摘要:

This paper concerns a method of estimation of variance components in a random effect linear model. It is mainly a resampling method and relies on the Jackknife principle. The derived estimators are presented as least squares estimators in an appropriate linear model, and one of them appears as a MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimator. Our resampling method is illustrated by an example given by C. R. Rao [7] and some optimal properties of our estimator are derived for this example. In the last part, this method is used to derive an estimation of variance components in a random effect linear model when one of the components is assumed to be known.

ISSN:0233-1888    

DOI:10.1080/02331889508802506

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Consistent variance estimators for certain stochastic processes are suggested using the fact that (weak or strong) invariance principles may be available. Convergence rates are also derived, the latter being essentially determined by the approximation rates in the corresponding invariance principles. As an application, a change point test in a simple AMOC renewal model is briefly discussed, where variance estimators possessing good enough convergence rates are required.

ISSN:0233-1888    

DOI:10.1080/02331889508802507

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In the general linear model consider the experimental design problem for the Gauß-Markov estimator or least squares estimator when the observations are correlated. We prove new formulas for the efficiency of an exact design with respect to theD-criterion. For models with intercept term, for example, these formulas are useful to derive better lower bounds for the efficiency than the bounds recently given for an arbitrary linear model. These bounds are applied in examples to symmetrical regular circulants as covariance matrices. A byproduct of the investigations is some insight as to what kinds of designs might retain their optimality or high efficiency (for the uncorrelated homoscedastic case) under correlated observations.

ISSN:0233-1888    

DOI:10.1080/02331889508802508

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Satterthwaite's approximation of the distribution of a nonnegative linear combination of independent mean squares is addressed in this article. A necessary and sufficient condition for the approximation to be exact is presented for the case of a general balanced mixed model. A test is subsequently developed for detecting any significant departure from this condition using the data under consideration. An example is given to illustrate the proposed methodology.

ISSN:0233-1888    

DOI:10.1080/02331889508802509

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Consider an i.i.d. sample for a random vectorWe are interested in recursive estimates of the regression functionand of the variance function Var. We use recursive kernel estimates for both problems and prove pointwise mean square convergence with rates under appropriate conditions. The results are compared with nonrecursive estimators, which have recently been suggested by various authors.

ISSN:0233-1888    

DOI:10.1080/02331889508802510

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Two types of non-global bandwidth, which may be calledlocalandvariable,have been defined in attempts to improve the performance of kernel density estimators. In nonparametric regression, local linear fitting has become a method of much popularity. It is natural, therefore, to consider the use of non-global bandwidths in the local linear context, and indeedlocalbandwidths are often used. In this paper, it is observed that a natural proposal in the literature for combiningvariablebandwidths with local linear fitting fails in the sense that the resulting mean squared error properties are those normally associated withlocalrather than variable bandwidths. We are able to understand why this happens in terms of weightings that are involved. We also attempt to investigate how the bias reduction expected of well-chosen variable bandwidths might be achieved in conjunction with local linear fitting.

ISSN:0233-1888    

DOI:10.1080/02331889508802511

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

We note that some classical functional estimation problems may be reduced to a general unique framework and study an estimator within this general framework that reduces to the classical histogram type estimators in various examples presented. The convergence in probability and the almost complete convergence of this general estimator are studied obtaining convergence conditions which reduce to the classical conditions in each case. Finally, this general framework provides conditions for the convergence of the finite dimensional distributions of the associated empirical process.

ISSN:0233-1888    

DOI:10.1080/02331889508802512

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

We regard the simple linear calibration problem where only the responseyof the regression liney= β0+ β1tis observed with errors. The experimental conditionstare observed without error. For the errors of the observationsywe assume that there may be some gross errors providing outlying observations. This situation can be modeled by a conditionally contaminated regression model. In this model the classical calibration estimator based on the least squares estimator has an unbounded asymptotic bias. Therefore we introduce calibration estimators based on robust one-step-M-estimators which have a bounded asymptotic bias. For this class of estimators we discuss two problems: The optimal estimators and their corresponding optimal designs. We derive the locally optimal solutions and show that the maximin efficient designs for non-robust estimation and robust estimation coincide.

ISSN:0233-1888    

DOI:10.1080/02331889508802513

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

We propose a study of asymptotic properties in an extension of the Nelder-Wedderburn generalized linear models (GLM) and we apply the results to a model choice in Mandel's models of analysis of variance (ANOVA). This study concerns the behaviour of the maximum likelihood estimators (MLE) when the scale parameter of the GLM tends to zero. Finally, to allow the use of our results, we give some specifications of this limit in three cases of the GLM.

ISSN:0233-1888    

DOI:10.1080/02331889508802514

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Considernobservations on,,generated independently by a distribution functionFwhich is only partially specified: We require thatFhas in its upper tail a densityfsuch thatas x tends to the right endpoint θ ofF. The parameters of interest are a > 0 andb,.

ISSN:0233-1888    

DOI:10.1080/02331889508802515

出版商:Gordon & Breach Science Publishers    

年代:1995

数据来源: Taylor