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 ...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.展开更多
A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense t...A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.展开更多
Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing d...Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.展开更多
An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical...An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.展开更多
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 als...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.展开更多
Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobse...Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).展开更多
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 param...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.展开更多
Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of ...Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.展开更多
In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose a...In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.展开更多
Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of ...Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.展开更多
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. T...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.展开更多
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. wh...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.展开更多
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 ...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.展开更多
In studies of HIV, interval-censored data occur naturally. HIV infection time is not usually known exactly, only that it occurred before the survey, within some time interval or has not occurred at the time of the sur...In studies of HIV, interval-censored data occur naturally. HIV infection time is not usually known exactly, only that it occurred before the survey, within some time interval or has not occurred at the time of the survey. Infections are often clustered within geographical areas such as enumerator areas (EAs) and thus inducing unobserved frailty. In this paper we consider an approach for estimating parameters when infection time is unknown and assumed correlated within an EA where dependency is modeled as frailties assuming a normal distribution for frailties and a Weibull distribution for baseline hazards. The data was from a household based population survey that used a multi-stage stratified sample design to randomly select 23,275 interviewed individuals from 10,584 households of whom 15,851 interviewed individuals were further tested for HIV (crude prevalence = 9.1%). A further test conducted among those that tested HIV positive found 181 (12.5%) recently infected. Results show high degree of heterogeneity in HIV distribution between EAs translating to a modest correlation of 0.198. Intervention strategies should target geographical areas that contribute disproportionately to the epidemic of HIV. Further research needs to identify such hot spot areas and understand what factors make these areas prone to HIV.展开更多
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 pres...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.展开更多
基金This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(Grant Number IMSIU-RG23142).
文摘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.
基金Supported by the National Natural Science Foundation of China (70171008)
文摘A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.
文摘Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.
文摘An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.
文摘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.
文摘Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).
基金Supported by the National Natural Science Foundation of China (11071022)the Key Project of Hubei Provincial Department of Education (D20092207)
文摘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.
文摘Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1110111911126332)+2 种基金the National Social Science Foundation of China(Grant No.11CTJ004)the Natural Science Foundation of Guangxi Province(Grant No.2010GXNSFB013051)the Philosophy and Social Sciences Foundation of Guangxi Province(Grant No.11FTJ002)
文摘In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.
文摘Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.
文摘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.
文摘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.
文摘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.
文摘In studies of HIV, interval-censored data occur naturally. HIV infection time is not usually known exactly, only that it occurred before the survey, within some time interval or has not occurred at the time of the survey. Infections are often clustered within geographical areas such as enumerator areas (EAs) and thus inducing unobserved frailty. In this paper we consider an approach for estimating parameters when infection time is unknown and assumed correlated within an EA where dependency is modeled as frailties assuming a normal distribution for frailties and a Weibull distribution for baseline hazards. The data was from a household based population survey that used a multi-stage stratified sample design to randomly select 23,275 interviewed individuals from 10,584 households of whom 15,851 interviewed individuals were further tested for HIV (crude prevalence = 9.1%). A further test conducted among those that tested HIV positive found 181 (12.5%) recently infected. Results show high degree of heterogeneity in HIV distribution between EAs translating to a modest correlation of 0.198. Intervention strategies should target geographical areas that contribute disproportionately to the epidemic of HIV. Further research needs to identify such hot spot areas and understand what factors make these areas prone to HIV.
文摘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.
