Accelerated life tests for log-normal series system with dependent masked data under Type-I progressive hybrid censoring

This article considers the constant stress accelerated life test for series system products, where independent log-normal distributed lifetimes are assumed for the components. Based on Type-I progressive hybrid censored and masked data, the expectation-maximization algorithm is applied to obtain the estimation for the unknown parameters, and the parametric bootstrap method is used for the standard deviation estimation. In addition, Bayesian approach combining latent variable with Gibbs sampling is developed. Further, the reliability functions of the system and components are estimated at use stress level. The proposed method is illustrated through a numerical example under different masking probabilities and censoring schemes.     

Tempered stable Ornstein– Uhlenbeck processes: A practical view

We study the one-dimensional Ornstein–Uhlenbeck (OU) processes with marginal law given by tempered stable and tempered infinitely divisible distributions. We investigate the transition law between consecutive observations of these processes and evaluate the characteristic function of integrated tempered OU processes with a view toward practical applications. We then analyze how to draw a random sample from this class of processes by considering both the classical inverse transform algorithm and an acceptance–rejection method based on simulating a stable random sample. Using a maximum likelihood estimation method based on the fast Fourier transform, we empirically assess the simulation algorithm performance.     

Estimation of population mean in two-occasion successive sampling

In the present article, we have proposed some classes of estimators based on transformed auxiliary variable. The biases and mean squared errors (MSEs) of the proposed estimators have been obtained. The proposed estimators have been compared with simple mean estimator when there is no matching and the optimum estimator, which is a combination of the means of the matched and unmatched portion of the sample at the second occasion. Optimum replacement policy and the efficiency of the proposed estimators have been discussed. Theoretical results are well supported with an empirical study.     

Evaluation of the predictive performance of the Liu type estimator

This article discusses the predictive performance of the Liu type (LT) estimator compared to ordinary least squares, principal components, ridge regression, and Liu estimators. The theoretical results are illustrated by a numerical example and a region is established where the LT estimator is uniformly superior to the other mentioned estimators.     

An efficient use of moment's ratios of scrambling variables in a randomized response technique

This paper aimed at providing an efficient new unbiased estimator for estimating the proportion of a potentially sensitive attribute in survey sampling. The suggested randomization device makes use of the means, variances of scrambling variables, and the two scalars lie between “zero” and “one.” Thus, the same amount of information has been used at the estimation stage. The variance formula of the suggested estimator has been obtained. We have compared the proposed unbiased estimator with that of Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimators. Relevant conditions are obtained in which the proposed estimator is more efficient than Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimators. The optimum estimator (OE) in the proposed class of estimators has been identified which finally depends on moments ratios of the scrambling variables. The variance of the optimum estimator has been obtained and compared with that of the Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimator. It is interesting to mention that the “optimum estimator” of the class of estimators due to Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) depends on the parameter π under investigation which limits the use of Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) OE in practice while the proposed OE in this paper is free from such a constraint. The proposed OE depends only on the moments ratios of scrambling variables. This is an advantage over the Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimator. Numerical illustrations are given in the support of the present study when the scrambling variables follow normal distribution. Theoretical and empirical results are very sound and quite illuminating in the favor of the present study.     

Estimating and contextualizing the attenuation of odds ratios due to non collapsibility

The odds ratio is a measure commonly used for expressing the association between an exposure and a binary outcome. A feature of the odds ratio is that its value depends on the choice of the distribution over which the probabilities in the odds ratio are evaluated. In particular, this means that an odds ratio conditional on a covariate may have a different value from an odds ratio marginal on the covariate, even if the covariate is not associated with the exposure (not a confounder). We define the individual odds ratio (IORs) and population odds ratios (PORs) as the ratio of the odds of the outcome for a unit increase in the exposure, respectively, for an individual in the population and for the whole population, in which case the odds are averaged across the population. The attenuation of conditional odds ratio, marginal odds ratio, and PORs from the IOR is demonstrated in a realistic simulation exercise. The degree of attenuation differs in the whole population and in a case–control sample, and the property of invariance to outcome-dependent sampling is only true for the IOR. The relevance of the non collapsibility of odds ratios in a range of methodological areas is discussed.     

Pseudo-likelihood for case–cohort studies under length-biased sampling

A case–cohort design was proposed by Prentice (1986) Prentice, R.L. (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika 73:1–11.[Crossref], [Web of Science ®] , [Google Scholar] in order to reduce costs. It involves the collection of covariate data from all subjects who experience the event of interest, and from the members of a random subcohort. This case–cohort design has been extensively studied, but is exclusively considered for right-censored data. In this article, we propose case–cohort designs adapted to length-biased data under the proportional hazards assumption. A pseudo-likelihood procedure is described for estimating parameters and the corresponding cumulative hazard function. The large sample properties, such as consistency and weak convergence, for such pseudo-likelihood estimators are presented. We also conduct simulation studies to show that the proposed estimators are appropriate for practical use. A real Oscar Awards data is provided.     

Double sampling max chart

This study proposes a double sampling (DS) Max chart for monitoring shifts in the process mean and standard deviation. The design of the DS Max chart depends on five parameters, i.e. first and second sample sizes, warning limit at Stage 1, upper control limits at Stages 1 and 2. The optimization design of the DS Max chart is conducted using a genetic algorithm by minimizing the average run length. The comparison shows that the DS Max chart performs better than the existing charts in the literature. An example is provided to illustrate the application of the DS Max chart.     

On the comparison of Warner's and unrelated question randomized response plans for estimating sensitive finite population proportions

We consider the problem of estimation of a finite population proportion (P) related to a sensitive attribute under Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) randomized response plan and the unrelated question plan due to Horvitz et al. (1967 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) plan with any given value of the plan parameter, there exists an LUE of P based on the unrelated question plan with a uniformly smaller variance for suitable choices of the plan parameters. Assuming that only the attribute is sensitive but its complement is innocuous, the same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same specified level of privacy.