Estimation and Testing in Elliptical Functional Measurement Error Models

The purpose of this article is to investigate estimation and hypothesis testing by maximum likelihood and method of moments in functional models within the class of elliptical symmetric distributions. The main results encompass consistency and asymptotic normality of the method of moments estimators. Also, the asymptotic covariance matrix of the maximum likelihood estimator is derived, extending some existing results in elliptical distributions. A measure of asymptotic relative efficiency is reported. Wald-type statistics are considered and numerical results obtained by Monte Carlo simulation to investigate the performance of estimators and tests are provided for Student-t and contaminated normal distributions. An application to a real dataset is also included.     

Restricted estimation and testing of hypothesis in linear measurement errors models

ABSTRACT

In this article, the linear models with measurement error both in the response and in the covariates are considered. Following Shalabh et al. (2007 Shalabh, Garg, G., Misra, N. (2007). Restricted regression estimation in measurement error models. Comput. Stat. Data Anal. 52:1149–1166.[Crossref], [Web of Science ®] , [Google Scholar], 2009 Shalabh, Garg, G., Misra, N. (2009). Use of prior information in the consistent estimation of regression coefficients in measurement error models. J. Multivariate Anal. 100:1498–1520.[Crossref], [Web of Science ®] , [Google Scholar]), we propose several restricted estimators for the regression coefficients. The consistency and asymptotic normality of the restricted estimators are established. Furthermore, we also discuss the superiority of the restricted estimators to unrestricted estimators under Pitman closeness criterion. We also develop several variance estimators and establish their asymptotic distributions. Wald-type statistics are constructed for testing the linear restrictions. Finally, Monte Carlo simulations are conducted to illustrate the finite-sample properties of the proposed estimators.     

Matching pseudocounts for interval estimation of binomial and Poisson parameters

ABSTRACT

For interval estimation of a binomial proportion and a Poisson mean, matching pseudocounts are derived, which give the one-sided Wald confidence intervals with second-order accuracy. The confidence intervals remove the bias of coverage probabilities given by the score confidence intervals. Partial poor behavior of the confidence intervals by the matching pseudocounts is corrected by hybrid methods using the score confidence interval depending on sample values.     

A Note on Confidence Intervals for a Linear Function of Poisson Rates

We consider three interval estimators for linear functions of Poisson rates: a Wald interval, a t interval with Satterthwaite's degrees of freedom, and a Bayes interval using noninformative priors. The differences in these intervals are illustrated using data from the Crash Records Bureau of the Texas Department of Public Safety. We then investigate the relative performance of these intervals via a simulation study. This study demonstrates that the Wald interval performs poorly when expected counts are less than 5, while the interval based on the noninformative prior performs best. It also shows that the Bayes interval and the interval based on the t distribution perform comparably well for more moderate expected counts.     

Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood

Interval estimation of the difference of two independent binomial proportions is an important problem in many applied settings. Newcombe (1998 Newcombe , R. G. ( 1998 ). Interval estimation for the difference between independent proportions: comparison of seven methods . Statistics in Medicine 17 : 873 – 890 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) compared the performance of several existing asymptotic methods, and based on the results obtained, recommended a method known as Wilson's method, a modified version of a method originally proposed for single binomial proportion. In this article, we propose a method based on profile likelihood, where the likelihood is weighted by noninformative Jeffrey' prior. By doing extensive simulations, we find that the proposed method performs well compared to Wilson's method. A SAS/IML program implementing this method is also given with this article.     

高斯混合分布杂波下ARM的Wald检测方法

提出一种在高斯混合分布杂波下检测反辐射导弹(ARM)的Wald检测方法.针对基于期望最大化(EM)算法估计杂波参数时,由于初始化不当使迭代运算落入初值陷阱、导致估计错误的问题,提出基于矩-EM算法估计杂波参数的方法,导出了高斯混合分布杂波下ARM目标的Wald检测统计量.不同参数条件下的仿真表明,矩-EM算法能够更准确地估计杂波参数;基于高斯混合分布杂波假设的Wald检测性能明显优于基于高斯分布杂波假设的Wald检测性能.     

Multivariate statistics books are reviewed

Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K≤2 (particularly on cases of one proportion and the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest. In order to make this inference, there are several procedures which have not been compared: the score method (S0) and the method proposed by Martín Andrés et al. (W3) for adjusted Wald (which is a generalization of the method proposed by Price and Bonett) on the one hand and, on the other hand, the method of Zou et al. (N0) based on the Wilson confidence interval (which is a generalization of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c, respectively) and, finally, a simulation is made to compare the eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that the S0c method is the best, although for very small samples (n _i ≤10, ? i) the W3 method is better. The P0 method would be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide CIs. The W3 and P0 methods have the additional advantage of being very easy to apply. A free programme which allows the application of the S0 and S0c methods (which are the most complex) can be obtained at http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE.     

Likelihood inference for small variance components

The authors explore likelihood‐based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the restricted likelihood (REML). Also, they show that general REML estimates are less likely to fall on the boundary of the parameter space than maximum‐likelihood estimates and that the likelihood‐ratio test based on the local asymptotic approximation has higher power than the likelihood‐ratio test based on the usual chi‐squared approximation. They examine the finite‐sample properties of the proposed intervals by means of a simulation study.     

Regression spline bivariate probit models: A practical approach to testing for exogeneity

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested.     

Vector autoregression and causality: a theoretical overview and simulation study

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's). The theory is based on results in Toda and Phillips (1991a) and allows for stochastic and deterministic trends as well as arbitrary degrees of cointegration. We recommend some operational procedures for conducting Granger causality tests that are based on the Gaussian maximum likelihood estimation of ECM's. These procedures are applicable in the important practical case of testing the causal effects of one variable on another group of variables and vice versa. This paper also investigates the sampling properties of these testing procedures through simulation exercises. Three sequential causality tests in ECM's are compared with conventional causality tests in levels and differences VAR's.