摘要:

AbstractTechniques developed for the study of time series, point processes, and marked point processes can suggest corresponding techniques for each other, and common techniques can be recognized. In this paper connections are drawn based on conceptual foundations, basic parameters, analyses, displays, algorithms, problems, models. The definitions and techniques are brought out by specific scientific problems. The emphasis is on the single‐realization stationary case and on the use of second‐ and third‐order moments to help understand the realization. The tool of stacking, at a particular period, is employed in several of the exa

ISSN:0319-5724    

DOI:10.2307/3315583

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper discusses five methods for constructing approximate confidence intervals for the binomial parameter Θ, based on Y successes in n Bernoulli trials. In a recent paper, Chen (1990) discusses various approximate methods and suggests a new method based on a Bayes argument, which we call method I here. Methods II and III are based on the normal approximation without and with continuity correction. Method IV uses the Poisson approximation of the binomial distribution and then exploits the fact that the exact confidence limits for the parameter of the Poisson distribution can be found through the x2distribution. The confidence limits of method IV are then provided by the Wilson‐Hilferty approximation of the x2. Similarly, the exact confidence limits for the binomial parameter can be expressed through the F distribution. Method V approximates these limits through a suitable version of the Wilson‐Hilferty approximation. We undertake a comparison of the five methods in respect to coverage probability and expected length. The results indicate that method V has an advantage over Chen's Bayes method as well as over the other three met

ISSN:0319-5724    

DOI:10.2307/3315584

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractWe consider the problem of robust M‐estimation of a vector of regression parameters, when the errors are dependent. We assume a weakly stationary, but otherwise quite general dependence structure. Our model allows for the representation of the correlations of any time series of finite length.We first construct initial estimates of the regression, scale, and autocorrelation parameters. The initial autocorrelation estimates are used to transform the model to one of approximate independence. In this transformed model, final one‐step M‐estimates are calculated.Under appropriate assumptions, the regression estimates so obtained are asymptotically normal, with a variance‐covariance structure identical to that in the case in which the autocorrelations are known a priori. The results of a simulation study are given. Two versions of our estimator are compared with the L1‐estimator and several Huber‐type M‐estimators. In terms of bias and mean squared error, the estimators are generally very close. In terms of the coverage probabilities of confidence intervals, our estimators appear to be quite superior to both the L1‐estimator and the other estimators. The simulations also indicate that the approach to normalit

ISSN:0319-5724    

DOI:10.2307/3315585

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractWe introduce and study a class of rank‐based estimators for the linear model. The estimate may be roughly described as being calculated in the same manner as a generalized M‐estimate, but with the residual being replaced by a function of its signed rank. The influence function can thus be bounded, both as a function of the residual and as a function of the carriers. Subject to such a bound, the efficiency at a particular model distribution can be optimized by appropriate choices of rank scores and carrier weights. Such choices are given, with respect to a variety of optimality criteria. We compare our estimates with several others, in a Monte Carlo study and on a real data set from the literat

ISSN:0319-5724    

DOI:10.2307/3315586

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractStatistical problems in modelling personal‐income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum‐likelihood and least‐squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation pro

ISSN:0319-5724    

DOI:10.2307/3315587

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractLet μ be an infinitely divisible positive measure on R. If the measure ρμis such that x‐2[ρμ(dx)—ρμ({0})δ0(dx)] is the Lévy measure associated with μ and is infinitely divisible, we consider for all positive reals α and β the measure Tα,β(μ) which is the convolution of μ*αand ρμ*β. For example, if μ is the inverse Gaussian law, then ρμis a gamma law with paramter 3/2. Then Tα,β(μ) is an extension of the Lindsay transform of the first order, restricted to the distributions which are infinitely divisible. The main aim of this paper is to point out that it is possible to apply this transformation to all natural exponential families (NEF) with strictly cubic variance functions P. We then obtain NEF with variance functions of the form □ΔP(□Δ), where A is an affine function of the mean of the NEF. Some of these latter types

ISSN:0319-5724    

DOI:10.2307/3315588

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second‐order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized varianc

ISSN:0319-5724    

DOI:10.2307/3315589

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove that the profile log‐likelihood function for the removal method of estimating population size is unimodal. The result is obtained by a variation‐diminishing property of the Laplace transform. An implication of this result is that the likelihood‐ratio confidence region for the population size is always an interval. Necessary and sufficient conditions for the existence of a finite maximum‐likelihood estimator are presented. We also present evidence that the likelihood‐ratio confidence interval for the population size has acceptable small‐sample coverage

ISSN:0319-5724    

DOI:10.2307/3315590

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY

摘要:

AbstractThe standard Parzen‐Rosenblatt kernel density estimator is known to systematically deviate from the true value near critical points of the density curve. To overcome this difficulty, we extend the Rao‐Blackwell method by using locally sufficient statistics: we define a new estimator and study its asymptotic behaviour. The interest of the method is shown by means of simulati

ISSN:0319-5724    

DOI:10.2307/3315591

出版商:Wiley‐Blackwell    

年代:1994

数据来源: WILEY