摘要:

In this article we consider cases where data consist of many small and independent groups of correlated failure time observations. For each failure time, which may be censored, some important covariates are also recorded. Our goal is to examine the covariate effects on the individual failure time observations. We assume that the logarithm of each failure time is linearly related to its covariates. We then take a population-averaged model approach to obtain inference procedures for the regression parameters without specifying the joint distribution of the observations within the group. The new proposals do not need complicated and unstable nonparametric estimates for the hazard function of the error term. Their properties are extensively examined for practical sample sizes. Comparisons among various procedures are also performed. All the methods studied in this article are illustrated with examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476307

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

IfFandGare cumulative distribution functions on [0, ∞) governing the lifetimes of specific systems under study, and ifFandGare their corresponding survival functions, thenFis said to be uniformly stochastically smaller thanG, denoted byF<(+)G, if and only if the ratiol(x) =G(x)/F(x) is nondecreasing forx∈ [0, sup{t: [0, sup {(t:F(t) > 0}). WhenFandGare absolutely continuous,F(+)Gis equivalent to the assumption that the corresponding failure rates are ordered. The applicability of the notion of uniform stochastic ordering in reliability and life testing is discussed. Given that a random sampleX1, …,Xnof lifetimes has been obtained fromF, whereFis assumed to satisfy the uniform stochastic ordering constraintF<(+)G(or alternatively,F>(+)G), whereGis fixed and known, the problem of estimatingFis addressed. It has been shown elsewhere that the method of nonparametric maximum likelihood estimation fails to provide consistent estimators in this type of problem. Here, a recursive approach is shown to provide estimators that converge uniformly toFwith probability 1 and are as close or closer toF, in the sup norm, than is the empirical distribution function. This leads to a proof of the inadmissibility of the empirical distribution function, relative to the sup norm loss criterion, when estimatingF<(+)G(orF>(+)<G) withGcontinuous. The two-sample estimation problem is also discussed briefly.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476308

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We show that the survival curve is identifiable in bivariate censored data problems under weaker independence assumptions than have commonly been made. The common assumption has been mutual independence of (T1,T2) and (Z1,Z2), where (T1,T2) is the true survival vector, (Z1,Z2) is a nuisance censoring vector, and bivariate right-censored data is observed. We show that the distribution of (T1,T2) is identifiable under weaker, conditional independence assumptions for distributions with full support. Bivariate survival analysis is a more powerful analysis tool than univariate analysis if multiple, possibly related, times are of interest. The mutual independence model has become popular as a nonparametric way of analyzing such data. Analysis of the bivariate problem and analogy with univariate models are used to show that the conditional independence model is more widely applicable as a general nonparametric model for bivariate survival data.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476309

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The elemental set algorithm involves performing many fits to a data set, each fit made to a subsample of size just large enough to estimate the parameters in the model. Elemental sets have been proposed as a computational device to approximate estimators in the areas of high breakdown regression and multivariate location/scale estimation, where exact optimization of the criterion function is computationally intractable. Although elemental set algorithms are used widely and for a variety of problems, the quality of the approximation they give has not been studied. This article shows that they provide excellent approximations for the least median of squares, least trimmed squares, and ordinary least squares criteria. It is suggested that the approach likely will be equally effective in the other problem areas in which exact optimization of a criterion is difficult or impossible.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476310

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This article is concerned with the estimation of a regression model with a stochastic trend component. It is shown that the probability of estimating the trend to be deterministic is very sensitive to the type of likelihood function used as the basis of inference.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476311

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Test procedures for detecting overdifferencing or a moving average unit root in Gaussian autoregressive integrated moving average (ARIMA) models are proposed. The tests can be used when an autoregressive unit root is a serious alternative but the hypothesis of primary interest implies stationarity of the observed time series. This is the case, for example, if one wishes to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical cointegration vector. A priori knowledge of the mean value of the observations turns out to be crucial for the derivation of our tests. In the special case where the differenced series follows a first-order moving average process, the proposed tests are exact and can be motivated by local optimality arguments. Specifically, when the mean value of the series is a priori known, we can obtain a locally best invariant (LBI) test that is identical to a one-sided version of the Lagrange multiplier test. But when the mean value is a priori not known, this test breaks down and we derive a locally best invariant unbiased (LBIU) test. After having tests in this special case, we develop extensions to general ARIMA models. These tests are asymptotic, but under the null hypothesis they have the same limiting distributions as in the just-mentioned special case. When the mean value is a priori known, an asymptotic χ21distribution is obtained, when it is unknown, the limiting distribution agrees with that of the Cramer–von Mises goodness-of-fit test statistic.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476312

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Knowledge of the rate of a biological process is important for characterizing the system and is necessary for gaining a deeper understanding of the process. Consider measurements,Y, made over time on a system following the modelY=f(t) +e, wherefis a smooth, unknown function andeis measurement error. Although most statistical methodology has focused on estimatingf(t) orf′(t), in some applications what is of real biological interest is the relationship betweenfandf′. One example is the study of nitrogen absorption by plant roots through a solution depletion experiment. In this casef(t) is the nitrate concentration of the solution surrounding the roots at timetand –f′(t) is the absorption rate of nitrate by plant roots at timet. One is interested in the rate of nitrate absorption as a function of concentration; that is, one is interested in Φ, where Φ(f) = –f′. Knowledge of Φ is important in quantifying the ability of a particular plant species to absorb nitrogen and in comparing the absorption ability of different crop varieties. A parametric model forfis usually not available, and thus a nonparametric estimate of Φ is particularly appropriate. This article proposes using spline-based curve estimates with the smoothing parameter chosen by cross-validation and suggests a method for obtaining confidence bands using a form of the parametric bootstrap. These methods are used to analyze a series of solution depletion experiments and are also examined by a simulation study designed to mimic the main features of such data. Although the truefis a monotonic function, simulation results indicate that for our specific application, constraining the estimate offto be monotonic does not reduce the average squared error of the rate curve estimate, Φ. Although using a cross-validated estimate of the smoothing parameter tends to inflate the average squared error of the rate estimate, an analysis of a set of solution depletion experiments is still possible. Using the proposed methods, we are able to detect a difference in rate curves obtained under different experimental conditions. This is established by applying an analysis of variance (ANOVA)-like test to the estimated rate curves, where the critical value is determined by a parametric version of the bootstrap, and by examining confidence bands for the difference of two rate cures. This finding is important, because it suggests that the shape of Φ may not be constant under the experimental conditions examined.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476313

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all finite sample sizes. Furthermore, it is shown that this estimator asymptotically behaves the same as the usual maximum likelihood estimator.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476314

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Several chronic diseases are characterized by an initial asymptomatic stage during which, if detected by screening, they can be cured in a more effective way. This article considers two statistical design problems in screening for chronic disease: the choice of examination ages and the choice of the part of the population to be screened. One main goal is capturing the trade-off between the costs of examination and the losses due to late detection, while accounting for the effects of age on the incidence of the disease, on mortality, and on the relative advantages of early detection. The problem is posed in a decision theoretic way. The model adopted considers a single individual, whose history relative to the disease is represented by a discrete-valued stochastic process. The transition structure is general, but known. The decision space includes all sequences of examination times, as well as no examination. The optimality criterion accounts for the cost of examinations and, in a general way, for the goals of screening in terms of mortality and morbidity. So the optimality criterion may depend on survival, quality-adjusted life years, cost of care, and so on, as well as on combinations of these factors. A general solution and computational algorithms are derived by extending to this context methodologies developed in reliability theory. The case in which the test used for screening has high sensitivity is studied in detail; then the determination of the optimal schedule and stopping rule is reduced to a one-dimensional optimization problem by recursive dynamic methods. Moreover, sufficient conditions for screening to be increasingly worthwhile with age are derived. Under these conditions, the optimal number of planned examinations is either 0 or infinity, and there is a simple check to establish whether or not to screen without having to compute the optimal schedule. Under slightly stronger conditions, the times between examinations decrease and the optimal solution is unique and easy to compute. The conditions mentioned relate increasing times between checks to properties of the failure rate of the time to onset of the disease and of the relative incidence of the disease. Applications of the results include developing guidelines for screening for breast and cervical cancers—currently a controversial issue.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476315

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Sample surveys often have complex sample designs with multistage cluster sampling, stratification, and differential selection probabilities. This article is concerned with testing the null hypothesisH0:θ=θ, where thep-dimensional parameterθ=g(μ) andμis aq-dimensional vector of means. The asymptotic framework that consists of a sequence of increasing finite populations is used to defineμas the limit of finite population means. As part of the inference, we use replicated estimates of variances that take into account the complex sample design. The Wald statistic can be used to testH0. But inference forθbased on the Wald statistic can have low power. Thus an alternative to using a Wald test is pursued in this article. First, define a classical quadratic test statistic that would be used if one had a simple random sample of the population. Second, treating this quadratic form as a population parameter, use design-based methods to estimate it from the observed survey data. Last, use a replication method to approximate the distribution of this estimated quadratic form to perform the hypothesis test. Specific applications of this general approach have been used previously in contingency table analysis. For small numbers of sampled first-stage clusters and largep, modified versions of the Fay procedure are proposed. Simulations show that these modified procedures maintain nominal levels better than the original Fay and the Rao-Scott procedures for testing a vector of means and a vector of regression coefficients. An application is given for testing whether design-based regression coefficients differ from ordinary least squares regression coefficients.

ISSN:0162-1459    

DOI:10.1080/01621459.1993.10476316

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor