摘要:

Methods for fitting continuous spatial autoregressive moving average (ARMA) models to unequally spaced observations in two dimensions are reviewed and extended. These are models with rational two-dimensional spectra. Assuming Gaussian input noise and observational errors, maximum likelihood methods are used to estimate the ARMA parameters and the regression coefficients of the deterministic trend. When the number of observations is too large for exact maximum likelihood estimation, approximate maximum likelihood estimation is used based on nearest neighbors. Comparisons of nearest-neighbor methods with exact likelihood methods are presented. Predictions of the height of the field at unobserved points can be calculated with confidence intervals.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476362

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We consider in this article a class of nonlinear additive autoregressive models with exogenous variables for nonlinear time series analysis and propose two modeling procedures for building such models. The procedures proposed use two backfitting techniques (the ACE and BRUTO algorithms) to identify the nonlinear functions involved and use the methods of best subset regression and variable selection in regression analysis to determine the final model. Simulated and real examples are used to illustrate the analysis.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476363

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476364

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Multiple event timedata (e.g., carcinogenic growths in different times and locations, multiple attacks of cardiac arrest) arise in various medical studies. A Bayesian analysis of such data based onproportional intensity modelof multiple event time data is presented in this paper. The Bayesian structure is somewhat analogous to that used by Kalbfleisch in a proportional hazard model. An unobserved randomfrailtycomponent is used in the proportional intensity model to take care of heterogeneity among the intensity processes in different subjects. The Monte Carlo method of sampling from multivariate distributions, the so-called Gibbs sampler, is used to sample from the joint posterior distribution of the unknown parameters. The methodology developed here is exemplified with the well-known data set on rat tumors of Gail, Santner, and Brown.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476365

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

One approach to inference for means or linear regression parameters when the outcome is subject to nonignorable nonresponse is mixture modeling. Mixture models assume separate parameters for respondents and nonrespondents; implementation by multiple imputation consists of repeatedly filling in missing values for nonrespondents, estimating parameters using the filled-in data, and then adjusting for variability between imputations. We evaluated the performance of this scheme using simulated data with a 25% sample of nonrespondents followed up. We conclude that it provides a generally satisfactory and robust approach to inference for means and regression parameters in this case, although a greater number of imputations may be required for good performance compared to the number required for estimation when nonresponse is ignorable.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476366

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Many finite populations which are sampled repeatedly change slowly over time. Then estimation of finite population characteristics for the current occasion,l, may be improved by the use of data from previous surveys. In this article we investigate the use of empirical Bayes procedures based on two superpopulation models. Each model has the same first stage: The values of the population units on theith occasion are a random sample from the normal distribution with meanμiand varianceσ2i. At the second stage we assume that either (a)μ1, …,μlare a random sample from the normal distribution with meanθand varianceδ2, or (b) givenσ2iandτ,μihas the normal distribution with meanθand varianceσ2iτ(independently for eachi), whereas theσ2iare a random sample from the inverse gamma distribution with parametersη/2 andκ/2. In (a) theσ2i,θ, andσ2are assumed to be unknown, whereas in (b)θ, τ, andκare unknown. We develop empirical Bayes point estimators and confidence intervals for the finite population mean on thelth occasion and make large-sample comparisons with the corresponding Bayes estimators and intervals. These are asymptotic results obtained within the framework of “classical” empirical Bayes theory. To complement the asymptotic results we present the results of an extensive numerical investigation of the properties of these estimators and intervals when sample sizes are moderate. The methodology described here is also appropriate for “small area” estimation.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476367

