摘要:

SummaryIf the asymptotic normality of a statistic is inadequate for approximating its distribution in practice, then the statistic may be transformed in order to improve the approximation by accelerating the convergence to normality. We treat a goodness‐of‐fit statistic, the sum of the logarithms of generalized uniform spacings introduced by Cressie (1976, 1978), in this spirit. Specifically, we apply the method of maximum likelihood to simulations of the statistic in order to estimate a power transformation, as in Box&Cox (1964), and hence develop a small sample normal approximation. This approximation provides a more versatile method of applying the statistic than currently available tables of percenti

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01007.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryWe exploit the fact that the Wilcoxon score R‐estimator of the slope in a linear regression model minimises Gini's mean difference of the residuals to obtain a Berry‐Esseen rate of convergence result for the Wilcoxon R‐esti

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01008.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryWhen presenting research results to a mixed audience, it is common for seminar speakers either to address the specialists or the uninitiated (thus alienating the other, uncatered‐for group of listeners), or to risk falling between these two stools (and so satisfy no one). We suggest a way that the lecturer's dilemma might often be more optimally resolved; and, in so doing, present material which could provide useful ideas for wider application in enlivening formal class‐room instruction in time‐series analysis. Finally, we pre‐empt some of the predicted response that the content of this paper may trigger from certain experts; and discuss the general lack of emphasis on assumptions in statistical t

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01009.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryKlotz's (1973) Markov chain model for dependent Bernoulli trials is applied to magazine exposure distributions. Simple parameter estimates are derived and are shown to compare well with the maximum likelihood estimates. The Markov model is fitted to forty magazines from a large print media survey and compares favourably with the most popular non‐proprietary magazine model, the beta‐binomial model. In addition, the Markov model is used to simulate magazine exposure distributi

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01010.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryWe describe methods for constructing bootstrap hypothesis tests, illustrating our approach using analysis of variance. The importance of pivotalness is discussed. Pivotal statistics usually result in improved accuracy of level. We note that hypothesis tests and confidence intervals call for different methods of resampling, so as to ensure that accurate critical point estimates are obtained in the former case even when data fail to comply with the null hypothesis. Our main points are illustrated by a simulation study and application to three real data sets.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01011.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryThis paper gives a method for decomposing many sequential probability ratio tests into smaller independent components called “modules”. A function of some characteristics of modules can be used to determine the asymptotically most efficient of a set of statistical tests in which a, the probability of type I error equals β, the probability of type II error. The same test is seen also to give the asymptotically most efficient of the corresponding set of tests in which a is not equal to β. The “module” method is used to give an explanation for the super‐efficiency of the play‐the‐winner and play‐the‐loser rules in two‐sample binomial sampling. An example showing how complex cases can be analysed numerically using this

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01012.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryGiven time series data for fixed intervalt= 1,2,…,Mwith non‐autocorrelated innovations, the regression formulae for the best linear unbiased parameter estimates at each timetare given by the Kalman filter fixed interval smoothing equations. Formulae for the variance of such parameter estimates are well documented.However, formulae for covariance between these fixed interval best linear parameter estimates have previously been derived only for lag one. In this paper more general formulae for covariance between fixed interval best linear unbiased estimates at timestandt ‐ lare derived fort= 1,2,…,Mandl= 0,1,…,t‐ 1. Under Gaussian assumptions, these formulae are also those for the corresponding conditional covariances between the fixed interval best linear unbiased parameter estimates given the data to timeM.They have application, for example, in determination via the expectation‐maximisation (EM) algorithm of exact maximum likelihood parameter estimates for ARMA processes expressed in statespace form when multiple observations are available at ea

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01013.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryFor a nonparametric regression modely = m(x)+ewithnindependent observations, we analyze a robust method of finding the root ofm(x)based on anM‐estimation first discussed by Härdle&Gasser (1984). It is shown here that the robustness properties (minimaxity and breakdown function) of such an estimate are quite analogous to those of anM‐estimator in the simple location model, but the rate of convergence is somewhat limited due to the nonparametric nature of the pro

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01014.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryPatterson&Thompson (1971) introduced residual maximum likelihood estimation in the case of unbalanced incomplete block designs. Harville (1974) and Cooper&Thompson (1977) give alternative derivations of the likelihood function. The purpose of this note is to provide another derivation of the likelihood function which may be useful in teaching.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01015.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

SummaryAn upper bound for the efficiency factor of a block design, which in many cases is tighter than those reported by other authors, is derived. The bound is based on a lower bound for E(1/X) in terms of E(X) and var(X) for a random variableXon the unit interval. For the special case of resolvable designs, an improved bound is given which also competes with known bounds for resolvable designs in some cases.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1990.tb01016.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY