Diagnostics for generalized Poisson regression models with errors in variables

In this paper, we develop diagnostic methods for generalized Poisson regression (GPR) models with errors in variables based on the corrected likelihood. The one-step approximations of the estimates in the case-deletion model are given and case-deletion and local influence measures are presented. Meanwhile, based on a corrected score function, the testing statistics for the significance of dispersion parameters in GPR models with measurement errors are investigated. Finally, illustration of our methodology is given through numerical examples.     

Performance of some multiple comparison tests under heteroscedasticity and dependency

In this article, 18 multiple comparison tests are compared according to powers and type I error measures under some violations of analysis of variance assumptions with a Monte Carlo simulation study. Considered violations of assumptions are heterogeneity in subgroup variances and dependency between subgroups. Various numbers of subgroups and subgroup sizes are considered simultaneously with the violations of assumptions. Simulation results are analysed by using visual inspection, graphical representations, decision-tree and correspondence analyses. Wide inferences are drawn on the behaviour of considered tests with respect to measures used. Some general suggestions are given on which tests should be used or avoided under violations of assumptions.     

Reliability estimation in Maxwell distribution with progressively Type-II censored data

There may be situations in which either the reliability data do not fit to popular lifetime models or the estimation of the parameters is not easy, while there may be other distributions which are not popular but either they provide better goodness-of-fit or have a smaller number of parameters to be estimated, or they have both the advantages. This paper proposes the Maxwell distribution as a lifetime model and supports its usefulness in the reliability theory through real data examples. Important distributional properties and reliability characteristics of this model are elucidated. Estimation procedures for the parameter, mean life, reliability and failure-rate functions are developed. In view of cost constraints and convenience of intermediate removals, the progressively Type-II censored sample information is used in the estimation. The efficiencies of the estimates are studied through simulation. Apart from researchers and practitioners in the reliability theory, the study is also useful for scientists in physics and chemistry, where the Maxwell distribution is widely used.     

Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators

The purpose of this paper is to combine several regression estimators (ordinary least squares (OLS), ridge, contraction, principal components regression (PCR), Liu, r?k and r?d class estimators) into a single estimator. The conditions for the superiority of this new estimator over the PCR, the r?k class, the r?d class, β?(k, d), OLS, ridge, Liu and contraction estimators are derived by the scalar mean square error criterion and the estimators of the biasing parameters for this new estimator are examined. Also, a numerical example based on Hald data and a simulation study are used to illustrate the results.     

Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring

In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindley's approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes.     

Bayesian statistical inference of the loglogistic model with interval-censored lifetime data

Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods.     

Analysis of cointegrated models with measurement errors

We study the asymptotic properties of the reduced-rank estimator of error correction models of vector processes observed with measurement errors. Although it is well known that there is no asymptotic measurement error bias when predictor variables are integrated processes in regression models [Phillips BCB, Durlauf SN. Multiple time series regression with integrated processes. Rev Econom Stud. 1986;53:473–495], we systematically investigate the effects of the measurement errors (in the dependent variables as well as in the predictor variables) on the estimation of not only cointegrating vectors but also the speed of the adjustment matrix. Furthermore, we present the asymptotic properties of the estimators. We also obtain the asymptotic distribution of the likelihood ratio test for the cointegrating ranks. We investigate the effects of the measurement errors on estimation and test through a Monte Carlo simulation study.     

Orthogonal series estimators and cross-validation

The use of cross-validation is considered in conjunction with orthogonal series estimators for a probability density function. We attempt to establish a data-based procedure which will select both the optimal choice of series, and the best trade-off between bias-squared and variance, i.e. series length. Although the expected value of the estimator looks promising, the rate of convergence is very slow. Simulations illustrate the theoretical results.     

Percentiles from a set of classes or from the raw data? an argument based on the trinomial distribution

In a former study (Chatillon, Gelinas, Martin and Laurencelle, 1987), the authors arrived at the conclusion that for small to moderate sample sizes (n≦90), and for population distributions that are not too skewed nor heavy tailed, the percentiles computed from a set of 9 classes are at least as precise as the corresponding percentiles computed with raw data. Their proof was based essentially on Monte Carlo simulations. The present paper gives a different and complementary proof, based on an exact evaluation of the mean squared error. The method of proof uses the trinomial distribution in an interesting way.