nxiong Li

Asymptotic properties of the GMLE with case 2 interval-censored data

In case 2 interval censoring the random survival time X of interest is not directly observable, but only known to have occurred before Y, between Y and Z, or after Z, where (Y, Z) is a pair of observable inspection times such that Y

On Consistency of the Self-Consistent Estimator of Survival Functions with Interval-Censored Data

The self-consistent estimator is commonly used for estimating a survival function with interval-censored data. Recent studies on interval censoring have focused on case 2 interval censoring, which does not involve exact observations, and double censoring, which involves only exact, right-censored or left-censored observations. In this paper, we consider an interval censoring scheme that involves exact, left-censored, right-censored and strictly interval-censored observations. Under this censoring scheme, we prove that the self-consistent estimator is strongly consistent under certain regularity conditions.

Estimation of the Parameters of the Birnbaum–Saunders Distribution

Some alternative estimators to the maximum likelihood estimators of the two parameters of the Birnbaum–Saunders distribution are proposed. Most have high efficiencies as measured by root mean square error and are robust to departure from the model as well as to outliers. In addition, the proposed estimators are easy to compute. Both complete and right-censored data are discussed. Simulation studies are provided to compare the performance of the estimators.

Asymptotic Properties of Self-Consistent Estimators with Mixed Interval-Censored Data

Mixed interval-censored (MIC) data consist of n intervals with endpoints Li and Ri, i = 1, ..., n. At least one of them is a singleton set and one is a finite non-singleton interval. The survival time Xi is only known to lie between Li and Ri, i = 1, 2, ..., n. Peto (1973, Applied Statistics, 22, 86–91) and Turnbull (1976, J. Roy. Statist. Soc. Ser. B, 38, 290–295) obtained, respectively, the generalized MLE (GMLE) and the self-consistent estimator (SCE) of the distribution function of X with MIC data. In this paper, we introduce a model for MIC data and establish strong consistency, asymptotic normality and asymptotic efficiency of the SCE and GMLE with MIC data under this model with mild conditions.

Regression models with arbitrarily interval-censored observations

By arbitrarily interval censoring we mean a lifetime could be either ughl-censored, left-censored, strictly interval-censored, or observed exactly. In this paper, we shall study the least squares regression and Cox regression models when data are subject to said censoring scheme. Simulations and an application of a set of cancer treatment data are studied for investigating the performance of the proposed methods.

Nonparametric Estimation of the Limiting Availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.

Rank Estimation of Log-Linear Regression with Interval-Censored Data

Interval-censored data arise in a wide variety of research and application fields such as cancer and AIDS studies. In this paper, we study a log-linear regression model when data are subject to interval censoring. We use a U-statistic based on ranks to estimate regression coefficients and establish large sample properties of the estimator. We illustrate the performance of the proposed estimate with simulations and a numerical example.

Resilience and reliability analysis of P2P network systems

This paper conducts resilience and reliability analysis of P2P network by studying the isolation probability and the durable time of a single user. The network with users lifetime having stronger NWUE property is proved to be more resilient. Further, both graphical and nonparametric methods are developed to test the NWUE order between two data sets.

Nonparametric confidence intervals for the renewal function with censored data

An asymptotic nonparametric method for constructing confidence intervals for the renewal function using censored data is presented. The method is based on the fact that the productlimit estimator of the renewal function converges weakly to a Gaussian process as the sample size increases

Lifelength in a random environment

Let T denote the lifelength of a component, the distribution of which, conditional on a parameter y, is known. It is supposed that y is a realization of nonnegative stochastic process {Y,t[greater-or-equal, slanted]0}, reflecting random variation in the environment in which the component is operating. Conditions are determined under which the distribution of T given {Y(t),t[greater-or-equal, slanted]0} is IFR, DFR, IFRA, DFRA, NBU or NWU. Further, conditions are determined under which, if the conditional distributions of T1 and T2, the lifelengths of two components, are ordered stochastically or in variability, a similar order holds for the corresponding marginal distributions.