Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data: a Bayesian approach

In this paper, we introduce classical and Bayesian approaches for the Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data. This distribution is considered for the analysis of bivariate lifetime as an alternative to some existing bivariate lifetime distributions assuming continuous lifetimes as the Block and Basu or Marshall and Olkin bivariate distributions. Maximum likelihood and Bayesian estimators are presented. Two examples are considered to illustrate the proposed methodology: an example with simulated data and an example with medical bivariate lifetime data.     

Inference Under Right Censoring in a Discrete Setup

In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/θ₁ and 1/θ₂, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior Regret Gamma Minimax estimators of the parameters for the two cases when the prior distributions are dependent and independent, assuming a squared error loss function. We then discuss the Proportional Hazard model, and obtain Maximum Likelihood estimators of the unknown parameters and derive the Bayes estimators assuming squared error loss using Markov Chain Monte Carlo methods.     

Reduced-Variance Methods for Detectability Correction of Population Abundance

Detectability issues create uncertainty in field surveys of animal and plant populations. Detectability correction is one method employed to deal with this problem when there is reasonable certainty that detectability is roughly constant with time or in different areas. Two new reduced-variance estimators of detectability are introduced and evaluated for the case of using a detectability correction for new areas that are surveyed only once. The new estimates are unbiased or nearly unbiased and produce population estimates with smaller variance than the Lincoln–Petersen estimate.     

Optimal simple step stress accelerated life test design for reliability prediction

A step stress accelerated life testing model is presented to obtain the optimal hold time at which the stress level is changed. The experimental test is designed to minimize the asymptotic variance of reliability estimate at time ζ$\zeta$. A Weibull distribution is assumed for the failure time at any constant stress level. The scale parameter of the Weibull failure time distribution at constant stress levels is assumed to be a log-linear function of the stress level. The maximum likelihood function is given for the step stress accelerated life testing model with Type I censoring, from which the asymptotic variance and the Fisher information matrix are obtained. An optimal test plan with the minimum asymptotic variance of reliability estimate at time ζ$\zeta$ is determined.     

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.     

Functional version of the delta method and its application

Nonparametric estimation of the time varying parameter of a semimartingal e model is considered. Stochastic version of the delta method is given. Variance process o"f the estimators and the functionals of the estimators are studied in detail. As an application, a new estimate "for the variance of the product limit estimator is proposed.     

Estimators of Influence Function

ABSTRACT

This article discusses estimators of influence function with some new counter-examples and tries to uphold their usefulness mathematically as well as through simulation. It is suggested that some estimators of influence function of uniformly Fréchet differentiable functional has more desirable properties.     

Comparison of the finite mixture of ARMA-GARCH,back propagation neural networks and support-vector machines in forecasting financial returns

The use of GARCH type models and computational-intelligence-based techniques for forecasting financial time series has been proved extremely successful in recent times. In this article, we apply the finite mixture of ARMA-GARCH model instead of AR or ARMA models to compare with the standard BP and SVM in forecasting financial time series (daily stock market index returns and exchange rate returns). We do not apply the pure GARCH model as the finite mixture of the ARMA-GARCH model outperforms the pure GARCH model. These models are evaluated on five performance metrics or criteria. Our experiment shows that the SVM model outperforms both the finite mixture of ARMA-GARCH and BP models in deviation performance criteria. In direction performance criteria, the finite mixture of ARMA-GARCH model performs better. The memory property of these forecasting techniques is also examined using the behavior of forecasted values vis-à-vis the original values. Only the SVM model shows long memory property in forecasting financial returns.     

Bayesian Inference in Dependent Right Censoring

In this article, we consider dependent right censoring when the lifetime and censoring variables have a Marshall–Olkin bivariate exponential distribution and obtain MLEs, MMEs and UMVUEs of the unknown parameters. The Bayes estimators as well as the Posterior Regret Gamma Minimax (PRGM) estimators of the parameters of interest under the SEL function are also obtained and a Monte Carlo simulation study is carried out to compare these estimators.