ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01401.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

The various stages in the history of statistical computing are illustrated by personal experiences. The stages include batch processing, interactive working, and the consultative mode. Statistical aspects associated with one or more of these stages include the development of general algorithms, procedures for model checking, and data‐driven non‐parametric modell

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01402.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages tosupportinvestigations, by performing calculations, ankl their use toimplement structure;to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other isitovsn3, an implementation of the semimartingale stochastic calculus. It is described howitovsn3may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01403.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

This paper reviews the state of the art in the computation of robust estimates of multivariate location and shape using combinatorial estimators such as the minimum volume ellipsoid (MVE) and iterativeM‐and S‐estimators. We also present new results on the behavior ofM‐and S‐estimators in the presence of different types of outliers, and give the first computational evidence on compound estimators that use the MVE as a starting point for an S‐estimator. Problems with too many data points in too many dimensions cannot be handled by any available technology; however, the methods presented in this paper substantially extend the size of problem that can be successfull

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01404.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

We analyse additive regression model fitting via the backfitting algorithm. We show that in the case of a large class of curve estimators, which includes regressograms, simple step‐by‐step formulae can be given for the back‐fitting algorithm. The result of each cycle of the algorithm may be represented succinctly in terms of a sequence ofdprojections in n‐dimensional space, where d is the number of design coordinates andnis sample size. It follows from our formulae that the limit of the algorithm is simply the projection of the data onto that vector space which is orthogonal to the space of all n‐vectors fixed by each of the projections. The formulae also provide the convergence rate of the algorithm, the variance of the backfitting estimator, consistency of the estimator, and the relationship of the estimator to that obtained by directly minimizing mean squared

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01405.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre‐Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distribution

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01406.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Statistica Neerlandica has decided to encourage the reporting on theses in probability, statistics, biometrics, econometrics, and operations research, submitted to Dutch universities. The main purpose of this section is to inform the reader briefly of the nature, the practical and theoretical importance, the methods used, and the results presented in recent theses. It is understood that contributions to this section meet with the approval of the supervisor(s) of the thesis.Notes (not exceeding 300 words) should be sent to the column editor.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01407.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1993.tb01408.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY