摘要:

In one-parameter exponential families such as the binomial and Poisson, the variance is a function of the mean. Double exponential families allow the introduction of a second parameter that controls variance independently of the mean. Double families are used as constituent distributions in generalized linear regressions, in which both means and variances are allowed to depend on observed covariates. The theory is applied to two examples—a logistic regression and a large two-way contingency table. In such cases the binomial model of variance is often untrustworthy. For example, because genuine random sampling was infeasible, the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes. Clumped sampling is just one of many possible causes ofoverdispersion, a habitual source of concern to users of binomial and Poisson models. This article concerns a class of regression families that allow the statistician to model overdispersion while carrying out the usual regression analyses for the mean as a function of the predictors. Close connections with previous ideas concerning generalized linear models are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478327

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

For many studies in which data are collected sequentially in time, the sensitivity of the measurement is limited and an exact value can be recorded only if it falls within a specified range. This gives rise to a censored time series. In this article, we present a methodology for regression analysis of censored time series data. We fit autoregressive models to account for the time dependence. Two numerical methods for full likelihood estimation and an approximate method are discussed. The methods are illustrated with air pollution data subject to lower limits of detection.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478328

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The criterion of second-order efficiency is used to distinguish among estimators, which have the same asymptotic variance, of the mean of a stationary autoregressive process. The best linear unbiased estimator is typically unknown, since it depends on the parameters of the process. It is demonstrated by second-order efficiency that the sample mean performs poorly under certain conditions, whereas some weighted averages maintain a more consistent performance as the parameters of the underlying process are allowed to vary. Numerical examples are shown for second-and third-order autoregressive processes.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478329

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The problem of decomposing an observed series, assumed to follow an ARIMA process, into signal plus noise is considered. It is well known that the preliminary estimates of the signal will be subject to revisions as more data become available. For a general ARIMA process, the revision in the concurrent estimate of the signal is seen to follow a stationary ARMA process, easily derived from the overall series model. The results are extended to non-concurrent preliminary estimates. Finally, it is found that, except for a scale factor, the revisions are the same for all admissible decompositions and the canonical decomposition maximizes the variance of the revision.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478330

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Practical aspects of a new technique for monitoring and controlling the predictive performance of Bayesian forecasting models are discussed. The basic features of the approach to model monitoring introduced in a general setting in West (1986) are described and extended to a wide class of dynamic, nonnormal, and nonlinear Bayesian forecasting models. An associated method of automatically detecting and rejecting outliers and adapting models to abrupt structural changes in the time series is also discussed. The resulting forecast monitoring and control scheme is simply constructed and applied and is illustrated in two applications.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478331

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

We show how to define and then compute efficiently the marginal likelihood of an ARIMA model with missing observations. The computation is carried out by using the univariate version of the modified Kalman filter introduced by Ansley and Kohn (1985a), which allows a partially diffuse initial state vector. We also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478332

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A method for modeling and fitting multivariate spatial time series data based on current spatial methodology coupled with the parameterization of the ARMAX model is presented. Because of the physical constraints imposed on multivariate data collection in both space and time, the estimation and identification procedures tolerate general patterns of missing or incomplete data.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478333

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The criteria of homogeneity and structure were proposed by Goodman (1981a) for determining whether certain rows or columns of a contingency table should be grouped. A data-based procedure (using the canonical form of bivariate distributions) is presented in this article to guide exploratory analysis to determine which rows or columns of a table may be grouped. This procedure facilitates the application of the homogeneity criterion. Relationships between the proposed method of grouping and the structural criterion are discussed as well as simultaneous inference for grouped tables. The grouping method is extended to multiway tables. The use of canonical forms as a model exploratory tool is addressed. Examples are discussed in detail.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478334

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Canonical analysis has often been employed instead of log-linear models to analyze the relationship of two polytomous random variables; however, until the last few years, analysis has been informal. In this article, models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained. Maximum likelihood is used to obtain parameter estimates for these restricted models. Approximate confidence intervals are derived for parameters, and chi-squared tests are used to check adequacy of models. The resulting models may be used to determine the appropriateness of latent-class analysis or to determine whether a set of canonical scores has specified patterns. Results are illustrated through analysis of two tables previously analyzed in the statistical literature. Comparisons are made with alternate methods of analysis based on a log-linear parameterization of cell probabilities. It is shown that canonical analysis, which uses interpretations based on regression and correlation, is an alternative to log-linear parameterizations interpreted in terms of cross-product ratios.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478335

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic questions. What effects can the sample design have on methods of multivariate analysis? How should such effects be taken into account? This article considers the case of principal component analysis and, in particular, the point estimation of the eigenvalues and eigenvectors of a covariance matrix. It is assumed that the selection of the sample depends on the population values of auxiliary variables as, for example, in stratified sampling. The conventional estimators, based on the assumption of simple random sampling, are compared with alternative probability-weighted and maximum likelihood estimators. Under a multivariate normal model, simple expressions are presented for the approximate model bias of the different estimators. The validity of these results is assessed in a simulation study involving a disproportionate stratified design.

ISSN:0162-1459    

DOI:10.1080/01621459.1986.10478336

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor