摘要:

Estimating monotone dose—response curves with independent, normal errors has been studied in detail in the literature. A simple procedure using a generalization of the studentized maximum modulus technique is proposed for constructing confidence bands for monotone regression functions. This procedure is shown to compare well with its predecessors. The center of this smooth and efficient confidence band is then used to estimate a smooth monotone regression function. Its pointwise mean squared errors compare favorably with the maximum likelihood estimate, a weighted average of the isotonic regression and the least squares line, and the rank-transformed regression. A numerical example of a binding inhibition assay is included to illustrate the proposed interval and point estimation procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476981

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article discusses a model in which both the dependent variable and the explanatory variables are ordinal and have an arbitrary number of categories. Assuming joint normality of the underlying continuous latent variables, we compare estimation based on the joint distribution to estimation based on the conditional distribution. Because the explanatory variables arenotweakly exogenous in this model, the latter approach implies a loss in efficiency that can be substantial in many cases, as shown in detail for the special case of trichotomous data with symmetric thresholds. Therefore, latent variables underlying the observed ordinal variables should always be considered to be jointly endogenous; that is, the joint distribution should be considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476982

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

An asymptotic representation of the mean weighted integrated squared error for the kernel-based estimator of the hazard rate in the presence of right-censored samples is obtained for different bootstrap resampling methods. As a consequence, a new bandwidth selector based on the bootstrap is introduced. Very satisfactory simulations results are obtained in comparison to the cross-validation selector for different models, using WARPed (i.e., binned) versions of the estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476983

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of Gaussians subject to the constraint that the component variances be greater than or equal to some minimum valueh. This approach can lead to estimates of many shapes, with smoothness controlled by parameterh. We show that the resulting estimate will always be a finite mixture of Gaussians, each having varianceh. The nonparametric maximum likelihood estimate can be viewed as a special case, withh= 0. The method can be extended to estimate multivariate mixing distributions. Examples and the results of a simulation study are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476984

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Bivariate estimation with survival data has received considerable attention recently; however, most of the work has focused on random censoring models. Another common feature of survival data, random truncation, is considered in this study. Truncated data may arise if the time origin of the events under study precedes the observation period. In a random right-truncation model, one observes the iid samples of (Y, T) only if (Y ≤ T), whereYis the variable of interest andTis an independent variable that prevents the complete observation ofY. Suppose that (Y, X) is a bivariate vector of random variables, whereYis subject to right truncation. In this study the bivariate reverse-hazard vector is introduced, and a nonparametric estimator is suggested. An estimator for the bivariate survival function is also proposed. Weak convergence and strong consistency of this estimator are established via a representation by iid variables. An expression for the limiting covariance function is provided, and an estimator for the limiting variance is presented. Alternative methods for estimating the bivariate distribution function are discussed. Obtaining large-sample results for the bivariate distribution functions present more technical difficulties, and thus their performances are compared via simulation results. Finally, an application of the suggested estimators is presented for transfusion-related AIDS (TR-AIDS) data on the incubation time.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476985

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In many prospective and retrospective studies, survival data are subject to left truncation in addition to the usual right censoring. For left-truncated data without covariates, only the conditional distribution of the survival timeYgivenY≥ τ can be estimated nonparametrically, where τ is the lower boundary of the support of the left-truncation variableT. If the data are also right censored, then the conditional distribution can be consistently estimated only at points not larger than τ*, where τ* is the upper boundary of the support of the right-censoring variableC. In this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution ofY, with the trimming inside the observable range between τ and τ*. We then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variableY. Asymptotic normality of M estimators of the regression parameters derived from this approach is established, and the result is used to construct confidence regions for the regression parameters. We also apply our methods of nonparametric estimation, correlation analysis, and curve fitting for left-truncated and right-censored data to analyze transfusion-induced AIDS data, and present a simulation study comparing our approach with another kind of M estimators for regression analysis in the presence of left truncation and right censoring.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476986

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The random truncation model has been considered extensively in the literature. Tsai has noted that many previous results hold under the weaker assumption of quasi-independence between the failure time and the truncation time in the observable region of truncated data. We generalize the Pearson product-moment correlation coefficient to measure the association between both time variables in the observable region. We show that if the failure time and the truncation time follow a truncated bivariate normal distribution, then a zero value of the generalized correlation coefficient is equivalent to the quasi-independence. We propose a corresponding sample correlation coefficient and consider its asymptotic behavior. We also study an application of quasi-independence to truncated linear regression with its asymptotic results. The proposed estimator, stemming directly from the least-squares approach, is computationally much simpler and has a natural extension to multiple linear regression. A simulation study shows that the proposed estimator for regression slope competes well with available nonparametric estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476987

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Equivalence and interval tests for Lehmann's alternative that extend the well-known Savage test for one-sided hypotheses are proposed. The proposed tests are shown to be unbiased with a strictly unimodal power function, provided the sample sizes in both treatment groups are equal. By means of a numerical investigation of the bias in the case of unequal sample sizes that are not too far apart, the suggested tests still turn out to provide practicable solutions. Because the computational effort to perform the suggested tests is considerable, tables containing the critical values are displayed to perform these tests easily. A numerical analysis of the power function of the interval test establishes this procedure as a powerful tool for detection of a significantly relevant difference in the small-sample case. In contrast to the case of interval testing, the fact arises that the performance of a powerful equivalence study under Lehmann's alternative requires an extensive amount of data. Because the proposed tests are based on the locally optimal scores under Lehmann's alternative, we cannot improve the suggested equivalence test essentially. Therefore, we also provide the asymptotic version of this test and display tables containing the required numerical values.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476988

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors. We focus on the choice of predictors in linear models, and mix over possible subsets of candidate predictors. Our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix. Advantages are both statistical and computational. Statistically, orthogonalization often leads to a reduction in the number of competing models by eliminating correlations. Computationally, large model spaces cannot be enumerated; recent approaches are based on sampling models with high posterior probability via Markov chains. Based on orthogonalization of the space of candidate predictors, we can approximate the posterior probabilities of models by products of predictor-specific terms. This leads to an importance sampling function for sampling directly from the joint distribution over the model space, without resorting to Markov chains. Compared to the latter, orthogonalized model mixing by importance sampling is faster in sampling models and is also more efficient in finding models that contribute significantly to the prediction. Further advantages are in the speed of convergence and the availability of more reliable convergence diagnostic tools. We illustrate these in practice, using a data set on prediction of crime rates. The model space is small enough so that enumeration of all models is available for comparison and convergence checks. Also, we demonstrate the feasibility of orthogonalized model mixing in a large-size problem, which is very difficult to attack by other methods. The data set is from a designed experiment dealing with predicting protein activity under different storage conditions. The model space is large (the rank of the design matrix is 88) and very difficult to explore if expressed in terms of the original variables. We obtain prediction intervals and a probability distribution of the setting that produces the highest response.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476989

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We adopt a Bayesian approach to analyze the occurrence times of seismic events and their magnitudes. We choose an epidemic model for the process of occurrence times conditional on the observed magnitude values. The locations of, and dependencies between, the model parameters are determined on the basis of historical and physical information. The overall prior variability is deliberately made diffuse. We generate samples from the joint posterior distribution of the model parameters by using a variant of the Metropolis—Hastings algorithm. We use the results in a variety of ways, including the construction of pointwise posterior confidence bands for the conditional intensity of the point process as a function of time.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476990

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor