ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01320.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryConsideration of multivariate statistical procedures leads to description of robust methods of estimation of location and scale for real random variables. This paper outlines asymptotic theory for estimating location and scale by viewing it as a trimmed likelihood estimator. An appeal is made to results from empirical processes linking the proofs to compact differentiability of estimating functionals. The estimator for location does not depend on the scale estimate and is robust against asymmetric contamination. Coincidentally the location estimator denned at the normal distribution is similar to the least trimmed squares estimator. Simulations corroborate the asymptotic theory and illustrate robustness against asymmetric contamination.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01321.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryAmemiya's estimator is a weighted least squares estimator of the regression coefficients in a linear model with heteroscedastic errors. It is attractive because the heteroscedasticity is not parametrized and the weights (which depend on the error covariance matrix) are estimated nonparametrically. This paper derives an asymptotic expansion for Amemiya's form of the weighted least squares estimator, and uses it to discuss the effects of estimating the weights, of the number of iterations, and of the choice of the initial estimate. The paper also discusses the special case of normally distributed errors and clarifies the particular consequences of assuming normality.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01322.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryThis paper considers the estimation of the ratio of two scale parameters when the data are censored. It emphasises characteristics of the asymptotic variance under censoring from a practical point of view. The estimator proposed by Padgett&Wei (1982) for the two‐sample scale model is extended to the competing risks model. Asymptotic properties of the estimator are studied via its influence function. The use of influence functions permits a unified treatment of both models. Examples show and illustrate that under both models the variance can become infinite under some circumstance

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01323.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryLet π1and π2be two exponential populations with location parameters α and β respectively. It is shown that the probability of misclassification for the optimal rule,RE, depends on α and β only through their ratio α/β=r, and that the smaller the ratior(i.e. the smaller α is compared to β), the greater the superiority of the optimal ruleREover the commonly used ruleRN.When α and β are unknown, the sample‐based versionRE(s) ofREexhibits the same pattern of superiority over the sample‐

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01324.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryThis article considers optimal prediction of the finite population distribution function under Gaussian superpopulation models, which allows auxiliary prior information to be incorporated into the estimation process. Large sample approximations for the variance of the optimal predictors are derived in some special important cases. A small scale Monte Carlo study illustrates comparisons between the optimal predictor and some others which are proposed in the literature. The conclusion is that the optimal predictor can be considerably more efficient in situations where the normal superpopulation model is adequate.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01325.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryWe consider the problem of finding an equi‐tailed confidence interval, with coverage probability (1‐α), for a scalar parameter θ0in the presence of a (possibly infinite dimensional) nuisance parameter ψ0. It is supposed that the value taken by θ0does not restrict the value that ψ0may take and vice‐versa. Given a sensible estimate ψnof ψ0, profile bootstrap confidence interval for θ0is defined to be the exact equi‐tailed confidence interval with coverage probability (1‐α) assuming that ψ0=ψn. We compare the properties of the profile bootstrap confidence interval and the ordinary bootstrap confidence interval when they are based on studentised and unstudentised quantities. Under mild regularity conditions the profile bootstrap confidence interval is always a subset of the set of allowable values of θ0and is transformation‐respecting when based on either an unstudentised quantity or a studentised quantity satisfying certain restrictions. As a confidence interval for the autoregressive parameter of an AR(1) process, the profile bootstrap confidence interval has important advantages over the ordinary bootstrap confidence interval based on

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01326.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryGōtze&Kūnsch (1990) announced that a certain version of the bootstrap percentile‐tmethod, and the blocking method, can be used to improve on the normal approximation to the distribution of a Studentized statistic computed from dependent data. This paper shows that this result depends fundamentally on the method of Studentization. Indeed, if the percentile‐tmethod is implemented naively, for dependent data, then it does not improve by an order of magnitude on the much simpler normal approximation despite all the computational effort that is required to implement it. On the other hand, if the variance estimator used for the percentile‐tbootstrap is adjusted appropriately, then percentile‐tcan improve substantially on the normal appr

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01327.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryLetX1,…,Xnbe mutually independent non‐negative integer‐valued random variables with probability mass functionsfi(x)>0 forz= 0,1,…. LetEdenote the event that {X1≥X2≥…≥Xn}. This note shows that, conditional on the eventE, Xi‐Xi+ 1 andXi+ 1 are independent for all t = 1,…,kif and only ifXi(i= 1,…,k) are geometric random variables, where 1 ≤k≤n‐1. Thekgeometric distributions can have diffe

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01328.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

SummaryUpper bounds axe derived for the efficiency factor of a class of resolvable incomplete block designs known as latinized designs. These designs are particularly useful in glasshouse and field trials, and can be readily extended to two‐dimensional blocking structures. Existing bounds for resolvable designs axe also reviewed and a comparison is made between the third moment bounds discussed by Jarrett (1989) and the second moment bounds of Tjur (1990

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1993.tb01329.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY