Empirical Entropy for Right Censored Data

The maximum entropy method has been widely used in many fields, such as statistical mechanics,economics, etc. Its crucial idea is that when we make inference based on partial information, we must use the distribution with maximum entropy subject to whatever is known. In this paper, we investigate the empirical entropy method for right censored data and use simulation to compare the empirical entropy method with the empirical likelihood method. Simulations indicate that the empirical entropy method gives better coverage probability than that of the empirical likelihood method for contaminated and censored lifetime data.

Mallows Model Averaging Estimation for Linear Regression Model with Right Censored Data

This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is,the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically.Some numerical studies are conducted to evaluate the finite-sample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.

THE STRONG LAW FOR THE P-L ESTIMATE IN THE LEFT TRUNCATED AND RIGHT CENSORED MODEL (I)

For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.

Reliability Estimators for the Components of Series and Parallel Systems:The Weibull Model

This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.

Random weighting estimation for survival function under right censorship

The random weighting method is an emerging computing method in statistics.In this paper,we propose a novel estimation of the survival function for right censored data based on the random weighting method.Under some regularity conditions,we prove the strong consistency of this estimation.

Nonparametric Inference for the Stress-Strength Model under Right Censoring

The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.

Asymptotic Properties of Self-Consistent Estimatorswith Doubly-Censored Data

The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observable everywhere in the interval [a, b], where a=inf{x: F(x)】0} and b=sup{x: F(x)【1}. Such an assumption does not allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. However, often in practice this assumption is not satisfied. In this manuscript we establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the SCE under a set of assumptions that allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. Finally, we point out a gap in the proofs of the existing results in the literature due to the definition of the SCE.

BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.

Hazard Model with Random Treatment Time-Lag Effect

In clinical studies,it is often that the medical treatments take a period of time before having an effect on patients and the delayed time may vary from person to person.Even though there exists a rich literature developing methods to estimate the time-lag period and treatment effects after lag time,most of these existing studies assume a fixed lag time.In this paper,we propose a hazard model incorporating a random treatment time-lag effect to describe the heterogeneous treatment effect among subjects.The EM algorithm is used to obtain the maximum likelihood estimator.We give the asymptotic properties of the proposed estimator and evaluate its performance via simulation studies.An application of the proposed method to real data is provided.

Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d, observations of the true distribution, empirical likelihood （EL） procedure is proposed for the inference on mean residual life （MRL） of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio （LR） directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.

Assessing the lifetime performance index of weighted Lomax distribution based on progressive type-Ⅱ censoring scheme for bladder cancer

In this paper,Health-related quality of life has not been adequately measured in bladder cancer.A recently developed reliable and disease-specific quality of life instrument(Bladder Cancer Index,RCI)was used to measure.Progressive type Ⅱ censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessity for the speedy test.To test the process capability,the lifetime performance index Cl is widely recommended for evaluating the performance of the producfs lifetime and evaluating the lifetime performance index GL for the three-parameter Weighted-Lomax distribution(WLx)under progressive type-II censoring sample for a lower specification limit(L).The statistical inference concerning CL is conducted via obtaining the maximum likelihood of Cl on the base of progressive type-II censoring.The asymptotic normal distribution of the MLE of CL and the confidence interval is proposed.Moreover,the hypothesis testing of CL for evaluating the lifetime performance of WLx data is conducted.Also,assuming the conjugate prior distribution and squared error loss function,this study constructs a Bayes estimator of CL.The Bayes estimator of CL is then utilized to develop a credible interval in the condition of known L.Moreover,we propose a Bayesian test to assess the lifetime performance of products.We also propose a Bayesian test to assess the lifetime performance of products.Finally,two examples are given,one of them is considering a real life data of the remission times of bladder cancer patients in endurance lifetime test and the other is a simulated example to illustrate the usage of the proposed procedure.