摘要:

In August of 1988 when Bob Hogg was President of the ASA he invited me as a vice-president elect to attended my first meeting of the ASA Board of Directors. I have thus been part of the ASA Board's activities for five full years. It has been a period of many changes for the Association: the new constitution, the newly structured Board, many new Sections, several new publications, a membership campaign, the assorted activities of the ASA Center for Statistical Education, and most recently the modification in the ASA dues structure with its “cafeteria plan” allowing members to select their publications. These many changes are indications that the entire statistics profession, represented at this meeting by the ASA, the IMS, and the Biometric Society, is being challenged not only to meet the needs of its membership but also those of society at large. These are exciting times, much like sailing when the wind comes up. And I still have a year and a half ahead on the ASA Board of Directors. I must remember to ask my favorite actuary Bob Hogg what my chances are of surviving.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476440

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In many epidemiologic studies of human immunodeficiency virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. Two such problems are considered here, estimation of the distribution of time or number of sexual contacts between infection of an individual (an index case) and transmission of HIV to their sexual partner, and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody. Data regarding these two problems are available from certain partner studies, and the HIV Lookback Study. In both cases the statistical development is complicated by the fact that the times of both events are interval censored, so that the length of time between the events is never observed exactly. Nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution; particular attention is paid to identifiability issues.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476441

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Cells grown in culture can be tracked for several generations and measurements taken on size or age at division and other cell characteristics. The observations for the offspring of each cell form a family tree of dependent data. Such cell lineage data are here modeled as repeated measurements on different family trees arising from individual ancestor cells selected at random from a population of cultured cells. The bifurcating autoregression model is embedded in a process that allows for measurement error and variation from tree to tree. Robust methods are presented that accommodate outliers in this time-dependent and branching environment while allowing the statistician to interactively build a variance components model for the process. The methodology is illustrated on a substantial data set of 41 trees of EMT6 cells, with the surprising conclusion that after removing measurement error, sister-cell lifetimes are nearly identical.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476442

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The National Stream Survey (NSS) and Environmental Monitoring and Assessment Program (EMAP) use variable probability, systematic sampling, and the Horvitz-Thompson estimator to estimate population parameters of ecological interest. A common strategy of variance estimation for systematic sampling is to assume that the population order had been randomized prior to sampling and to estimate variance under this randomized population model. The Yates-Grundy variance estimator is generally recommended for estimating the variance of the Horvitz-Thompson estimator under this model. But design features of NSS and EMAP preclude application of the Yates-Grundy estimator, so use of the Horvitz-Thompson variance estimator is required. Further, because the first-order inclusion probabilities are known only for the sample units and not the entire population, neither the actual pairwise inclusion probabilities (πuv's) nor the Hartley-Rao approximation of the πuv's can be computed. Thus the variance estimator proposed for use in these surveys was the Horvitz-Thompson variance estimator computed with a new approximation to the πuv's. Having to use this estimator, denotedvoHT, motivated exploration of the general question of when behaviors of the Horvitz-Thompson and Yates-Grundy variance estimators differ and also investigation of the specific performance of the estimatorvoHT.To permit comparison of variance estimators, we restricted attention to fixed sample size, variable probability systematic sampling, from a randomly sorted list. Properties ofvoHTwere compared to those of three other variance estimators; the Yates-Grundy estimator calculated with both the new πuvapproximation and the Hartley-Rao approximation, and the Horvitz-Thompson variance estimator calculated with the Hartley-Rao approximation. An empirical study, designed to permit generalization beyond a few special case populations, demonstrated that superiority of the Yates-Grundy variance estimator was restricted to populations having both high correlation between the response variable,y, and the selection variable,x, and approximately equal coefficients of variation for thexandypopulations. With the exception of these populations,voHTperformed nearly the same as the Yates-Grundy estimators studied and performed better than the Horvitz-Thompson variance estimator computed with the Hartley-Rao approximation. In NSS and EMAP most response variables are not expected to be highly correlated with the selection variable, sovoHTshould furnish an adequate variance approximation when the randomized population model holds.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476443

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

When categorical outcomes are subject to nonignorable nonresponse, log-linear models may be used to adjust for the nonresponse. The models are fitted to the data in an augmented frequency table in which one index corresponds to whether or not the subject is a respondent. The likelihood function is maximized over pseudo-observed cell frequencies with respect to this log-linear model using an EM algorithm. EachEstep of the EM algorithm determines the pseudo-observed cell frequencies, and theMstep yields the maximum likelihood estimators (MLE's) of these pseudo-observed cell frequencies. This approach may produce boundary estimates for the expected cell frequencies of the nonrespondents. In these cases the estimators of the log-linear model parameters are not uniquely determined and may be unstable. Following the approach of Clogg et al., we propose a Bayesian method that uses smoothing constants to adjust the pseudo-observed cell frequencies so that the solution is not on the boundary. The role of smoothing constants is similar to that of the flattening constantkin ridge regression; the use ofkis intended to overcome ill-conditioned situations where correlations between the various predictors in the regression model produce unstable parameter estimates. The Bayesian estimation procedure is illustrated using data from a cross-sectional study of obesity in school-age children. Through a simulation study, we show that when fitting nonignorable nonresponse models, the mean squared errors of the expected cell frequencies obtained by the Bayesian procedure can be much smaller than those of the MLE's.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476444

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We develop a nonlinear generalization of principal components analysis. A principal surface of the data is constructed adaptively, using some ideas from the MARS procedure of Friedman. We explore applications to curve and surface reconstruction and to data summarization.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476445

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy-tailed error distribution. The two standard approaches to such a problem are each flawed. Robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form, whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods, which are not resistant against outliers. Existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares. Neither of these two approaches combines computational ease with asymptotic theoretical results. Furthermore, application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable. In this article a new hybrid method is proposed that combines nonparametric regression with theL1norm. Applying theL1norm on the regression residuals leads naturally to a robust estimator in any dimension. Unlike diagnostic and influence approaches, theL1metric can handle many outliers, whether isolated or clumped, without any requirement to estimate the scale of the residuals. DespiteL1's reputation for being computationally intractable, fitting a polynomial by the least absolute deviations criterion is equivalent to solving a linear program with special structure. By using theL1norm over local neighborhoods, a method that is also nonparametric is constructed. Additionally, the new method generalizes easily to several dimensions. To date, the problem of robust smoothing directly in several dimensions has met with little success, without resorting to robust additive models. A proof of consistency for theL1algorithm is presented, and results from both real and simulated data are shown.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476446

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article presents a two-stage estimation procedure that uses an ad hoc but very easily implemented isotonization of a kernel estimator. This procedure yields an isotonic estimator with the convergence properties of the kernel estimator. Although the isotonization in the second stage does not satisfy the least squares condition, this hybrid estimator may be considered to be a multidimensional generalization of similar procedures for the one-dimensional case suggested by Friedman and Tibshirani and by Mukarjee. We derive some of the asymptotic properties of our estimator and demonstrate other statistical properties with Monte Carlo studies. We conclude by providing a real data example.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476447

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article considers a distribution-free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology. Without parametric modeling of the missing mechanism or the joint distribution, kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern. A generalization of the method of Cheng and Wei is verified under the assumption of missing at random. Asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study. The nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study. The comparison shows that the proposed nonparametric estimators attain reliable performances in general.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476448

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In this article we consider regression models for two-dimensional spatial data when the errors follow a spatial unilateral first-order autoregressive moving average (ARMA) model studied by Basu and Reinsel. We give details on the convenient computation of the generalized least squares (GLS) estimator of the regression parameters in the presence of spatially correlated errors, and compare the GLS estimator to the ordinary least squares (OLS) estimator in some special cases. We also consider the restricted maximum likelihood estimators of the spatial correlation model parameters, which may be preferred over the maximum likelihood estimators. For the special case of the spatial unilateral first-order AR model, details of the maximum likelihood as well as the restricted maximum likelihood estimation are given. A numerical example is presented to illustrate the methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476449

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor