Pmc-optimal nonparametric quantile estimator

According to Pitman's Measure of Closeness, if T₁and T₂are two estimators of a real parameter $[d], then T₁is better than T₂if Po[d]{T₁-o[d] < T₂-0[d]} > 1/2 for all 0[d]. It may however happen that while T₁is better than T₂and T₂is better than T₃, T₃is better than T₁. Given q ? (0,1) and a sample X₁, X₂, ..., X_nfrom an unknown F ? F, an estimator T* = T*(X₁,X₂...X_n)of the q-th quantile of the distribution F is constructed such that P_F{F(T*)-q <[d] F(T)-q} >[d] 1/2 for all F?F and for all T€T, where F is a nonparametric family of distributions and T is a class of estimators. It is shown that T* =X_j:n'for a suitably chosen jth order statistic.     

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.     

A note on Stein-type shrinkage estimator in partial linear models

In this paper, an exact sufficient condition for the dominance of the Stein-type shrinkage estimator over the usual unbiased estimator in a partial linear model is exhibited. Comparison result is then done under the balanced loss function. It is assumed that the vector of disturbances is typically distributed according to the law belonging to the sub-class of elliptically contoured models. It is also shown that the dominance condition is robust. Furthermore, a nonparametric estimation after estimation of the linear part is added for detecting the efficiency of the obtained results.     

On estimation and diagnostics analysis in log-generalized gamma regression model for interval-censored data

The interval-censored survival data appear very frequently, where the event of interest is not observed exactly but it is only known to occur within some time interval. In this paper, we propose a location-scale regression model based on the log-generalized gamma distribution for modelling interval-censored data. We shall be concerned only with parametric forms. The proposed model for interval-censored data represents a parametric family of models that has, as special submodels, other regression models which are broadly used in lifetime data analysis. Assuming interval-censored data, we consider a frequentist analysis, a Jackknife estimator and a non-parametric bootstrap for the model parameters. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some techniques to perform global influence.     

Generalized varying-coefficient single-index model

In this paper, the generalized varying-coefficient single-index model is discussed based on penalized likelihood. All the unknown functions are fitted by penalized spline. The estimates of the unknown parameters and the unknown coefficient functions are obtained and the estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. Two simulation studies are carried out to illustrate the performance of the estimates. An application of the model to the Hong Kong environmental data further demonstrates the potential of the proposed modelling procedures.     

Bayes designs for multiple linear regression on the unit sphere

We deal with experimental designs minimizing the mean square error of the linear BAYES estimator for the parameter vector of a multiple linear regression model where the experimental region is the k-dimensional unit sphere. After computing the uniquely determined optimum information matrix, we construct, separately for the homogeneous and the inhomogeneous model, both approximate and exact designs having such an information matrix.     

An Exponential Model for Damage Accumulation

In this article, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the Wöhler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then discussed and some methods are described. Some examples are finally presented to illustrate the derived model and the proposed methods of estimation.     

A comparison of several analysis of variance programs with unequal cell size

Various programs in statistical packages for analysis of variance with unequal cell size give different results to the same data because of nonorthogonality of the main effects and interactions. This paper explains how these programs treat the problem of analysis of variance of unbalanced data.     

Bayes Estimation Based on Joint Progressive Type II Censored Data Under LINEX Loss Function

In the lifetime experiments, the joint censoring scheme is useful for planning comparative purposes of two identical products manufactured coming from different lines. In this article, we will confine ourselves to the data obtained by conducting a joint progressive Type II censoring scheme on the basis of the two combined samples selected from the two lines. Moreover, it is supposed that the distributions of lifetimes of the two products satisfy in a proportional hazard model. A general form for the distributions is considered, and we tackle the problem of obtaining Bayes estimates under the squared error and linear-exponential (LINEX) loss functions. As a special case, the Weibull distribution is discussed in more detail. Finally, the estimated risks of the various estimators obtained are compared using the Monte Carlo method.     

EGARCH Model with Weighted Liquidity

We analyze a variant of the EGARCH model which captures the variation of the intra-day price. We study the asymptotic behavior of the estimators for the parameters of the model. We also illustrate our theoretical results by empirical studies.