiency and find the most efficient algorithm (Algorithm 2.1). We then compare these algorithms with known generation algorithms presented in the work of Balakrishnan, So, and Zhu (2016 Balakrishnan, N., H. Y. So, and X. J. Zhu. 2016. On Box-Muller transformation and simulation of normal record data. Communication in Statistics – Simulation and Computations 45(10):3670–82.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).