摘要:

In this article we develop new plotting positions for normal plots. The use of the plots usually centers on detecting irregular tail behavior or outliers. Along with the normal plot, we develop tests for various departures from normality, especially for skewness and heavy tails. The tests can be considered as components of a Shapiro-Wilk type test that has been decomposed into different sources of nonnormality. Convergence to the limiting distributions is slow, so finite sample corrections are included to make the tests useful for small sample sizes.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476736

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The likelihood ratio test is often used to test hypotheses involving a stochastic ordering. Distribution theory for the likelihood ratio test has been developed only for two stochastically ordered distributions. For testing equality of distributions against a stochastic ordering in several populations, this paper derives the null asymptotic distribution of the likelihood ratio test statistic, which is characterized by minimization problems and has no closed form. A Monte Carlo simulation is conducted to study the limiting distribution. Because the limiting distribution depends on the specific values of the unknown distributions under the null hypothesis, asymptotic and bootstrap approaches are proposed to overcome practical difficulties and implement tests based on the likelihood principle. Asymptotic validities for these tests are established and simulations are carried out to check their performances for finite sample sizes. The tests are applied to an example involving data for survival time for carcinoma of the oropharynx.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476737

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

IfSandTare survival functions for two life distributions, thenSis said to be uniformly stochastically smaller thanT, denoted byS≪T, if θ(x) ≡S(x)/T(x) is nonincreasing inxon {x:T(x) > 0}. This ordering is transitive. Uniform stochastic ordering (USO) has found important applications in nonparametric accelerated life testing, among other areas. It has been shown that the nonparametric maximum likelihood estimator (NPMLE) ofSunder USO whenTis known is inconsistent. Dykstra, Kochar Robertson derived the restricted NPMLE's of several unknown survival functions linearly ordered by USO. This article shows that these too are inconsistent in general. Rojo and Samaniego gave excellent ad hoc estimators ofSandTwhen the other is known. Based on their idea for the one-sample problem, they gave two ad hoc estimators (one of them only implied) ofSandTwhen they are both unknown. These are consistent, but they lack some desirable properties. This article introduces a one-parameter family of estimators that contains both of these estimators as extreme members. Some heuristic arguments are given to show that an interior member of this family is the appropriate one to choose.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476738

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We are interested in testing Ψ =0against an alternative in the presence of some nuisance parameter λ. The usual procedure for such problems is to use a test statistic that is a function of the data only. Letq(λ) denote thep-value at a given value λ. Ifq(λ) does not depend on λ, then in principle we can apply this procedure. However, a major difficulty that arises in many situations is thatq(λ) depends on λ and therefore cannot be used as ap-value. In such cases, the usual approach is to define thep-value as the supremum ofq(λ) over the nuisance parameter space. Because this approach ignores sample information about λ, it may be unnecessarily conservative; this is a serious problem in order restricted inference. To overcome this, I propose the following. Obtain, say, a 99% confidence region for λ under the null hypothesis. Now, for a given λ, letT(λ) be a test statistic andr(λ) be thep-value. The test procedure is to reject the null hypothesis if {0.01 + supremum ofr(λ) over the 99% confidence region for λ} is less than the nominal level such as 0.05. In contrast to the usual procedure, an attractive feature of this procedure is that it allows us to choose a test statistic as a function of λ. A data example is used to illustrate the procedure in a simulation study I observed that this test performed better than the traditional conservative procedure. Although this approach was originally developed for order restricted inference problems, the main results have wide applicability.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476739

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Shewhart charts are widely accepted as standard tools for monitoring manufacturing processes of univariate, independent “nearly” normal measurements. They are not as well developed beyond these types of data. We generalize the idea of Shewhart charts to cover other types of data commonly encountered in practice. More specifically, we develop some valid control charts for dependent data and for independent data that are not necessarily “nearly” normal. We derive the proposed charts from the moving blocks bootstrap and the standard bootstrap methods. Their constructions are completely nonparametric no distributional assumptions are required. Some simulated as well as real data examples are included they are very supportive of the proposed methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476740

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A Markov chain approximation is used to determine the run length performance of a multivariate statistical process control chart. The Markov chain approach is widely used in the analysis of univariate control charts we extend the advantages of this type of analysis to a multivariate exponentially weighted moving averages control chart. The analysis can be applied whenever the multivariate control statistic can be modeled as a Markov chain and the run length performance depends on the off-target mean only through the noncentrality parameter.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476741

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The problem of calibration in which the response variable is measured bykdifferent methods or using different instruments is considered. It is well known that the usual classical estimator for the unknown explanatory variable has infinite mean and mean squared error whenk= 1. In this article a linear combination of the classical estimators is proposed. It is shown that the combined estimator has finite mean provided thatk≥ 2 and finite mean squared error provided thatk≥ 3. Expressions for asymptotic bias and mean squared error are given. Also, two confidence sets for the unknown exploratory variable are developed sufficient conditions under which they will be finite intervals are given. The results are illustrated by a practical example.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476742

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Minimum Hellinger distance estimates are considered for finite mixture models when the exact forms of the component densities are unknown in detail but are thought to be close to members of some parametric family. Minimum Hellinger distance estimates are asymptotically efficient if the data come from a member of the parametric family and are robust to certain departures from the parametric family. A new algorithm is introduced that is similar to the EM algorithm a specialized adaptive density estimate is also introduced. Standard measures of robustness are discussed some difficulties are noted. The robustness and asymptotic efficiency of the estimators are illustrated using simulations.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476743

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In more conventional analytic surveys, we sample the response variatesythrough a sampling design that is dependent on the covariatex. Thexvalues are assumed known for all the units in the population. However, contrary to these situations, there are areas of statistical application when the values of the response variable are known for all the individuals but not the values of covariate (for example, in epidemiology and reliability). Here we sample thexvalues the sampling design used depends on the response variatey. The problem that we study is the same as usual—namely, inference regarding dependence of the responseyon the covariatex. Some work in this direction has already been done. In this article we use estimating function theory to establish optimum estimation for the parameter of interest. This optimality holds conditionally when the response variable is fixed as well as unconditionally. We demonstrate that here for response-dependent sampling stratification plays the same role as in conventional surveys; that is, balancing on or eliminating nuisance parameters. As a special case, for the logistic model we establish a version of the conjecture that “the prospective score is equal to the retrospective score.” In simulation studies, the above-mentioned optimal estimation performs much better than the estimation in more common use.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476744

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Suppose that data are collected fromkindependent but closely related populations and that a canonical correlation analysis is to be performed within each group. In such a situation, it may turn out that the transformation to canonical variates is similar across allkgroups. The common canonical variates model studied in this article assumes that the transformation to canonical variates is actually identical across groups, while the canonical correlations may vary. We develop some algebra of the common canonical variates model, discuss normal theory maximum likelihood estimation and likelihood ratio testing give illustrative examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476745

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor