摘要:

This article presents a method of obtaining smoothed curves for a sample of individuals that permits an arbitrary number and spacing of observations for each individual. We consider the case where each individual's curve cannot be separately estimated because either theni's are too small or no suitable parametric forms for the random effects are available. The model assumes a parametric form for the population mean curve and the correlation of the repeated measures. The assumed correlation structure is evaluated using the empirical semivariogram, a function of the sum of the squared differences of within-individual residuals. A method is proposed to validate the form and stationarity of the correlation structure. Maximum likelihood estimates for the population mean parameters and variance components are obtained simultaneously. These estimates may be used to create a semiparametric differentiable curve and to predict future values for each individual using a method called kriging. This method also yields instantaneous estimates of growth velocity. An example of this method is presented, and connections to kriging are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476599

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Critical values are provided for four new tests for cointegration based on the canonical correlations and variates of a development of the Box-Tiao procedure. It is found that in finite samples the power of three of these tests, unlike the power of Johansen's and Engle and Yoo's tests, is highly robust to the correlation between the disturbances in the cointegrating relationships and those generating the common trends. The proposed tests perform well against these alternatives, but neither set of tests dominates over the entire parameter space.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476600

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We consider the problem of interval estimation of probabilities for randomly truncated data. The best-known method is based on the normal approximation of the product-limit estimator and has a drawback that it may produce intervals containing impossible values outside the range [0, 1]. Its small-sample performance is also not satisfactory. In this article we investigate an alternative approach that derives confidence intervals directly from a conditional nonparametric likelihood ratio. The method is an exact nonparametric analog of the classical parametric likelihood ratio theory, with the parameter space now being the family of all distributions. It has an appealing property that the resulting confidence intervals are always subintervals of [0, 1]. It also demonstrated a better small-sample performance in our simulation studies. This approach is generalized to obtain confidence intervals for the ratio of two probabilities, make joint inferences on any finite number of probabilities, and test goodness of fit of a given distribution function. The small-sample performances of three different methods are investigated in a Monte Carlo study. An illustration is also given using the Centers for Disease Control's transfusion related acquired immune deficiency syndrome data.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476601

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Motivated by some problems arising from multiclinic trials, we consider stratified two-sample designs. Nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment, centers (strata), and interactions are assumed to be fixed factors. The interpretation of the nonparametric effects and hypotheses is analyzed in two classes of semiparametric models: the linear models and models with Lehmann alternatives. The case where centers and interactions are assumed to be random factors, the so-called mixed model, is also considered. Nonparametric effects and hypotheses are defined for general models, and their properties are analyzed in corresponding linear models and in models with Lehmann alternatives. The nonparametric effects are estimated by linear rank statistics where the ranks over all centers are used. The mixed model for repeated (baseline and endpoint) observations is briefly considered, and rank procedures are also proposed for this model. All procedures are related to the nonparametric effects and are not restricted to the two classes of semiparametric models, which are used only for interpretation of the nonparametric effects. Moreover, we do not assume continuity of the underlying distribution functions of the observations, to be as general as possible. We exclude only the trivial case where the distribution function arises from a point mass; that is, a “one-point distribution.” Thus, not only data coming from continuous distribution functions, but also data with ties—especially discrete ordinal data—can be handled with the proposed procedures. In all cases, the results are derived for unbalanced designs so that there are no restrictions for practical applications. The small-sample properties of the proposed statistics are investigated by simulation studies, and the relevant asymptotic distribution theory is considered. Applications of the proposed procedures are demonstrated by means of examples related to multicenter clinical trials.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476602

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from one or more blocks. Conditional on the pattern of missing observations, the resulting statistics are shown to be asymptotically normal. For a particular pattern of missing observations, the asymptotic efficiency of the extended Page test is found, in many cases, to be not much lower than for the standard Page test.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476603

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We present a general method of improving the power of linear and approximately linear tests when deviations from a translation family of distributions must be taken into account. This method involves the combination of a linear statistic measuring location and a quadratic statistic measuring change of shape of the underlying distribution. The tests (“funnel tests”) are constructed as certain Bayes tests. In general they gain a sizeable amount of power over the linear tests adapted to the translation family when a change of shape of the underlying distribution occurs, while losing little for translation alternatives (“power robustification”). We introduce the concept of funnel tests in an Gaussian framework first. The effect of power robustification is studied by means of a power function expansion, which applies to a large class of tests sharing a certain invariance property. The funnel tests are characterized by a maximin property over a region defined by a rotational cone. The idea of the construction is then carried over to a finite sample situation where the Gaussian model is used as an approximation. As a particular application, we construct power-robustified nonlinear rank tests in the standard two-sample situation. A simulation study demonstrates the good overall performance of these tests as compared to other nonlinear tests.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476604

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered. We extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators. We also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense. Finally, we examine a data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and compare our testing procedure to testing procedures for other stochastic orderings.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476605

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A new model for the analysis of lifetime data in the presence of a covariate is derived based on physical and statistical considerations. The model depends on five parameters that have clear physical interpretations. Two methods for the estimation of the parameters and of the quantiles are presented: one based on the order statistics and the other a regression estimator. The quantile estimators as well as the estimators of four of the five parameters are given in closed form. The fifth parameter can be estimated independently of the other parameters using either a closed form or a numerically simple algorithm. A simulation study shows that the regression estimators are better for estimating the parameters but the order statistics estimators perform better for the estimation of low quantiles. The methodology is also illustrated by an example of a real life data.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476606

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Statistical modeling of the largestkobservations or the exceedances over a high threshold based on extreme value theory has produced powerful methods for drawing inferences about the tail behavior of a distribution; however, a method for selectingkhas not been established. We suggest using a forward selection procedure based on a suitable goodness-of-fit statistic to search for the optimalkwhen the sample is of finite size and from a distribution in the domain of attraction of the Gumbel distribution. Two criteria are examined: generalized least squares and the Shapiro-Wilk goodness of fit. Simulation studies indicate that the latter is preferable in terms of variation. Extension of the selection procedure to distributions in the domains of attraction of the Fréchet and Weibull distributions is also discussed. The use of the proposed method is illustrated through two examples based on real data.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476607

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Consider the model whereXij, i= 1, 2, …,k;j= 1, …,niare independent uniform random variables with scale parameter θi> 0. TestH0: θl= ··· = θkversusH2: notH0. Also consider the alternativeH1: θl≤ ··· ≤ θk. ForH0versusH2andni=n, we obtain a complete class of constant-size permutation invariant tests and show that each test in the class is unbiased. The likelihood ratio test and others are in this class. ForH0versusH1we obtain a complete class of constant-size tests based on a set of variables that is a transformation of the sufficient statistics. Again we show that each test in the class is unbiased. The likelihood ratio test is in this class. We derive the exact and asymptotic distribution of the likelihood ratio test. All results also hold for testing homogeneity of location parameters of exponential distributions. This latter case is of considerable practice importance in reliability.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476608

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor