Pseudo maximum likelihood estimation of the univariate GARCH (2,2) and asymptotic normality under dependent innovations

In this paper, we first consider the pseudo maximum likelihood estimation of the univariate GARCH (2,2) model and derive the underlying estimator. Then, we make use of the technique of martingales to establish the asymptotic normality of the pseudo-maximum likelihood estimator (PMLE) of the univariate GARCH (2,2) model. Contrary to previous approaches encountered in the statistical literature, the pseudo-likelihood function uses the general form of the density laws of the quadratic exponential family.     

Estimation of parameters of 1-out-of-n:g repairable system

A single unit system supported by N-l inactive standbys and a repair facility is considered when λ,μ are unknown, λand μbeing failure and repair rates of the unit respectively. Three sampling schemes are considered to obtain moment estimators λ^?:and μ _?:when the performance of the unit have to be observed in the system only. Asymptotic variances of the estimates are supplied.     

Asymptotic bayesian inference in some nonstandard cases: Bernstein–von Mises Results and regular bayes' estimators

Asymptotically with probability close to one, the convergence in variation (also in distribution) to the multivariate normal, of the aposteriori density function of a parameter agains an apriori density, viz. the BERNSTEIN–VON MISES results are established when observations are not necessarily indenpendent or identically distributed but satisfy weak regularity assumptions on their joint density function. Regular BAYES' estimators are defined with respect to regular loss functions and a positive apriori density and proved consistent, asymptotically efficient and asymptotically normal. Examples and applications to conjugate families of densities, to inference in MARKOV Chains and other nonstandard cases illustrate results     

On a generalized stein estimator of regression coefficients

This paper studies a generalized Stein estimator of regression coefficients. The small disturbance approximations for the bias and mean square error matrix of the estimator are derived and a necessary and sufficient condition is obtained for the estimator to dominate the ordinary least squares estimator under the mean square error criterion.     

On a fisherian detour of the step-down procedure for manova

The well known step-down procedure for MANOVA given by J. Roy (1958) can be modified by combining the step-down tests using a B-optimal combination method such as Fisher's. The Fisherian detour of the stepwise MANOVA is shown to be asymptotically equivalent to the likelihood ratio test.     

Uniform convergence of an empirical cdf based on a relatively small number of order statistics

An empirical distribution function F_m, defined on a subset of order statistics of a random sample of size n taken from the distribution of a random variable with continuous distribution function F, is shown to converge uniformly with probability one to F. Small sample distributions of the one and two sided deviations and the asymptotic normality of the standardized F_m are established. The relative efficiency of F_m as compared to the classical empirical distribution function is calculated and tabled. for n = 10, 20, 50, 100, 200.     

缺失数据下指数族分布参数的经验Bayes检验

文章在加权线性损失下讨论了带有非随机缺失数据连续型单参数指数族分布参数的经验Bayes检验问题.利用非参数插补的方法,重新构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优性,并获得了它的收敛速度.     

Finite-sample properties of limited-iinformation estimators in misspecified simultaneous equation models

The two most common limited-information estimators in Simultaneous Equation Models are the two-stage least squares and limited-information maximum likelihood estimators. As both of these estimators are complicated functions of the underlying random variables, their exact distributions are difficult to derive. Consequently, their use was first justified on the basis of large sample criteria, such as consistency and asymptotic efficiency. However, in the early 1960s the analysis of the exact distributions and moments of these estimators began, and since this time substantial progress has been made. Although these estimators are asymptotically equivalent, recent research has shown that their finite-sample properties are substantially different. However, the majority of this research has simply concentrated on a correctly specified system of equations, even though, since typically in applied studies theory provides some guidance but falls short of specifying the precise form of structural relationship, the possibilities for misspecification in simultaneous equation models are numerous. The objective of this paper is to extend the finite-sample analysis of these two estimators to include various cases of misspecification.     

On Testing Exponentiality against NBAFR Alternatives

In this article, we propose an interesting approach for testing exponentiality against NBAFR alternatives. A measure of deviation from exponentiality has been derived on the basis of an inequality which we have proved. A test statistic has been constructed using density estimators and its asymptotic normality established. The consistency of the said test is also proved.     

Robust M-estimators of scale: Minimax bias versus maximal variance

In the location-scale estimation problem, we study robustness properties of M-estimators of the scale parameter under unknown ?-contamination of a fixed symmetric unimodal error distribution F₀. Within a general class of M-estimators, the estimator with minimax asymptotic bias is shown to lie within the subclass of α-interquantile ranges of the empirical distribution symmetrized about the sample median. Our main result is that as ? → 0, the limiting minimax asymptotic bias estimator is sometimes (e.g., when F_o is Cauchy), but not always, the median absolute deviation about the median. It is also shown that contamination in the neighbourhood of a discontinuity of the influence function of a minimax bias estimator can sometimes inflate the asymptotic variance beyond that achieved by placing all the ?-contamination at infinity. This effect is quantified by a new notion of asymptotic efficiency that takes into account the effect of infinitesimal contamination of the parametric model for the error distribution.