摘要:

SummaryConsider a discrete time Markov chainX(n) denned on {0,1,…} and let P be the transition probability matrix governingX(n).This paper shows that, if a transformed matrix of P is totally positive of order 2, thenpoj(n) andpio(n) are unimodal with respect to n, wherepij(n) = Pr[X(n) = j |X(0) = i]. Furthermore, the modes ofpoj(n) andpio(n) are non‐increasing injand I, respectively, when additionally P itself is totally positive of order 2. These results are transferred to a class of semi‐Markov processes via a uniformiz

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00994.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryMethods of detecting influential observations for the normal model for censored data are proposed. These methods include one‐step deletion methods, deletion of observations and the empirical influence function. Emphasis is placed on assessing the impact that a single observation has on the estimation of coefficients of the model. Functions of the coefficients such as the median lifetime are also considered. Results are compared when applied to two sets of dat

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00995.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryLehmann&Stein (1948) proved the existence of non‐similar tests which can be more powerful than best similar tests. They used Student's problem of testing for a non‐zero mean given a random sample from the normal distribution with unknown variance as an example. This raises the question: should we use a non‐similar test instead of Student'sttest? Questions like this can be answered by comparing the power of the test with the power envelope. This paper discusses the difficulties involved in computing power envelopes. It reports an empirical comparison of the power of thettest and the power envelope and finds that the two are almost identical especially for sample sizes greater than 20. These findings suggest that, as well as being uniformly most powerful (UMP) within the class of similar tests, Student'sttest is approximately UMP within the class of all tests. For practical purposes it might also be regarded as UMP when moderate or large sample sizes are inv

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00996.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryA framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so‐called mixed model, with both fixed and random effect

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00997.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryA class of distribution‐free tests based on U‐statistics has been proposed for testing the null hypothesis of independence against positive quadrant dependence. The tests are based on U‐statistics and the Kendall's‐tau test belongs to thi

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00998.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryThe problem of testing for treatment effect based on binary response data is considered, assuming that the sample size for each experimental unit and treatment combination is random. It is assumed that the sample size follows a distribution that belongs to a parametric family. The uniformly most powerful unbiased tests, which are equivalent to the likelihood ratio tests, are obtained when the probability of the sample size being zero is positive. For the situation where the sample sizes are always positive, the likelihood ratio tests are derived. These test procedures, which are unconditional on the random sample sizes, are useful even when the random sample sizes are not observed. Some examples are presented as illustration.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb00999.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryA Monte Carlo study of the size and power of tests of equality of two covariance matrices is carried out. Tests based upon normality assumptions, elliptical distribution assumptions as well as distribution‐free tests are compared. Samples are generated from normal, elliptical and non‐elliptical populations. The elliptical‐theory tests, in particular, have poor size properties for both elliptical distributions with moderate sample sizes and for non‐elliptical distri

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01000.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryThis paper considers the problem of testing for nonzero values of the equicorrelation coefficient of a standard symmetric multivariate normal distribution. Recently, SenGupta (1987) proposed a locally best test. We construct a beta‐optimal test and present selected one and five percent critical values. An empirical power comparison of SenGupta's test with two versions of the beta‐optimal test and the power envelope shows the relative strengths of the three tests. It also allows us to assess and confirm Efron's (1975) rule of when to question the use of a locally best test, at least for this testing problem. On the basis of these results, we argue that the two beta‐optimal tests can be considered as approximately uniformly most powerful tests, at least at the five percent significance

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01001.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryThe hat matrix is widely used as a diagnostic tool in linear regression because it contains the leverages which the independent variables exert on the fitted values. In some experiments, cases with high leverage may be avoided by judicious choice of design for the independent variables. A variety of methods for constructing equileverage designs for linear regression are discussed. Such designs remove one of the factors, namely large leverage points, which can lead to nonrobust estimators and tests. In addition, a method is given for combining equileverage designs to test for lack of fit of the linear model.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01002.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01003.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY