摘要:

This paper is concerned with testing the equality of scale parameters of K(> 2) two-parameter exponential distributions in presence of unspecified location parameters based on complete and type II censored samples. We develop a marginal likelihood ratio statistic, a quadratic statistic (Qu) (Nelson, 1982) based on maximum marginal likelihood estimates of the scale parameters under the null and the alternative hypotheses, a C(a) statistic (CPL) (Neyman, 1959) based on the profile likelihood estimate of the scale parameter under the null hypothesis and an extremal scale parameter ratio statistic (ESP) (McCool, 1979). We show that the marginal likelihood ratio statistic is equivalent to the modified Bartlett test statistic. We use Bartlett's small sample correction to the marginal likelihood ratio statistic and call it the modified marginal likelihood ratio statistic (MLB). We then compare the four statistics, MLBi Qut CPL and ESP in terms of size and power by using Monte Carlo simulation experiments. For the variety of sample sizes and censoring combinations and nominal levels considered the statistic MLB holds nominal level most accurately and based on empirically calculated critical values, this statistic performs best or as good as others in most situations. Two examples are given.

ISSN:0361-0918    

DOI:10.1080/03610919008812896

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The use of general linear modeling (GLM) procedures based on log-rank scores is proposed for the analysis of survival data and compared to standard survival analysis procedures. For the comparison of two groups, this approach performed similarly to the traditional log-rank test. In the case of more complicated designs - without ties in the survival times - the approach was only marginally less powerful than tests from proportional hazards models, and clearly less powerful than a likelihood ratio test for a fully parametric model; however, with ties in the survival time, the approach proved more powerful than tests from Cox's semi-parametric proportional hazards procedure. The method appears to provide a reasonably powerful alternative for the analysis of survival data, is easily used in complicated study designs, avoids (semi-)parametric assumptions, and is quite computationally easy and inexpensive to employ.

ISSN:0361-0918    

DOI:10.1080/03610919008812897

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Fractional Principal Components (FPC) is a large class of estimators that include, among others, least squares (LS), ridge and generalized ridge, principal components, fractional rank, and Stein estimators (see Hocking, et. al 1976). The object of this paper is to analyze the influence of single observations and propose diagnostics for this class of estimators. Approximate deletion formulas are obtained and their agreement with the "true" influence analyzed. These diagnostics are illustrated using two examples.

ISSN:0361-0918    

DOI:10.1080/03610919008812898

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we consider five well known and widely used ridge estimators when the convenient assumption of normality of the disturbances is abandoned and report on a Monte Carlo study of their small sample properties. The Monte Carlo experiment is applied to four different data sets with artificially varied degrees of multicollinearity, while the disturbances follow normal, lognormal, uniform and Laplace distributions with small and large variances. The results show that the best estimates are obtained for all ridge estimators when the disturbances follow the lognormal distribution. Also, none of the examined ridge estimators shows a consistent behavior under the different settings considered.

ISSN:0361-0918    

DOI:10.1080/03610919008812899

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We study the performances of the two-stage non-eliminating procedure of Bechhofer, Dunnett and Sobel (1954), the two-stage eliminating procedure of Gupta and Kim (1984) and the multi-stage eliminating procedure of Paulson (1964) as modified by Hartmann (1990) for selecting the normal population which has the largest mean when the common variance is unknown. Constants to implement the procedures are provided. All of these procedures are open and guarantee the indifference-zone probability require-ment of Bechhofer (1954). The following performance characteristics are estimated by Monte Carlo sampling: the achieved probability of a correct selection, the expected number of vector-observations and the expected total number of observations to termination of experimentation. The critical role of the common initial sample size per population is discussed. Guidance is provided as to which procedure to use in different environments.

ISSN:0361-0918    

DOI:10.1080/03610919008812901

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Anderson and Darling introduced the statistic W2n for use in testing the hypothesis that a random sample of size n came from a population with a specified continuous distribution function. Lewis provided a table of values of the cumulative distribution of W2n for small sample sizes. A more accurate and slightly enlarged reconstruction of this table, useful to applied statisticians, is provided.

ISSN:0361-0918    

DOI:10.1080/03610919008812902

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

A compact table, yielding attribute double sampling plan indexed by AQL, AOQL and LQL and double sampling scheme indexed by AQL is presented. Method of selecting the plans are indicated through examples.

ISSN:0361-0918    

DOI:10.1080/03610919008812903

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

For two given estimators of a parameter vector the covariance structure of their difference is used to compare them in terms of their mean square error matrices. The results obtained are applied to the covariance adjustment technique and regression

ISSN:0361-0918    

DOI:10.1080/03610919008812904

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Linear controls are a well known simple technique for achieving variance reduction in computer simulation. Unfortunately the effectiveness of a linear control depends upon the correlation between the statistic of interest and the control, which is often low. Since statistics often have a nonlinear relation-ship with the potential control variables, nonlinear controls offer a means for improvement over linear controls. This paper focuses on the use of nonlinear controls for reducing the variance of quantile estimates in simulation. It is shown that one can substantially reduce the analytic effort required to develop a nonlinear control from a quantile estimator by using a strictly monotone transformation to create the nonlinear control. It is also shown that as one increases the sample size for the quantile estimator, the asymptotic multivariate normal distribution of the quantile of interest and the control reduces the effectiveness of the nonlinear control to that of the linear control. However, the data has to be sectioned to obtain an estimate of the variance of the controlled quantile estimate. Graphical methods are suggested for selecting the section size that maximizes the effectiveness of the nonlinear control

ISSN:0361-0918    

DOI:10.1080/03610919008812905

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The power law process, a nonhomogeneous Poisson process with intensity function µ(t) = (β/θ)(t/θ) , is frequently used to model the occurence of events in time. Often, an important quantity is the value of the intensity function at the current time, that is, the time when data collection is ceased. In this article, the problem of estimating this quantity is addressed when the data are time truncated, that is, when data collection is stopped at a predetermined time T. The class of multiples of the conditional MLE is suggested, and some members are analyzed. In addition, the class of estimators formed by first performing a preliminary test of significance on the parameter β is analyzed. Expressions for the bias and MSE of these estimators are derived and evaluated for several values of the parameters

ISSN:0361-0918    

DOI:10.1080/03610919008812906

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor