Progressive stress accelerated life tests under finite mixture models

In this paper, progressive stress accelerated life tests are considered when the lifetime of a product under use condition follows a finite mixture of distributions. The experiment is performed when each of the components in the mixture follows a general class of distributions which includes, among others, the Weibull, compound Weibull, power function, Gompertz and compound Gompertz distributions. It is assumed that the scale parameter of each component satisfies the inverse power low, the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the parameters under consideration are obtained. A special attention is paid to a mixture of two Rayleigh components. Simulation results are carried out to study the precision of the MLEs and to obtain confidence intervals for the parameters involved.     

Efficiency Considerations in the Additive Hazards Model with Current Status Data

For current status data, L IN , O AKES and Y ing (1998) proposed a procedure for estimation of the regression parameters in the additive hazards model that makes clever use of martingale theory. However, one of the outstanding problems posed in the paper was the issue of efficient estimation, as their estimators do not attain the semiparametric information bound. In this paper, we explore this issue and provide a characterization of the NPMLE. We conduct efficiency comparisons between the NPMLE and the procedure of L IN et al . (1998) analytically and numerically through analysis of a dataset from a tumorigenicity experiment.     

A NONPARAMETRIC TEST AGAINST ORDERED ALTERNATIVES FOR DATA DEFINED BY INTERVALS

Abstract. The paper deals with a generalization of the Jonckheere test against ordered alternatives which allows for arbitrary censoring. It includes some previously published tests as special cases.     

A Sample Selection Approach to Censored Demand Systems

The multivariate sample selection model is extended to a nonlinear equation system with partial selection and applied to household meat consumption in China. Elasticity estimates differ from those obtained from conventional maximum likelihood and Tobit estimates. Chinese meat products are gross complements while net substitution also exists in some cases.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Inference on endogenously censored regression models using conditional moment inequalities

Under a quantile restriction, randomly censored regression models can be written in terms of conditional moment inequalities. We study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring, endogenous censoring and endogenous regressors. These inequalities restrict the parameters to a set. We show regular point identification can be achieved under a set of interpretable sufficient conditions. We then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content. Our method obviates the need for nonparametric estimation, which would require the selection of smoothing parameters and trimming procedures. Without the point identification conditions, our objective function can be used to do inference on the partially identified parameter. Maintaining the point identification conditions, we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest, and has an asymptotically normal distribution. A small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance.     

Multivariate lifetime distributions for the exponential dispersion family

We consider a general form of a multivariate lifetime model in which dependence is induced via a common shock component. The univariate marginal distributions come from the well-known and widely applied exponential dispersion family that includes the normal, compound-Poisson, gamma and negative binomial distributions. Any combination of truncation or censoring, either left or right, is considered, for which all moments are derived. This allows for the model to be calibrated to any affine transformation of lifetime data.     

Expected termination times of progressively Type-I censored step-stress accelerated life tests under continuous and interval inspections

A step-stress accelerated life test is a special life test where test units are subjected to higher stress levels than normal operating conditions so that the information on the lifetime parameters of a test unit can be obtained more quickly in a shorter period of time. Also, progressive Type-I censoring is a generalized form of time censoring where functional test units are withdrawn successively from the life test at some prefixed nonterminal time points. Despite its flexibility and efficient utilization of the available resources, progressively censored sampling has not gained much popularity due to its analytical complexity compared to the conventional censoring schemes. In particular, understanding the mean completion time of a life test is of great practical interest in order to design and manage the life test optimally under frequent budgetary and time constraints. In this work, the expected termination time of a general k-level step-stress accelerated life test under progressive Type-I censoring is derived using a recursive relationship of the stochastic termination time based on the conditional block independence. To be comprehensive, two different modes of failure inspections are considered: continuous inspection, where the exact failure times are observed, and interval inspection, where the exact failure times are not available but only the number of failures that occurred.     

Multi-sample simple step-stress experiment under time constraints

In the context of accelerated life testing, a step-stress model allows for testing under different conditions at various intermediate stages of the experiment. The goal is to develop inference for the mean lifetime at each stress level. The maximum likelihood estimates (MLEs) exist only when some (at least one) failures are observed at each stress level. This limitation can be tackled by a multi-sample step-stress model, which imposes a weaker condition for the existence of the MLEs, i.e. at each stress level, some failures (at least one) must be observed in at least one of the samples. The step-stress experiment with multiple samples at the same stress levels was introduced by Kateri et al. ( Journal of Statistical Planning and Inference, 139 , 2009a ). In this article, we focus on the likelihood inference under such a multi-sample set-up for the case of a simple step-stress experiment under exponentially distributed lifetimes when time constraints are in place in the experimentation.     

Relative coarsening at random

Many types of data are often incompletely observed. How incompletely is typically randomly determined. H eitjan and R ubin ( Annals of Statistics , 1991) proposed a condition, "coarsened at random" or CAR, ensuring ignorability of this randomness in discrete sample spaces. In general sample spaces CAR comes in two flavors according to whether it is defined in terms of probabilities or densities. In this paper, CAR defined in terms of densities, called relative CAR, is discussed as a condition for ignorability in a statistical model allowing for partial observation of random elements determining the degree of incompleteness in the observation of the data.