摘要:

An empirical Bayes procedure is considered for estimating a mean value function imbedded within a collection ofNstationary time series. Two cases are considered: a mean value function that is a fixed function of time and one that is a stationary normal process. Estimators for the spectral densities are derived from prior data using an extension to time series of the usual one-way analysis of variance. These estimators are inserted into approximations for the classical Bayes estimators to obtain empirical Bayes estimators. Asymptotic mean square errors of the empirical Bayes and maximum likelihood estimators are compared by an example.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481008

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Estimation of the linear discriminant functionLis considered in the case where there aren1andn2observations from the populations II1and II2andMunclassified observations. Estimates ofLusing alln1+n2+Mobservations are proposed and evaluated in terms of the expected error rate under the assumption thatMis small relative ton1andn2. By appropriately weighting the sample means of the unclassified observations, an estimate ofLis given which dominates the usual estimate based on just then1+n2classified observations.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481009

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481010

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Loglinear models are classified as direct or indirect depending on whether the maximum likelihood estimates of cell values are explicit functions of the sufficient statistics or not. For saturated (hence, direct) models, Goodman (1970) and Bishop, Fienberg, and Holland (1975) used the δ method to calculate the asymptotic variances of various û terms in the loglinear models. In the present paper, this approach has been generalized to direct unsaturated hierarchical loglinear models. General rules for determining closed form expressions for asymptotic variances in such situations are obtained; bounds for the asymptotic variances of û terms in indirect models are considered; and these rules are compared with other methods of producing asymptotic variances.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481011

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Estimation of the value of a density function at a point of continuity using a kernel-type estimator is discussed and improvements of the technique are presented. The generalized jackknife method is employed to reduce the asymptotic and small sample mean square error and bias of these estimators. The procedure presented has the flexibility to afford the user a choice between bias reduction, variance reduction, or both.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481012

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Often, a sensible approach to a general design problem is to slightly expand the appropriate all-bias designs. This idea is applied to situations involving polynomial spline models in which it is necessary to (i) guard against second-degree models in some part, or all, of a cuboidal region of interest, while fitting first-degree models; (ii) guard against third-degree models, while fitting second-degree models. All joins are made on the axes. For (i), suitable designs include 2IVk—pfactorial designs in each 2k-tant. For (ii), consideration of symmetrical designs leads to cuboidal designs of the type previously considered in Draper and Lawrence (1965).

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481013

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

An attempt is made to develop a best linear unbiased estimator of β in the modely=Xβ +u, with known singular covariance matrixVofuand restrictions on β. Two operational criteria for optimality are considered: minimum expected quadratic loss and minimum generalized variance. It is shown that these criteria lead to the same estimator, the well-known least-squares estimator, as developed by Theil (1971).

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481014

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481015

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Admissibility and completeness of linear unbiased estimators in a linear model with general covariance structure are examined. Under rather unrestrictive conditions, a minimal complete class of linear unbiased estimators is described.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481016

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A uniform approximation of any arbitrary lag structure can be achieved from a distributed lag formulation which is a combination of the Almon and geometric lag formulations.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10481017

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor