Estimating Quantiles of Normal Populations with a Common Mean

Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known estimators of a common mean. Inadmissibility results are proved for estimators which are equivariant under affine and location groups of transformations. Risk values of various estimators of a quantile are compared numerically using a detailed simulation study.     

Locally Efficient Semiparametric Estimators for Proportional Hazards Models with Measurement Error

We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error‐prone covariates is specified correctly and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

Empirical likelihood inference in the presence of measurement error

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. The authors consider the problem of combining this information to make statistical inference on parameters of interest, in particular the population mean and cumulative distribution function. They develop maximum empirical likelihood estimators and study their asymptotic properties. They also present simulation results on the finite sample efficiency of these estimators.     

Exponentiated Teissier distribution with increasing,decreasing and bathtub hazard functions

This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.     

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.     

A new flexible hazard rate distribution: Application and estimation of its parameters

We introduce a new class of flexible hazard rate distributions which have constant, increasing, decreasing, and bathtub-shaped hazard function. This class of distributions obtained by compounding the power and exponential hazard rate functions, which is called the power-exponential hazard rate distribution and contains several important lifetime distributions. We obtain some distributional properties of the new family of distributions. The estimation of parameters is obtained by using the maximum likelihood and the Bayesian methods under squared error, linear-exponential, and Stein’s loss functions. Also, approximate confidence intervals and HPD credible intervals of parameters are presented. An application to real dataset is provided to show that the new hazard rate distribution has a better fit than the other existing hazard rate distributions and some four-parameter distributions. Finally , to compare the performance of proposed estimators and confidence intervals, an extensive Monte Carlo simulation study is conducted.     

Robust R-Estimation of a Consensus Value from Multi-Center Studies

We consider multi-center experiments (for determining a consensus value) conducted in possibly heterogeneous set-ups leading to unbalanced heteroscedastic one-way random effects models. When normality of both the random components and their homoscedasticity are in doubt, standard statistical methods may not be valid. Two robust R-estimators (for the common location parameter), based on signed-rank statistics, are proposed and their properties studied. When large heteroscedasticity is present or the distribution of random effect is abnormal, the proposed estimators perform better than the classical weighted least squares and selected estimators. This feature is illustrated with an arsenic in oyster tissue problem, along with some other simulation studies.     

Maximum likelihood estimator in a multi-phase random regression model

We consider a random regression model with several-fold change-points. The results for one change-point are generalized. The maximum likelihood estimator of the parameters is shown to be consistent, and the asymptotic distribution for the estimators of the coefficients is shown to be Gaussian. The estimators of the change-points converge, with n ^?1 rate, to the vector whose components are the left end points of the maximizing interval with respect to each change-point. The likelihood process is asymptotically equivalent to the sum of independent compound Poisson processes.     

Estimating the common hazard rate of two exponential distributions with ordered location parameters

This paper is concerned with estimating the common hazard rate of two exponential distributions with unknown and ordered location parameters under a general class of bowl-shaped scale invariant loss functions. The inadmissibility of the best affine equivariant estimator is established by deriving an improved estimator. Another estimator is obtained which improves upon the best affine equivariant estimator. A class of improving estimators is derived using the integral expression of risk difference approach of Kubokawa [A unified approach to improving equivariant estimators. Ann Statist. 1994;22(1):290–299]. These results are applied to specific loss functions. It is further shown that these estimators can be derived for four important sampling schemes: (i) complete and i.i.d. sample, (ii) record values, (iii) type-II censoring, and (iv) progressive Type-II censoring. A simulation study is carried out for numerically comparing the risk performance of these proposed estimators.     

ROBUST M-ESTIMATION OF THE INTRACLASS CORRELATION COEFFICIENT

Robust M-estimators of intraclass correlation coefficient, location and scale parameters are defined for familial data. It is shown that these estimators are strongly consistent. Also the asymptotic distributions of these estimators are derived when the underlying distribution is elliptically and permutationally symmetric.     

Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ₁, θ₂, …, θ_k and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the uniformly minimum risk-unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax, and the natural estimators.     

Point estimation of the stress–strength reliability parameter for parallel system with independent and non-identical components

In this article, the estimation problem of the multicomponent stress–strength reliability parameter is considered where the stress and the strength systems have arbitrary fixed numbers of independent and non-identical parallel components. It is assumed that the distribution functions of the stress and the strength components satisfy the proportional reversed hazard rate model. The study is done in more details when the baseline distributions are exponential. Maximum likelihood and uniformly minimum variance unbiased estimators are obtained and compared. Also, Bayes and empirical Bayes estimators are discussed and Monte Carlo simulations are carried out to compare their performances.     

The inverse weighted Lindley distribution: Properties,estimation and an application on a failure time data

In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented. The maximum likelihood estimators for the parameters in the presence of complete and censored data are presented. Two corrective approaches are considered to derive modified estimators that are bias-free to second order. A numerical simulation is carried out to examine the efficiency of the bias correction. Finally, an application using a real data set is presented in order to illustrate our proposed distribution.     

Shrinkage estimation of location parameters in a multivariate skew-normal distribution

Abstract

This paper studies decision theoretic properties of Stein type shrinkage estimators in simultaneous estimation of location parameters in a multivariate skew-normal distribution with known skewness parameters under a quadratic loss. The benchmark estimator is the best location equivariant estimator which is minimax. A class of shrinkage estimators improving on the best location equivariant estimator is constructed when the dimension of the location parameters is larger than or equal to four. An empirical Bayes estimator is also derived, and motivated from the Bayesian procedure, we suggest a simple skew-adjusted shrinkage estimator and show its dominance property. The performances of these estimators are investigated by simulation.     

Estimation of a change point in the hazard rate of Lindley model under right censoring

In this article, we consider a single change point model for a sudden change in the hazard rate of Lindley distribution to model right-censored survival data. We derive the quantile function to generate random numbers from the proposed distribution by using the Lambert function. The maximum likelihood estimation method is used to estimate parameters of the change point model. A simulation study is also carried out to analyze the performance of the estimators. To validate our findings, a dataset on bone marrow transplant for patients of acute lymphoblastic leukemia is analyzed using the proposed model and is compared with the existing exponential single change point model.     

The mixed model for survey regression estimation

Estimation of the population mean under the regression model with random components is considered. Conditions under which the random components regression estimator is design consistent are given. It is shown that consistency holds when incorrect values are used for the variance components. The regression estimator constructed with model parameters that differ considerably from the true parameters performed well in a Monte Carlo study. Variance estimators for the regression predictor are suggested. A variance estimator appropriate for estimators constructed with a biased estimator for the between-group variance component performed well in the Monte Carlo study.     

A unimodal hazard rate function and its failure distribution

A unimodal hazard rate function is suggested to model a failure rate that has a relatively high rate of failure in the middle of expected life time. This unimodal hazard rate function has two shape parameters. One of the parameters indicates the location (time) of the mode and the other controls the height of the mode. In effect, these two parameters index the class of unimodal hazard rate functions. The reliability function and the failure density function of the unimodal hazard rate function are relatively uncomplicated and mathematically tractable. The properties of the unimodal hazard rate function and the failure density function are investigated. The maximum likelihood method is used for the inference concerning the two parameters and an example based on real data is presented. This unimodal hazard rate function is particularly useful when the time of the peak failure rate is of prime interest. The failure distribution provides a practical way of estimating the peak failure time.     

Detecting change in a hazard regression model with right-censoring

The hazard function plays an important role in survival analysis and reliability, since it quantifies the instantaneous failure rate of an individual at a given time point t, given that this individual has not failed before t. In some applications, abrupt changes in the hazard function are observed, and it is of interest to detect the location of such a change. In this paper, we consider testing of existence of a change in the parameters of an exponential regression model, based on a sample of right-censored survival times and the corresponding covariates. Likelihood ratio type tests are proposed and non-asymptotic bounds for the type II error probability are obtained. When the tests lead to acceptance of a change, estimators for the location of the change are proposed. Non-asymptotic upper bounds of the underestimation and overestimation probabilities are obtained. A short simulation study illustrates these results.