摘要:

Abstract The relative compactness and weak convergence of reduced empirical, quantile and weighted empirical processes are demonstrated under mild conditions. For example, the reduced empirical proces of arbitrary independent iv'S is always relatively compact in any ‖/q‖ metric withqsquare integrable; and weak convergence takes place if and only if the covariance function converges. VanZuijlen'srepresentation of the general empirical process is a fundamental tool. This paper both unifies and extends the previous treatment of these processes ‐ processes that have application to rank statistics and linear combinations of order statistics. Most proofs are contained in Section 3. A brief introduction to weak convergence is presented in the appendix for readers lacking this background. Applications are indicated in Se

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00673.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

Abstract The performance of the sample mean and sample median to estimate location for contaminated normal distributions is investigated. Both scale and location contaminations are considered and the problem is illustrated by the “Weight Judging Competition” example introduced by Galtonin

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00674.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

Abstract The “classical” development of conditioning, due to Kolmogorov, does not agree with the “practical” (more intuitive, but unrigorous) way in which probabilists and statisticians actually think about conditioning. This paper describes an alternative to the classical development. It is shown that standard concepts and results can be developed, rigorously, along lines, which correspond to the “practical” approach, and so as to include the classical material as a special case. More specifically, let XandYbe random variables (r.v.‘s) from (Ω, f, P) to (x, fx) and (y. fy.), respectively. In this paper, the fundamental concept is the conditional probabilityP(AX = x), a function of xε x which satisfies a “natural” defining condition. This is used to define a conditional distribution Py/x, as a mapping x × fy‐R such that, as a function ofB, Pylx=x,(B) is a probability measure on fy. Then, for a numerical r.v.Y, conditional expectation E(Y/X) is defined as a mapping x →r̄ whose value atx isE(Y/X = x) = ydPY/x=i(y). Basic properties of conditional probabilities, distributions, and expectations, are derived and their existence and uniqueness are discussed. Finally, for a sub‐o‐algebra and a numerical r.v.Y, the classical conditional expectation E(Y) is obtained as E(Y/X) withX = i, the iden

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00675.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

Summary Best[1] found the variance of the minimum variance unbiased estimator of the parameterpof the negative binomial distribution. Mikulskiand Sm [2] gave an upper bound to it, easier to calculate than Best'sexpression and a good approximation for small values ofpand large values ofr(the number of successes). In this paper both lower bounds and closer upper bounds are derive

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00676.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

In this section, Statistica Neerlandica reports recent doctorates in statistics, biometrics, econometrics and operations research, conferred by Dutch universities. The main purpose of these reports is to inform the reader briefly of the nature, the practical and theoretical importance, the methods and the results of recent theses.Most Dutch theses are available for distribution; readers who are interested in obtaining a copy should contact the author.Ph.D. thesis supervisors are invited to submit contributions to this section to G. DE LEVE, Instituut voor Actuariaat en Econometric, 23 Jodenbreestraat, 101 1 NH Amsterdam.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00677.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1979.tb00678.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY