scholarly journals Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
T. Bouezmarni ◽  
A. El Ghouch ◽  
M. Mesfioui
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Kernel Smoothing ◽  
Mean Squared Error ◽  
Boundary Region ◽  
Law Of Iterated Logarithm ◽  
Linear Estimator ◽  
Right Censored Data ◽  
Squared Error ◽  
Rate Functions

The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.

scholarly journals A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data

Stats ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 120-136
Author(s):  
Ersin Yılmaz ◽  
Syed Ejaz Ahmed ◽  
Dursun Aydın
Keyword(s):  
Nonparametric Regression ◽  
Censored Data ◽  
Kernel Smoothing ◽  
Synthetic Data ◽  
Regression Function ◽  
Data Transformation ◽  
Smoothing Splines ◽  
Spline Regression ◽  
Real World Data ◽  
Right Censored Data

This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier estimator in the literature. In the context of synthetic data, there have been different studies on the estimation of right-censored nonparametric regression models based on smoothing splines, regression splines, kernel smoothing, local polynomials, and so on. It should be emphasized that synthetic data transformation manipulates the observations because it assigns zero values to censored data points and increases the size of the observations. Thus, an irregularly distributed dataset is obtained. We claim that adaptive spline (A-spline) regression has the potential to deal with this irregular dataset more easily than the smoothing techniques mentioned here, due to the freedom to determine the degree of the spline, as well as the number and location of the knots. The theoretical properties of A-splines with synthetic data are detailed in this paper. Additionally, we support our claim with numerical studies, including a simulation study and a real-world data example.

scholarly journals Bayesian Estimation and Prediction of Discrete Gompertz Distribution

2021 ◽  
pp. 1-21
Author(s):  
M. A. Hegazy ◽  
R. E. Abd El-Kader ◽  
A. A. El-Helbawy ◽  
G. R. Al-Dayian
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Hazard Rate ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Gompertz Distribution ◽  
Estimation And Prediction ◽  
Error Loss ◽  
Squared Error ◽  
Rate Functions

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

A Comparison of Hazard Rate Estimators for Left Truncated and Right Censored Data

Biometrika ◽  
1992 ◽  
Vol 79 (2) ◽  
pp. 297 ◽  
Author(s):  
Ulku Uzunogullari ◽  
Jane-Ling Wang
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Right Censored Data
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