Delta Method,Moment Convergence,and Inference

Statistics, as functions of the observations, are usually given by well-behaved functions. This fact is used to obtain limit distributions for statistics whose components are given by asymptotically linear functions. These results are then extended to the moments of distributions, covariance matrices and confidence regions for parameters of interest. These regions may be used to test, through duality, hypothesis on these parameters. A theoretical application is presented.     

A Note on Wald's Type Chi-squared Tests of Fit

The Wald's method for constructing chi-squared tests of fit has been formulated more accurately. It is shown that Wald's type statistics will follow the central chi-squared distribution if and only if the limit covariance matrix of standardized frequencies will not depend on unknown parameters. Several examples that illustrate this important fact are presented. In particular, it is shown that the goodness-of-fit statistic developed by Moore and Stubblebine does not follow the chi-squared limit distribution, and, hence, cannot be used for testing multivariate normality.     

Bayesian,MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT

We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.     

Efficient Estimation of Parameters of the Negative Binomial Distribution

In this article we investigate a class of moment-based estimators, called power method estimators, which can be almost as efficient as maximum likelihood estimators and achieve a lower asymptotic variance than the standard zero term method and method of moments estimators. We investigate different methods of implementing the power method in practice and examine the robustness and efficiency of the power method estimators.     

A Semiparametric Model for Line Transect Sampling

This paper introduces an appealing semiparametric model for estimating wildlife abundance based on line transect data. The proposed method requires the existence of a parametric model and then improves the estimator using a kernel method. Properties of the resultant estimator are derived and an expression for the asymptotic mean square error (AMSE) of the estimator is given. Minimization of the AMSE leads to an explicit formula for an optimal choice of the smoothing parameter. Small-sample properties of the proposed estimator using the parametric half-normal model are investigated and compared with the classical kernel estimator using both simulations and real data. Numerical results show that improvements over the classical kernel estimator often can be realized even when the true density is far from the half-normal model.     

Combining Univariate Tests for Multivariate Location Problem

In this article, three methods of combining dependent univariate tests are studied. The Bahadur approximate efficiencies are derived under the asymptotic normal assumption. These procedures are applied to the multivariate location problem and compared with two Hotelling-type tests. A Monte Carlo study indicates that in certain cases the powers of the combination methods are much better than Hotelling's T ² and other multivariate nonparametric tests.     

A Bivariate Distribution for the Reliability Analysis of Failure Data in Presence of a Forewarning or Primer Event

This article presents a bivariate distribution for analyzing the failure data of mechanical and electrical components in presence of a forewarning or primer event whose occurrence denotes the inception of the failure mechanism that will cause the component failure after an additional random time. The characteristics of the proposed distribution are discussed and several point estimators of parameters are illustrated and compared, in case of complete sampling, via a large Monte Carlo simulation study. Confidence intervals based on asymptotic results are derived, as well as procedures are given for testing the independence between the occurrence time of the forewarning event and the additional time to failure. Numerical applications based on failure data of cable insulation specimens and of two-component parallel systems are illustrated.     

Testing Treatment-Covariate Interaction in a Nonparametric Analysis of Covariance Model

We consider a recently introduced nonparametric model for Analysis of Covariance and derive an asymptotic test for interaction between covariate and treatment. Furthermore, we suggest data depth techniques to obtain joint confidence regions for the covariate effects in this model.

The finite sample behavior of the asymptotic method is evaluated in simulations. Application of the procedures is illustrated using an epileptic seizures and chemotherapy data set.     

Estimation of Survivorship Function Based on Doubly Censored Data with Application to HIV/AIDS

Left censoring concept has been defined in different ways in statistical applications. Turnbull (1974 Turnbull , B. W. ( 1974 ). Nonparametric estimation of a survivorship function with doubly censored data . J. Amer. Statist. Assoc. 69 : 169 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) defines it in a particular way. Whereas in recent literature, especially in epidemiological studies, it has been defined in another way. This difference between the two approaches is the main reason that despite simplicity, Turnbull method cannot be applicable in all cases of doubly censored data. In this article we present a modified Turnbull method for analysis of doubly censored data adequate with recent definition. Comparison has been done with other statistical methods, including imputation estimator, full likelihood-based and conditional likelihood-based approach using Iranian HIV data.     

Free Knot Splines with RJMCMC in Survival Data Analysis

The B-spline representation is a common tool to improve the fitting of smooth nonlinear functions, it offers a fitting as a piecewise polynomial. The regions that define the pieces are separated by a sequence of knots. The main difficulty in this type of modeling is the choice of the number and the locations of these knots. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm provides a solution to simultaneously select these two parameters by considering the knots as free parameters. This algorithm belongs to the MCMC techniques that allow simulations from target distributions on spaces of varying dimension. The aim of the present investigation is to use this algorithm in the framework of the analysis of survival time, for the Cox model in particular. In fact, the relation between the hazard ratio function and the covariates being assumed to be log-linear, this assumption is too restrictive. Thus, we propose to use the RJMCMC algorithm to model the log hazard ratio function by a B-spline representation with an unknown number of knots at unknown locations. This method is illustrated with two real data sets: the Stanford heart transplant data and lung cancer survival data. Another application of the RJMCMC is selecting the significant covariates, and a simulation study is performed.