摘要:

State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous work on filtering and smoothing for multicategorical time series and longitudinal data, our approach uses posterior mode estimation. Thus we have to maximize posterior densities or, equivalently, a penalized likelihood, which enforces smoothness of hazard functions and time-varying effects by a roughness penalty. Dropping the Bayesian smoothness prior and adopting a nonparametric viewpoint, one might also start directly from maximizing this penalized likelihood. We show how Fisher scoring smoothing iterations can be carried out efficiently by iteratively applying linear Kalman filtering and smoothing to a working model. This algorithm can be combined with an EM-type procedure to estimate unknown smoothing parameters or hyperparameters. The methods are applied to a larger set of unemployment duration data with one terminating event and, in a further analysis, multiple terminating events from the German socioeconomic panel GSOEP.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476726

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this article, under very general assumptions on Bernoulli trials, a simple numerical method based on the finite Markov chain imbedding technique is systematically developed to determine (a) the joint distribution of the number of success runs and the number of successes; (b) the conditional distribution of the number of success runs given the number of successes, that is, the exact distribution of the success runs test statistic; (c) the joint distribution of the length of the longest success run and the number of successes; and (d) the conditional distribution of the length of the longest success run given the number of successes, that is, the exact distribution of the longest success run test statistic. The critical regions and powers of these two tests (success runs and longest success run) are derived under the null hypothesis of independence and identical distribution (iid) as well as under the alternative hypothesis of Markov dependence. The application of the success runs test is illustrated using real datasets from a multicenter risk factor study on asthmatics.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476727

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Existing methods of testing for treatment effects for clustered binary data include the beta-binomial, quasilikelihood GEE procedures. All of these methods revolve around the mean response and the second-order correlation. However, these two parameters alone do not fully determine the effect of treatment. This article develops nonparametric likelihood ratio procedures to test for independence, heterogeneity dose-related trend in dose—response studies involving exchangeable binary data. The hypotheses of independence, heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates. Constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics. Unlike the test statistics for independence and heterogeneity, the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi-square. However, an upper bound of itspvalue is obtained by using a chi-squared distribution. A set of clustered binary data from the Shell Toxicology Laboratory, on the developmental effect of a chemical agent on banded Dutch rabbits, is used to illustrate the various test procedures. The same dataset is used to compare the proposed trend test with some existing trend tests, such as those based on a beta-binomial model, generalized estimating equations survey sampling methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476728

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Interdirection tests are proposed for a simple repeated-measures design. The test statistics proposed are applications of the one-sample interdirection sign test and interdirection signed-rank test to a repeated-measurement setting. The interdirection sign test has a small-sample distribution-free property and includes the two-sided univariate sign test and Blumen's bivariate sign test as special cases. The interdirection signed-rank test includes the two-sided univariate Wilcoxon signed-rank test as a special case. The proposed statistics are shown to have a limitingXp−12null distribution when the underlying distribution is elliptically symmetric. In addition, the asymptotic distributions of the proposed statistics under certain contiguous alternatives are obtained for elliptically symmetric distributions with a particular density function form. Pitman asymptotic relative efficiencies and Monte Carlo studies show the proposed interdirection tests to be robust as compared to several competitors. The sign test performs particularly well when the underlying distribution is heavy tailed or skewed, especially for non—H-type variance—covariance. For normal to light-tailed distributions, Hotelling'sT2test and the signed-rank test have good powers when the variance—covariance structure of the underlying distribution is non—H-type; otherwise analysis of variance (ANOVA)Fand the rank transformation test RT perform well.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476729

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Asymptotic properties of statistics designed to detect general alternatives in compound symmetric balanced incomplete repeated-measures designs with fixed treatment effects are investigated. Included in this study are the analysis of variance (ANOVA)Fstatistic, its rank transform Durbin's statistic. By making asymptotic relative efficiency comparisions among these statistics when they have been computed with and without mean alignment, valuable new insight into their large-sample performance characteristics is gained. Evidence is presented corroborating recent empirical studies that suggest that mean alignment can improve the performance of rank transformation statistics. Finally, it is noted that the rank transform of the ANOVAFstatistic when it is computed using mean aligned data is generally the most efficient among the statistics studied here.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476730

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In regression analysis, it is important to test the validity of the assumed model prior to making inferences regarding the population of interest. In this investigation, we utilize nonparametric regression techniques to test the validity of akth order polynomial regression model. The departures from the polynomial model are assumed to belong to a smooth class of functions; a parametric form is not assumed. A test based on nonparametric regression fits to the residuals fromkth order polynomial regression is proposed. It utilizes a smoothing spline fit of order 2kto the residuals fromkth order polynomial regression. A test statistic based on this estimator is formulated and its asymptotic distribution is derived under alternatives converging to the null at a rate of (nλ¼k)−½, where λ is the smoothing parameter. We note that this rate of convergence is slower than the parametric rate ofn−½. Power investigations are conducted through a small-scale simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476731

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Others have developed average derivative estimators of the parameter β in the modelE(Y|X=x) =G(xβ), whereGis an unknown function andXis a random vector. These estimators are noniterative and easy to compute but require thatXbe continuously distributed. This article develops a noniterative, easily computed estimator of β for models in which some components ofXare discrete. The estimator isn½consistent and asymptotically normal. An application to data on product innovation by German manufacturers illustrates the estimator's usefulness.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476732

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We consider the problem of how to combine a collection of general regression fit vectors to obtain a better predictive model. The individual fits may be from subset linear regression, ridge regression, or something more complex like a neural network. We develop a general framework for this problem and examine a cross-validation—based proposal called “model mix” or “stacking” in this context. We also derive combination methods based on the bootstrap and analytic methods and compare them in examples. Finally, we apply these ideas to classification problems where the estimated combination weights can yield insight into the structure of the problem.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476733

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

LetY1, …,Yndenote independent real-valued observations, each of the formYj=Xjβ + σεj, whereXjis a fixed covariate vector, β and σ are unknown parameters ε1, …, εnare identically distributed according to a symmetric densityp. This article considers the sensitivity of point estimates of β to the choice of estimator from classes of estimators based on theLestimators of Kroenker and Portnoy. Specific measures of sensitivity are proposed these measures are applied to several datasets.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476734

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Successful application of extreme value statistics for estimating the Pareto tail index relies heavily on the choice of the number of extreme values taken into account. It is shown that these tail index estimators can be considered estimates of the slope at the right upper tail of a Pareto quantile plot, obtained using a weighted least squares algorithm. From this viewpoint, based on classical ideas on regression diagnostics, algorithms can be constructed searching for that order statistic to the right of which one obtains an optimal linear fit of the quantile plot.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476735

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor