ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474136

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474137

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We propose a procedure for computing a fast approximation to regression estimates based on the minimization of a robust scale. The procedure can be applied with a large number of independent variables where the usual algorithms require an unfeasible or extremely costly computer time. Also, it can be incorporated in any high-breakdown estimation method and may improve it with just little additional computer time. The procedure minimizes the robust scale over a set of tentative parameter vectors estimated by least squares after eliminating a set of possible outliers, which are obtained as follows. We represent each observation by the vector of changes of the least squares forecasts of the observation when each of the data points is deleted. Then we obtain the sets of possible outliers as the extreme points in the principal components of these vectors, or as the set of points with large residuals. The good performance of the procedure allows identification of multiple outliers, avoiding masking effects. We investigate the procedure's efficiency for robust estimation and power as an outlier detection tool in a large real dataset and in a simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474138

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We discuss a technique that provides prediction intervals based on a model called an empirical linear model. The technique, high-dimensional empirical linear prediction (HELP), involves principal component analysis, factor analysis and model selection. In fact, a special case of the empirical model is the factor analysis model. A factor analysis model does not generally aim at prediction, however. Therefore, HELP can be viewed as a technique that provides prediction (and confidence) intervals based on a factor analysis model or a more generalized model, possibly with unknown dimension to be estimated. Although factor analysis models do not typically have justifiable theory due to nonidentifiability, we show that our intervals are justifiable asymptotically. An interval for a future response is called a prediction interval; an interval for the mean of the future response is called a confidence interval. These intervals were compared to the intervals of Hwang and Liu, which were derived using standard asymptotic theory where the relevant covariance matrix has a fixed dimension. In contrast, our intervals are derived asymptotically with the dimension of the covariance matrix approaching infinity, a result much more difficult to obtain. However, the numerical results show that the intervals of this article are much more satisfactory in many cases, including the motivating application. The application that motivated us arises from the work of a group of electrical engineers led by Souders and Stenbakken at the National Institute of Standards and Technology (NIST). Their aim is to reduce the number of measurements of a high-dimensional variable of dimension, 213= 8,192, called the future “measurements,” by using the past measurements of similar electric components, such as A/D converters. They claim that only 64 out of 8,192 measurements need to be measured to predict the rest of unobserved measurements well. In this article, we construct our intervals using only 64 measurements of the “future observations” and show that the intervals seem narrow enough to justify their claim.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474139

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

I examine the self-consistency of a principal component axis; that is, when a distribution is centered about a principal component axis. A principal component axis of a random vectorXis self-consistent if each point on the axis corresponds to the mean ofXgiven thatXprojects orthogonally onto that point. A large class of symmetric multivariate distributions are examined in terms of self-consistency of principal component subspaces. Elliptical distributions are characterized by the preservation of self-consistency of principal component axes after arbitrary linear transformations. A “lack-of-fit” test is proposed that tests for self-consistency of a principal axis. The test is applied to two real datasets.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474140

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Not all simultaneous inferences need multiplicity adjustment. If the sequence of individual inferences is predefined, and failure to achieve the desired inference at any step renders subsequent inferences unnecessary, then multiplicity adjustment is not needed. This can be justified using the closed testing principle to test appropriate hypotheses that arenestedin sequence, starting with the most restrictive one. But what hypotheses are appropriate may not be obvious in some problems. We give a fundamentally different, confidence set–based justification bypartitioningthe parameter space naturally and using the principle that exactly one member of the partition contains the true parameter. In dose–response studies designed to show superiority of treatments over a placebo (negative control) or a drug known to be efficacious (active control), the confidence set approach generates methods with meaningful guarantee against incorrect decision, whereas previous applications of the closed testing approach have not always done so. Application of the confidence set approach to toxicity studies designed to show equivalence of treated groups with a placebo is also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474141

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

It is desired to compare κ ≥ 3 treatments. Under the assumption of iid normal errors, it is well known that the Scheffé method produces exact simultaneous confidence bounds for all contrasts of the treatment means. Furthermore, it is known that the Scheffé method is conservative when one desires confidence bounds for a specific subset of contrasts of means. Exact methods, such as those due to Tukey and Dunnett, yield tighter bounds than the Scheffé method for specific subsets of contrasts of means. In this article, multiple comparisons of the κ treatments are done not in terms of their means, but rather in terms of a parametric function. The parametric function of interest is the simple linear regression model,E(Y|x). It is desired to find simultaneous confidence bounds for all contrasts of the κ simple linear regression models. Although the Scheffé method can be used to find such bounds, this is extremely conservative. The union-intersection method is used to develop simultaneous confidence bounds for these contrasts under the assumption of equal design matrices for each treatment. The method is based on a pivotal quantity whose distribution function is a linear combination ofFdistribution functions. Thus probability points can be computed using standard computing packages. The Scheffé bounds are about 5% wider than the exact bounds for κ = 3 and about 13% wider for κ = 6.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474142

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Recent years have seen suggested constructions of multiple confidence sets related to stagewise multiple tests by some authors. These methods are a type of mixture between test and confidence interval methods, because confidence interval statements are made only for some parameters, whereas test statements for fixed parameter values are made for the other parameters. In this article I define a concept—confidence directional set—giving a confidence bound for one parameter, which may depend on other parameters. Using this concept, one can construct multiple confidence sets, which are always confidence set statements and not test statements for fixed parameter values. The confidence sets correspond exactly to stagewise tests, which is theoretically appealing. Special examples of the general technique are given for the independent test statistic case and for comparison of a number of treatments to a control in the case of normally distributed observations with the same variance.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474143

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician. The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility. Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation. However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function. In this article we propose a novel semiparametric proportional hazards model for the subdistribution. Using the partial likelihood principle and weighting techniques, we derive estimation and inference procedures for the finite-dimensional regression parameter under a variety of censoring scenarios. We give a uniformly consistent estimator for the predicted cumulative incidence for an individual with certain covariates; confidence intervals and bands can be obtained analytically or with an easy-to-implement simulation technique. To contrast the two approaches, we analyze a dataset from a breast cancer clinical trial under both models.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474144

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Stochastic curtailment is a valuable tool in monitoring long-term medical studies. Under this approach, one calculates the conditional power, which is the probability of rejecting the null hypothesis at the scheduled end of the study given the existing data at the interim analysis, along with certain speculation about the future data. The conditional power may be used to aid the decision to terminate a study prematurely or to extend a study beyond its originally planned duration. This article provides a formal and systematic investigation into the use of stochastic curtailment in the context of censored survival data. To enhance generality, we introduce a broad class of statistics that includes two-sample weighted log-rank statistics, as well as the partial likelihood score statistic for testing treatment difference with covariate adjustment under the proportional hazards model. We establish the weak convergence under both the null hypothesis and contiguous alternatives for this class of statistics when calculated repeatedly over the calendar time (i.e., time of interim analysis). Further, we derive the conditional distributions of these statistics calculated at the end of the study given all the data collected up to the interim look or given the statistics calculated at the interim look, and provide analytic expressions for the corresponding conditional powers. These results enable us to address several subtle issues involved in the definition and implementation of conditional power for censored survival data, especially when there is staggered patient entry with a potential time trend in the survival distribution, when the Gehan-type weight function is used, or when treatment is not independent of covariates. For randomized clinical trials, we show that very simple formulas can be used to calculate the conditional powers of the unweighted log-rank test (with or without covariate adjustment) under both the null and alternative hypotheses. Simulation studies demonstrate that the conditional powers for survival studies can be accurately evaluated through the proposed formulas even when the sample size is small. An illustration with data taken from a colon cancer study is provided.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10474145

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor