Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

Heteroscedasticity and Distributional Assumptions in the Censored Regression Model

Data censoring causes ordinary least-square estimators of linear models to be biased and inconsistent. The Tobit estimator yields consistent estimators in the presence of data censoring if the errors are normally distributed. However, nonnormality or heteroscedasticity results in the Tobit estimators being inconsistent. Various estimators have been proposed for circumventing the normality assumption. Some of these estimators include censored least absolute deviations (CLAD), symmetrically censored least-square (SCLS), and partially adaptive estimators. CLAD and SCLS will be consistent in the presence of heteroscedasticity; however, SCLS performs poorly in the presence of asymmetric errors. This article extends the partially adaptive estimation approach to accommodate possible heteroscedasticity as well as nonnormality. A simulation study is used to investigate the estimators’ relative performance in these settings. The partially adaptive censored regression estimators have little efficiency loss for censored normal errors and appear to outperform the Tobit and semiparametric estimators for nonnormal error distributions and be less sensitive to the presence of heteroscedasticity. An empirical example is considered, which supports these results.     

Product-limit Estimators and Cox Regression with Missing Censoring Information

The Kaplan–Meier estimator of a survival function requires that the censoring indicator is always observed. A method of survival function estimation is developed when the censoring indicators are missing completely at random (MCAR). The resulting estimator is a smooth functional of the Nelson–Aalen estimators of certain cumulative transition intensities. The asymptotic properties of this estimator are derived. A simulation study shows that the proposed estimator has greater efficiency than competing MCAR-based estimators. The approach is extended to the Cox model setting for the estimation of a conditional survival function given a covariate.     

L p –Estimators as Estimates of a Parameter of Location for a Sharp–pointed Symmetric Density

We study the asymptotics of L _p estimators, p > 0, over a sample having a symmetric density with a sharp–point at the centre of symmetry of the distribution. The rates of convergence of the L _p estimators in this situation depend on p and on the shape of the density. To obtain some of the limit distributions, we present new results in the asymptotics of M–estimators. We extend the delta method to the case when the Euclidean norm of the conveniently normalized M–estimators converge to a power of the Euclidean norm of a (possibly Gaussian) stable distribution.     

The performance of alternative estimators for the probit model with first-order serial correlation 1

The purpose of the paper is to evaluate the relative performance of two generalized conditional moment (GCM) estimators in terms of their mean squared errors, for the Probit model with first-order serial correlation. The first estimator is a linearized one-step estimator described by Poirier and Ruud (1988). The second one is defined in the present paper. Monte Car10 experiments suggest that the GCM estimators outperform the ordinary Probit estimator. The two GCM estimators do almost equally well, except that the second one may be easier to calculate, especially in large samples.     

Bootstrapping estimators for the seemingly unrelated regressions model

In this paper we consider the possibility of using the bootstrap to estimate the finite sample variability of feasible generalized least squares and improved estimators applied to the seemingly unrelated regressions model. The improved estimators we employ include members of the Stein-rule family and a hierarchical Bayes estimator proposed by Blattberg and George (1991). Simulation experiments are carried out using several SUR examples as well as a very large example based on the price-promotion model, and data, from marketing research.     

An efficient and fast algorithm for estimating the frequencies of superimposed exponential signals in zero-mean multiplicative and additive noise

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains O _p (N ^?3/2), which is the best convergence rate in the case of only additive noise and constant amplitude.     

Asymptotically optimal shrinkage estimates for non-normal data

Motivated by several practical issues, we consider the problem of estimating the mean of a p-variate population (not necessarily normal) with unknown finite covariance. A quadratic loss function is used. We give a number of estimators (for the mean) with their loss functions admitting expansions to the order of p ^?1/2 as p→∞. These estimators contain Stein's [Inadmissibility of the usual estimator for the mean of a multivariate normal population, in Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. 1, J. Neyman, ed., University of California Press, Berkeley, 1956, pp. 197–206] estimate as a particular case and also contain ‘multiple shrinkage’ estimates improving on Stein's estimate. Finally, we perform a simulation study to compare the different estimates.     

A frequentist assessment of Bayesian inclusion probabilities for screening predictors

Bayesian inclusion probabilities have become a popular tool for variable assessment. From a frequentist perspective, it is often difficult to evaluate these probabilities as typically no Type I error rates are considered, neither are any explorations of power of the methods given. This paper considers how a frequentist may evaluate Bayesian inclusion probabilities for screening predictors. This evaluation looks at both unrestricted and restricted model spaces and develops a framework which a frequentist can utilize inclusion probabilities that preserve Type I error rates. Furthermore, this framework is applied to an analysis of the Arabidopsis thaliana with respect to determining quantitative trait loci associated with cotelydon opening angle.