摘要:

AbstractAn example of the classical occupancy problem is to sample with replacement from an urn containing several colours of balls and count the number of balls sampled until a given number of “quotas” are filled. This and the corresponding random variable for sampling without replacement will be referred to as quota fulfillment times. Asymptotic and exact methods for computing moments and distributions are given in this paper. Moments of quota fulfillment times are related to moments of order statistics of beta and gamma random variables. Most of the results for sampling without replacement and some of the results for sampling with replacement are believed to be new. Some other known sampling‐with‐replacement results are given for comparative p

ISSN:0319-5724    

DOI:10.2307/3314900

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractA wider‐tailed family of distributions is suggested as an alternative to the normal distribution having many of the desirable properties of the normal family. One advantage of this alternative is the greater robustness of maximum‐likelihood estima

ISSN:0319-5724    

DOI:10.2307/3314901

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractLet X1, …,Xn, and Y1, … Ynbe consecutive samples from a distribution function F which itself is randomly chosen according to the Ferguson (1973) Dirichlet‐process prior distribution on the space of distribution functions. Typically, prediction intervals employ the observations X1,…, Xnin the first sample in order to predict a specified function of the future sample Y1, …, Yn. Here one‐ and two‐sided prediction intervals for at least q of N future observations are developed for the situation in which, in addition to the previous sample, there is prior information available. The information is specified via the parameter α of the Dirichlet process prio

ISSN:0319-5724    

DOI:10.2307/3314902

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractConsider a linear function of order statistics (“L‐estimate”) which can be expressed as a statistical function T(Fn) based on the sample cumulative distribution function Fn. Let T*(Fn) be the corresponding jackknifed version of T(Fn), and let V2nbe the jackknife estimate of the asymptotic variance of n1/2T(Fn) or n1/2T*(Fn). In this paper, we provide a Berry‐Esséen rate of the normal approximation for a Studentized jackknife L‐estimate n1/2[T*(Fn) ‐ T(F)]/Vn, where T(F) is the basic functional associated with th

ISSN:0319-5724    

DOI:10.2307/3314903

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractThis paper considers the estimation of “structural” parameters when the number of unknown parameters increases with the sample size. Neyman and Scott (1948) had demonstrated that maximum likelihood estimators (MLE) of structural parameters may be inconsistent in this case. Patefield (1977) further observed that the asymptotic covariance matrix of the MLE is not equal to the inverse of the information matrix. In this paper we establish asymptotic properties of estimators (which include in particular the MLE) obtained via the usual likelihood approach when the incidental parameters are first replaced by their estimates (which are allowed to depend on the structural parameters). Conditions for consistency and asymptotic normality together with a proper formula for the asymptotic covariance matrix are given. The results are illustrated and applied to the problem of estimating linear functional relationships, and mild conditions on the incidental parameters for the MLE (or an adjusted MLE) to be consistent and asymptotically normal are obtained. These conditions are weaker than those imposed by previous auth

ISSN:0319-5724    

DOI:10.2307/3314904

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractObservations with correlated error structures are sometimes unavoidable. Appropriate designs and analyses are reviewed for such situations. Serious problems can occur if conventional designs and analyses are used when correlated errors and layout are ignored or when the error structure is not known. Robust designs are discussed which guard against these problems.

ISSN:0319-5724    

DOI:10.2307/3314905

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the problem of allocating a fixed number of trials between two independent binomial populations with unknown success probabilities θ1and θ2, in order to estimate θ1‐ θ2with squared error loss. Introducing independent beta priors on θ1and θ2, a heuristic allocation procedure is introduced and compared both with the optimal and with the best fixed allocation procedure. Numerical and asymptotic results of these comparisons are given and seem to indicate that there are situations when the best fixed allocation procedure performs almost as well as the optimal pr

ISSN:0319-5724    

DOI:10.2307/3314906

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY

摘要:

AbstractIn January 1981 a questionnaire was sent to 102 universities and colleges in Canada and the United States seeking information on enrolment in initial courses in statistics. That questionnaire has been analyzed and the results are presented in this paper.

ISSN:0319-5724    

DOI:10.2307/3314907

出版商:Wiley‐Blackwell    

年代:1982

数据来源: WILEY