Bayesian and Non-Bayesian Analysis for the Sine Generalized Linear Exponential Model under Progressively Censored Data

This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.

Composite Quantile Regression for Nonparametric Model with Random Censored Data

The composite quantile regression should provide estimation efficiency gain over a single quantile regression. In this paper, we extend composite quantile regression to nonparametric model with random censored data. The asymptotic normality of the proposed estimator is established. The proposed methods are applied to the lung cancer data. Extensive simulations are reported, showing that the proposed method works well in practical settings.

Asymptotic Properties of Wavelet Estimators in a Semiparametric Regression Model with Censored Data

Consider a semiparametric regression model Y_i=X_iβ＋g（t_i）＋e_i, 1 ≤ i ≤ n, where Y_i is censored on the right by another random variable C_i with known or unknown distribution G. The wavelet estimators of parameter and nonparametric part are given by the wavelet smoothing and the synthetic data methods. Under general conditions, the asymptotic normality for the wavelet estimators and the convergence rates for the wavelet estimators of nonparametric components are investigated. A numerical example is given.

Kernel Estimators of the ROC Curve with Censored Data

Receiver operating characteristic （ROC） curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed.

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.

Smoothed Estimator of Quantile Residual Lifetime for Right Censored Data

It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

LIMIT THEOREMS FOR INTEGRAL TYPE ESTIMATORS WITH CENSORED DATA

In survival analysis, the Kaplan-Meter estimator plays a very important role, and its asymptotic properties have been studied by many authors. In recefit years, people find that someimportant statistics can be expressed as the integrals with respect to it. In this paper we shalldiscuss the asymptotic behavior of such integrals. The strong convergence rste shall be givenand the weak convergence result in space D shall be proved.

THE RATE OF UNIFORM CONVERGENCE OF THE SURVIVAL FUNCTION ESTIMATOR FOR TRUNCATED AND CENSORED DATA

For left truncated and right censored data, based on a strong representation of the product-limit estimator of the survival function, we derive the sufficient and necessary condition for the rate of strong uniform convergence of the product-limit estimator over the whole line.

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA

Functional laws of the iterated logarithm are obtained for cumulative hazard processes in the neighborhood of a fixed point when the data are subject to left truncation and right censorship. On the basis of these results the exact rates of pointwise almost sure convergence for various types of kernel hazard rate estimators are derived.

Edgeworth expansion of the Studentized product-limit estimator for truncated and censored data

Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).

LAD estimation for nonlinear regression models with randomly censored data

The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.

Estimation and Prediction for Flexible Weibull Distribution Based on Progressive Type II Censored Data

In this work,we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample.Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems.The likelihood method as well as the Bayesian sampling techniques is applied for the inference problems.The point predictors and credible intervals of unobserved data based on an informative set of data are computed.Markov ChainMonte Carlo samples are performed to compare the so-obtained methods,and one real data set is analyzed for illustrative purposes.

Sequential Confidence Bands for Quantile Densities Under Truncated and Censored Data

In this paper an asymptotic distribution is obtained for the maximaldeviation between the kernel quantile density estimator and the quantile density when the data aresubject to random left truncation and right censorship. Based on this result we propose a fullysequential procedure for constructing a fixed-width confidence band for the quantile density on afinite interval and show that the procedure has the desired coverage probability asymptotically asthe width of the band approaches zero.

Nonparametric Regression with Interval-Censored Data

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.

Semiparametric Likelihood-based Inference for Censored Data with Auxiliary Information from External Massive Data Sources

Published auxiliary information can be helpful in conducting statistical inference in a new study.In this paper,we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is available.We express the auxiliary information as constraints on the regression coefficients and the covariate distribution,then use empirical likelihood method for general estimating equations to improve the efficiency of the interested parameters in the specified model.The consistency and asymptotic normality of the resulting regression parameter estimators established.Also numerical simulation and application with different supposed conditions show that the proposed method yields a substantial gain in efficiency of the interested parameters.

Weak Representation of the Survival Function Under Semiparametric Model for Truncated and Censored Data

In this paper we study semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. Weak representations of the two estimators are derived, which are valid up to a given order statistic of the observations.

Hypothesis Testing with Paired Partly Interval Censored Data

Partly interval censored data frequently occur in many areas including clinical trials,epidemiology research,and medical follow-up studies.When data come from observational studies,we need to carefully adjust for the confounding bias in order to estimate the true treatment effect.Pair matching designs are popular for removing confounding bias without parametric assumptions.With time-to-event outcomes,there are some literature for hypothesis testing with paired right censored data,but not for interval censored data.O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon scores.Akritas proposed the Akritas test and established its asymptotic properties.We extend Akritas test to partly interval censored data.We estimate the survival distribution function by nonparametric maximum likelihood estimation(NPMLE),and prove the asymptotic validity of the new test.To improve our test under small sample size or extreme distributions,we also propose a modified version using the rank of the score difference.Simulation results indicate that our proposed methods have very good performance.