Changepoint Estimation in a Segmented Linear Regression via Empirical Likelihood

For a segmented regression system with an unknown changepoint over two domains of a predictor, a new empirical likelihood ratio statistic is proposed to test the null hypothesis of no change. Under the null hypothesis of no change, the proposed test statistic is shown empirically to be Gumbel distributed with robust location and scale estimators against various parameter settings and error distributions. A power analysis is conducted to illustrate the performance of the test. Under the alternative hypothesis with a changepoint, the test statistic is utilized to estimate the changepoint between the two domains. A comparison of the frequency distributions between the proposed estimator and two parametric methods indicates that the proposed method is effective in capturing the true changepoint.     

SHIFTED HILL'S ESTIMATOR FOR HEAVY TAILS

Hill's estimator is a popular method for estimating the thickness of heavy tails. In this paper we modify Hill's estimator to make it shift-invariant as well as scale-invariant. The resulting shifted Hill's estimator is a more robust method of estimating tail thickness.

     

A note on approximate confidence limits for the negative binomial model

Four methods of approximating confidence limits for the single negative binomial parameter, P, are outlined and an empirical study is presented. Some remarks on prediction intervals are also included.     

On bias reduction estimators of skew-normal and skew-t distributions

A particular concerns of researchers in statistical inference is bias in parameters estimation. Maximum likelihood estimators are often biased and for small sample size, the first order bias of them can be large and so it may influence the efficiency of the estimator. There are different methods for reduction of this bias. In this paper, we proposed a modified maximum likelihood estimator for the shape parameter of two popular skew distributions, namely skew-normal and skew-t, by offering a new method. We show that this estimator has lower asymptotic bias than the maximum likelihood estimator and is more efficient than those based on the existing methods.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.     

Penalized proportion estimation for non parametric mixture of regressions

Abstract

In this article, we propose a penalized local log-likelihood method to locally select the number of components in non parametric finite mixture of regression models via proportion shrinkage method. Mean functions and variance functions are estimated simultaneously. We show that the number of components can be estimated consistently, and further establish asymptotic normality of functional estimates. We use a modified EM algorithm to estimate the unknown functions. Simulations are conducted to demonstrate the performance of the proposed method. We illustrate our method via an empirical analysis of the housing price index data of United States.     

Parameter estimation of Lindley step stress model with independent competing risk under type 1 censoring

Abstract

In literature, Lindley distribution is considered as an alternative to exponential distribution to fit lifetime data. In the present work, a Lindley step-stress model with independent causes of failure is proposed. An algorithm to generate random samples from the proposed model under type 1 censoring scheme is developed. Point and interval estimation of the model parameters is carried out using maximum likelihood method and percentile bootstrap approach. To understand the effectiveness of the resulting estimates, numerical illustration is provided based on simulated and real-life data sets.     

Abundance estimation with a categorical covariate subject to missing in continuous-time capture-recapture studies

Abstract

In continuous-time capture-recapture experiments, individual heterogeneity has a large effect on the capture probability. To account for the heterogeneity, we consider an individual covariate, which is categorical and subject to missing. In this article, we develop a general model to summarize three kinds of missing mechanisms, and propose a maximum likelihood estimator of the abundance. A likelihood ratio confidence interval of the abundance is also proposed. We illustrate the proposed methods by simulation studies and a real data example of a bird species prinia subflava in Hong Kong.     

Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.     

Empirical likelihood based detection procedure for change point in mean residual life functions under random censorship

The mean residual life (MRL) function is one of the basic parameters of interest in survival analysis that describes the expected remaining time of an individual after a certain age. The study of changes in the MRL function is practical and interesting because it may help us to identify some factors such as age and gender that may influence the remaining lifetimes of patients after receiving a certain surgery. In this paper, we propose a detection procedure based on the empirical likelihood for the changes in MRL functions with right censored data. Two real examples are also given: Veterans' administration lung cancer study and Stanford heart transplant to illustrate the detecting procedure. Copyright © 2016 John Wiley & Sons, Ltd.