Semiparametric quasi-likelihood estimation with missing data

Abstract

This article develops quasi-likelihood estimation for generalized varying coefficient partially linear models when the response is not always observable. This article considers two estimation methods and shows that under the assumption of selection on the observables the resulting estimators are asymptotically normal. As an application of these results this article proposes a new estimator for the average treatment effect parameter. A simulation study illustrates the finite sample properties of the proposed estimators.     

Testing for the mean of the inverse gaussian distribution and adaptive estimation of parameters

This paper provides the modified likelihood ratio criterion for testing whether the mean of the inverse Gaussian distribution can be set to unity giving rise to Standard form of the Wald distribution. Estimates of probability of correct selection has been obtained on the basis of a Monte Carlo study of 1,000 samples. Finally a set of adaptive estimators for the parameters are proposed and studied on the basis of data generated from the two distributions.     

POOLED SLICING METHODS VERSUS SLICING METHODS

We consider the semiparametric regression model introduced by [1] Duan, N. and Li, K. C. 1991. Slicing regression: a link-free regression method. The Annals of Statistics, 19: 505–530. [Crossref], [Web of Science ®] , [Google Scholar]. The dependent variable y is linked to the index x′ β through an unknown link function. [1] Duan, N. and Li, K. C. 1991. Slicing regression: a link-free regression method. The Annals of Statistics, 19: 505–530. [Crossref], [Web of Science ®] , [Google Scholar] and [2] Li, K. C. 1991. Sliced inverse regression for dimension reduction, with discussions. Journal of the American Statistical Association, 86: 316–342. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] present Slicing methods (the Sliced Inverse Regression methods SIR-I, SIR-II and SIR_α) in order to estimate the direction of the unknown slope parameter β. These methods are computationally simple and fast but depend on the choice of an arbitrary slicing fixed by the user. When the sample size is small, the number and the position of slices have an influence on the estimated direction. In this paper, we suggest to use the corresponding Pooled Slicing methods: PSIR-I (proposed by [3] Aragon, Y. and Saracco, J. 1997. Sliced Inverse Regression (SIR): an appraisal of small sample alternatives to slicing. Computational Statistics, 12: 109–130. [Web of Science ®] , [Google Scholar]), PSIR-II and PSIR_α. These methods combine the results from a number of slicings. We compare the sample behaviour of Slicing and Pooled Slicing methods on simulations. We also propose a practical choice of α in SIR_α and PSIR_α methods.     

Inference on Overlap for Two Inverse Gaussian Populations: Equal Means Case

The inverse Gaussian distribution is often suited for modeling positive and/or positively skewed data (see Chhikara and Folks, 1989 Chhikara , R. S. , Folks , J. L. ( 1989 ). The Inverse Gaussian Distribution . New York : Marcel Dekker . [Google Scholar]) and presents an interesting alternative to the Gaussian model in such cases. We note here that overlap coefficients and their variants are widely studied in the literature for Gaussian populations (see Mulekar and Mishra, 1994 Mulekar , M. , Mishra , S. N. ( 1994 ). Overlap coefficients of two normal densities: equal means case . J. Japan. Statist. Soc. 24 : 169 – 180 . [Google Scholar], 2000 Mulekar , M. , Mishra , S. N. ( 2000 ). Confidence interval estimation of overlap: equal means case . Computat. Statist. Data Anal. 34 : 121 – 137 .[Crossref], [Web of Science ®] , [Google Scholar], and references therein for further details). This article studies the properties and addresses point estimation for large samples of commonly used measures of overlap when the populations are described by inverse Gaussian distributions. The bias and mean square error properties of the estimators are studied through a simulation study.     

Bayesian Estimation of Change Point in Inverse Weibull Sequence

A sequence of independent lifetimes X ₁,…, X _m , X _m+1,…, X _n were observed from inverse Weibull distribution with mean stress θ₁ and reliability R ₁(t ₀) at time t ₀ but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X _m by change in mean stress θ₁ and in reliability R ₂(t ₀) at time t ₀. The Bayes estimators of m, R ₁(t ₀) and R ₂(t ₀) are derived when a poor and a more detailed prior information is introduced into the inferential procedure. The effects of correct and wrong prior information on the Bayes estimators are studied.     

M-Estimators Based on Inverse Probability Weighted Estimating Equations with Response Missing at Random

Asymptotic properties of M-estimators with complete data are investigated extensively. In the presence of missing data, however, the standard inference procedures for complete data cannot be applied directly. In this article, the inverse probability weighted method is applied to missing response problem to define M-estimators. The existence of M-estimators is established under very general regularity conditions. Consistency and asymptotic normality of the M-estimators are proved, respectively. An iterative algorithm is applied to calculating the M-estimators. It is shown that one step iteration suffices and the resulting one-step M-estimate has the same limit distribution as in the fully iterated M-estimators.     

Workload Process,Waiting Times,and Sojourn Times in a Discrete Time MMAP[K]/SM[K]/1/FCFS Queue

Abstract

In this paper, we study the total workload process and waiting times in a queueing system with multiple types of customers and a first-come-first-served service discipline. An M/G/1 type Markov chain, which is closely related to the total workload in the queueing system, is constructed. A method is developed for computing the steady state distribution of that Markov chain. Using that steady state distribution, the distributions of total workload, batch waiting times, and waiting times of individual types of customers are obtained. Compared to the GI/M/1 and QBD approaches for waiting times and sojourn times in discrete time queues, the dimension of the matrix blocks involved in the M/G/1 approach can be significantly smaller.