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Post-stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates. The basic technique divides the sample into post-strata, and computes a post-stratification weightwih=rPh/rhfor each sample case in post-stratumh, whererhis the number of survey respondents in post-stratumh,Phis the population proportion from a census, andris the respondent sample size. Survey estimates, such as functions of means and totals, then weight cases bywh. Variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions. Literature on post-stratification is limited and has mainly taken the randomization (or design-based) perspective, where inference is based on the sampling distribution with population values held fixed. This article develops Bayesian model-based theory for the method. A basic normal post-stratification model is introduced which yields the post-stratified mean as the posterior mean, and a posterior variance that incorporates adjustments for estimating variances. Modifications are then proposed for small sample inference, based on (a) changing the Jeffreys prior for the post-stratum parameters to borrow strength across post-strata, and (b) ignoring partial information about the post-strata. In particular, practical rules for collapsing post-strata to reduce posterior variance are developed and compared with frequentist approaches. Methods for two post-stratifying variables are also considered. Raking sample counts and respondent counts is shown to provide approximate Bayesian inferences when the margins of the two post-stratifiers are available but their joint distribution is not. When the joint distribution is available, raking effectively ignores the information it contains, and hence can be compared with other techniques that ignore information such as collapsing. For inference about means, it is suggested that raking is most appropriate when post-stratum means have an additive or near-additive structure, whereas collapsing is indicated when interactions are present.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476368

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We propose the namegeneralized rakingfor the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table. Our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1/πk, whereπkis the inclusion probability of elementk. New weights are derived by minimizing the total distance between original weights and new weights. The article makes contributions in three areas: (1) statistical inference conditionally on estimated cell counts, (2) simple calculation of variance estimates for the generalized raking estimators, and (3) presentation of the new computer software CALMAR. Our conditional approach highlights the role played by interaction between the factors that define the frequency table. Absence of interaction implies that generalized raking is as efficient as complete post-stratification. The variance estimates we propose are calculated with the aid of the residuals from the fit of an additive analysis of variance (ANOVA) model. The CALMAR software, recently developed at I.N.S.E.E., is now used in various national surveys for calculating generalized raking weights. We illustrate its use with the aid of data from the 1990 survey of living conditions in France. In this application a table in seven dimensions with known marginal counts is used for generalized raking.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476369

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Finney proposed the use of a fiducial interval for the median response dose based on Fieller's theorem. An alternative is to use the asymptotic confidence interval. The simulations by Abdelbasit and Plackett suggest that the two intervals have similar coverage probabilities. We compare the two intervals theoretically and in an expanded simulation study. Our results show that Fieller intervals are generally superior. An attempt is made to characterize how and when the two intervals differ.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476370

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The problem of evaluating tail probabilities for linear combinations of independent, possibly nonidentically distributed, bounded random variables arises in various statistical contexts, mainly connected with nonparametric inference. A remarkable inequality on such tail probabilities has been established by Eaton. The significance of Eaton's inequality is substantiated by a recent result of Pinelis showing that the minimumBEPof Eaton's boundBEand a traditional Chebyshev bound yields an inequality that is optimal within a fairly general class of bounds. Eaton's bound, however, is not directly operational, because it is not explicit; apparently, it never has been studied numerically, and its many potential statistical applications have not yet been considered. A simpler inequality recently proposed by Edelman for linear combinations of iid Bernoulli variables is also considered, but it appears considerably less tight than Eaton's original bound. This article has three main objectives. First, we put Eaton's exact boundBEinto numerically tractable form and tabulate it, along withBEP, which makes them readily applicable; the resulting conservative critical values are provided for standard significance levels. Second, we show how further improvement can be obtained over the Eaton-Pinelis boundBEPif the numbernof independent variables in the linear combination under study is taken into account. The resulting improved Eaton boundsB*EPand the corresponding conservative critical values are also tabulated for standard significance levels and most empirically relevant values ofn. Finally, various statistical applications are discussed: permutationttests against location shifts, permutationttests against regression or trend, permutation tests against serial correlation, and linear signed rank tests against various alternatives, all in the presence of possibly nonidentically distributed (e.g., heteroscedastic) data. For permutationttests and linear signed rank tests, the improved Eaton bounds are compared numerically with other available bounds. The results indicate that the sharpened Eaton bounds often yield sizable improvements over all other bounds considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476371

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor