Showing papers in "Communications in Statistics-theory and Methods in 1982"
TL;DR: The local regularity of solutions of degenerate elliptic equations was studied in this paper, where the authors showed that the solution of a degenerate Eq. 1 can be computed in a complete differential equation.
Abstract: (1982). The local regularity of solutions of degenerate elliptic equations. Communications in Partial Differential Equations: Vol. 7, No. 1, pp. 77-116.
965 citations
TL;DR: In this article, a procedure for transfer function identification (specification) based on least-squares estimates of transfer function weights using the original or filtered series is proposed. But this procedure is not suitable for the analysis of complex transfer functions.
Abstract: This paper proposes a procedure for transfer function identification (specification) based on least-squares estimates of transfer function weights using the original or filtered series. The corner method is then used to identify a parsimonious rational form of the transfer function. The procedure is illustrated in a simulated example; it is shown how this straightforward approach outperforms other identification methods such as Box and Jenkins' prewhitening and Haugh and Box1 double prewhitening techniques.
147 citations
TL;DR: In this article, the power and robustness of the Haseman and Elston test for sib-pair linkage between a marker locus and a locus affecting a quantitative trait was investigated.
Abstract: We investigate the power and robustness of Haseman and Elstonfs sib-pair test for genetic linkage between a marker locus and a locus affecting a quantitative trait, and compare the test to that of Penrose. The Haseman-Elston test is more powerful than Penrrose's test; its power is acceptable for cases of tight linkage and high heritability due to the hypothesized quantitative trait locus, but is quite low in other situations. Computer simulations indicate that both tests are valid for normally distributed trait values, and that the Haseman-Elston test is robust for a variety of continuous distributions of the trait values. Several linkage tests are developed for sib trios that are much more powerful , for the same total number of sibs, than the test on independent sib pairs. The Haseman-Elston test on all possible sib pairs is suggested for sibships of size larger than three and for samples including sibships of various sizes.
108 citations
TL;DR: The use of logistic regression analysis is widely applicable to epidemiologic studies concerned with quantifying an association between a study factor and a health outcome (i.e., disease status) as discussed by the authors.
Abstract: The use of logistic regression analysis is widely applicable to epidemiologic studies concerned with quantifying an association between a study factor (i.e., an exposure variable) and a health outcome (i.e., disease status). This paper reviews the general characteristics of the logistic model and illustrates its use in epidemiologic inquiry. Particular emphasis is given to the control of extraneous variables in the context of follow-up and case-control studies. Techniques for both unconditional and conditional maximum likelihood estimation of the parameters in the logistic model are described and illustrated. A general analysis strategy is also presented which incorporates the assessment of both interaction and confounding in quantifying an exposure-disease association of interest.
107 citations
TL;DR: In this paper, modifications of both maximum likelihood and moment estimators for parameters of the three-parameter Wei bull distribution are presented. But the modifications presented here are basically the same as those previously proposed by the authors (1980, 1981, 1982) in connection with the lognormal and the gamma distributions.
Abstract: This article is concerned with modifications of both maximum likelihood and moment estimators for parameters of the three-parameter Wei bull distribution. Modifications presented here are basically the same as those previously proposed by the authors (1980, 1981, 1982) in connection with the lognormal and the gamma distributions. Computer programs were prepared for the practical application of these estimators and an illustrative example is included. Results of a simulation study provide insight into the sampling behavior of the new estimators and include comparisons with the traditional moment and maximum likelihood estimators. For some combinations of parameter values, some of the modified estimators considered here enjoy advantages over both moment and maximum likelihood estimators with respect to bias, variance, and/or ease of calculation.
102 citations
TL;DR: In this article, a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings is introduced, and a test of symmetry and normality is suggested.
Abstract: This note introduces a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings. Another respect in which this family compares favourably with families like the Pearson family, the Bessel-Gram-Charlier family and the Johnson family is ease of maximum likelihood fitting. Fitting by the method of moments is also considered. Asymptotic distributions of maximum likelihood and moment estimators are worked out. A test of symmetry and normality is suggested.
101 citations
TL;DR: In this article, a class of matched-pairs permutation techniques based on distances between each pair of observed signed values is considered, and two simple rank tests of this class jointly possess both intuitive properties and location-alternative power characteristics which appear more appealing than the corresponding characteristics of either the sign test or the Wllcoxon signed-ranks test.
Abstract: A class of matched-pairs permutation techniques based on distances between each pair of observed signed values is considered. Although many commonly-used inference techniques for matched pairs are members of this class, some of the more appealing inference techniques among this class have received very little attention. Two new simple rank tests of this class jointly possess both intuitive properties and location-alternative power characteristics which appear more appealing than the corresponding characteristics of either the sign test or the Wllcoxon signed-ranks test. In particular, power comparisons based on slmula-tions indicate that these new rank tests are jointly as good or even vastly superior to the sign test or the Wilcoxon signed-ranks test for location alternatives involving five symmetric distributions. The five distributions selected for these com-parisons include the Laplace, logistic, normal, uniform and a U-shaped distribution
92 citations
TL;DR: In this article, an alternative to the conventional sample quantlle is proposed as a nonparametric estimator of a continuous population quantle, which is obtained by averaging an appropriate subsample quantle over all subsamples of.a fixed size.
Abstract: An alternative to the conventional sample quantlle Is proposed as a nonparametrlc estimator of a continuous population quantlle.The alternative estimator Is a "generalized sample quantlle" obtained by averaging an appropriate subsample quantlle over all subsamples of .a fixed size.Since the resulting statistic is a U-statistic with representation also as a linear combination of order statistics, known results are employed then to establish asymptotic normality.The alternative estimator is shown to be asymptotically efficient in the class of nonparametrlc models specified by Pfanzagl (1975).Analytic results and Monte Carlo studies with a moderate sample size for a variety of distributions Indicate that the proposed estimator usually provides mean square error of estimation less than that of the conventional sample quantile.
91 citations
TL;DR: In this article, the eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available, and simple asymptotically efficient estimators of the variance components are presented.
Abstract: By means of an example it is shown how eigenvalues and eigenvectors of variance components models can be obtained straightforwardly when balanced data are available. Simple asymptotically efficient estimators of the variance components are presented.
85 citations
TL;DR: The bootstrap principle is justified for robust M-estimates in regression, and a short proof justifying bootstrapping the empirical process is also given in this article, where the authors show that robust M estimations in regression can be computed using the bootstrap method.
Abstract: The bootstrap principle is justified for robust M-estimates in regression, (A short proof justifying bootstrapping the empirical process is also given)
81 citations
TL;DR: In this article, a CUSUM control scheme that ignores the first suspected outlier, but gives an out-of-control signal for two successive outliers is found to perform well.
Abstract: A standard CUSUM control scheme and four modified CUSUM control schemes are evaluated for robustness. The average run length (ARL) for each scheme is evaluated using a contaminated normal distribution, a distribution that has longer tails than the normal. A CUSUM control scheme that ignores the first suspected outlier, but gives an out-of-control signal for two successive outliers is found to perform well.
TL;DR: In this paper, a class of permutation techniques is presented for the randomized block design, specifically devised for analyses involving multivariate data, and a numerical example illustrates an application based on multiivariate data.
Abstract: A class of permutation techniques is presented for the randomized block design. This class is specifically devised for analyses involving multivariate data. A numerical example illustrates an application based on multivariate data. Many well known techniques are special cases of this class. Among these special cases are (i) the permutation version of the classical univariate technique for randomized blocks which 1s associated with analysis of variance, (ii) the Friedman randomized block test, (iii) one-sample matched-pair tests, (iv) the Pearson correlation measure, and (v) the Spearman rank correlation and foot-rule measures. Furthermore, variations and multivariate versions among this class suggest a variety of new techniques which have not received any previous attention.
TL;DR: In this article, a test for lack of fit in regression is presented, which can be used for linear or multiple regression, and would be easy to add to existing computer packages, without replicates or a prior estimate of variance.
Abstract: A test for lack of fit in regression is presented. Unlike other methods, this one doesn't require replicates or a prior estimate of variance. It can be used for linear or multiple regression, and would be easy to add to existing computer packages. It is based on comparing a fit over low leverage points with a fit over the entire set of data. Distribution theory results are pre¬sented, with examples of power. A discussion of its use for de¬tecting violations of other regression assumptions is also given.
TL;DR: In this article, a goodness of fit test for quantal response bioassays is described and extended to the multiple regressor situation, and the size and power characteristics of the test statistic are described by a chi square variate for sample sizes as small as SO.
Abstract: A goodness of fit test statistic for the univariate logistic response model proposed by Prentice (1976) for quantal response bioassays is described and extended to the multiple regressor. variable situation. The size and power characteristics of the test statistic was found to be adequately described by a chi square variate for sample sizes as small as SO and its power was found to be dependent upon both the sample size and the true underlying response model.
TL;DR: In this paper, the exact distribution of a linear combination of n independent negative exponential random variables, when the coefficients of the linear combination are distinct and positive quantities, is extended to the general case.
Abstract: The exact distribution of a linear combination of n independent negative exponential random variables, when the coefficients of the linear combination are distinct and positive quantities, is well-known. This paper extends the above result to the general case, namely when the coefficients are arbitrary real numbers, positive or negative, distinct or coincident.
TL;DR: In this article, the authors present a survey of recent papers which treat the more sophisticated and more realistic models in which components and systems may assume many states ranging from perfect functioning to complete failure.
Abstract: The vast majority of reliability analyses assume that ccmponents and system are in either of two states: functioning or failed. However, in many real life situations we are actually able to distinguish among various 'Ilevels of performance" for both system and components. For such situations, the existing dichotomous model is a gross oversimplification and so models assuming degradable (multistate) systems and components are preferable since they are closer to reality.We present a survey of recent papers which treat the more I sophisticated and more realistic models in which components and systems may assume many states ranging from perfect functioning to complete failure. Our survey updates and complements a previous survey by El-Neweihi and Proschan (1980). Some new results are included.
TL;DR: In this paper, the authors defined a similar statistic T (based on samples s with observations censored only on one side) and showed that this stat is tic is more powerful than T and nonparametric statistics, C for skew populations.
Abstract: For testing the equality of means (location parameters) of two populations, Tiku (1980a) defined a statistic Tc (based on symmetrically censored samples) and showed that this statistic is robust to underlying populations and is also remarkably powerful. In this paper, we define a similar statistic T (based on samples s with observations censored only on one side) and show that this stat is tic is more powerful than T and nonparametric statistics, C for skew populations. We also provide a modification of this statistic for testing the equality of two population variances.
TL;DR: In this paper, a quantification of the amount of robustness of the two-sample t-test procedure under violations of the assuaptioo of equal variances is presented.
Abstract: When the two-sample t-test has equal sample slies, it is widely considered to be a robust procedure (with respect to the significaoce level) under violatioa of the assuaptioo of equal variances. This paper is coa-earned with a quantification of the amount of robustness which this procedure has under such violations, The approach is through the concept of "religion of robustness" and the resluts show an extremely strong degree of robustness for the equal an extremely strong degree of robustness for the equal sample size t-test, probably more so than most statistyicians realise. This extremely high level of robustness, however, reduces quickly as the sample sizes begin to vary from equality. The regions of robustnes obtained show that while most users would likely be satisfied with the degree of robustness inherent when the two sample sizes each vary by 10% from equality, most would wish to be much more cautions when the variation is 20%. The study covers sample sizes n1 -= n 2 = 5(5)30(10)50 plus 10% and 2...
TL;DR: In this article, the use of several robust estimators of location with their associated variance estimates in a modified T-method for pairwise multiple comparisons between treatment means was compared with the sample mean and variance and with the k-sample rank sum test.
Abstract: The use of several robust estimators of location with their associated variance estimates in a modified T-method for pairwise multiple comparisons between treatment means was compared with the sample mean and variance and with the k-sample rank sum test. The methods were compared with respect to the stability of their experimentwise error rates under a variety of non-normal situations (robustness of validity) and their average confidence interval lengths (robustness of efficiency).
TL;DR: In this article, a four-parameter directional exponential family is discussed, and the moments of this distribution are found, and equations leading to maximum-likelihood estimates of the parameters along with an outline on numerical procedures for solving these equations are given.
Abstract: Directional distribution theory is very useful for the estimation of directional spectra needed for the analysis of time series data. A four parameter directional exponential family is discussed. Depending on the values of its parameters this distribution can be unimodal symmetric, bimodal symmetric, unimodal non-symmetric, or bimodal non-symmetric. The moments of this distribution are found, and equations leading to maximum-likelihood estimates of the parameters along with an outline on numerical procedures for solving these equations are given. FORTRAN subroutines implementing these procedures are available from the authors. Finally, some applications of the new directional density are given.
TL;DR: In this article, a product is considered when the product is a p component series system with WeibuH distributed component lifetimes liaving a caimon shape parameter and a general stress translation function is used and estimates of model parameters are obtained for various censoring schemes.
Abstract: Accelerated life testing of a product under more severe than normal conditions is cawiionly used to reduce test time and cost. Data collected at such accelerated conditions is used to obtain estimates of parameters of a stress translation function which is then used to make inference about the product's, per" formance under normal conditions. This problem is considered when the product is a p component series system with WeibuH distributed component lifetimes liaving a caimon shape parameter. A general stress translation function is used and estimates of model parameters are obtained for various censoring schemes.
TL;DR: Extensions to Cox's proportional hazards regression model (Cox, 1972) for the analysis of survival data are considered for a more general multistate framework in this article, allowing several transient disease states between initial entry state and death as well as incorporating possible competing causes of death.
Abstract: Extensions to Cox's proportional hazards regression model (Cox, 1972) for the analysis of survival data are considered for a more general multistate framework. This framework allows several transient disease states between initial entry state and death as well as incorporating possible competing causes of death. Methods for parameter and function estimation within this extension are presented and applied to the analysis of data from the Stanford Heart Transplantation Program (Crowley and Hu,1977).
TL;DR: In this paper, confidence intervals of prescribed width for the lo-cation parameter of an exponential distribution are obtained for the coverage probability and expected sample size, from which an asymptotic expression for the variance of the sample size is deduced.
Abstract: We study confidence intervals of prescribed width for the lo-cation parameter of an exponential distribution. Asymptotic expan-sions up to terms tending to zero are obtained for the coverage probability and expected sample size. The limiting distribution of the sample size is given from which an asymptotic expression for the variance of the sample size is deduced. Sequential procedures with non-asymptotic coverage probability are also investigated
TL;DR: In this article, the exact critical points for the analysis of means are given for k means with degrees of freedom m and level of significance a for k = 3(1)20, 24, 30, 40, 60 m = k(l)20.
Abstract: Tables of the exact critical points for the analysis of means are given for k means with degrees of freedom m and level of significance a for k = 3(1)20, 24, 30, 40, 60 m = k(l)20, 24, 30, 40, 60, 120, ∞ α = 0.10, 0.05, 0.01.
TL;DR: In this article, a method for selecting a distributional model for a random variable, given a random sample of observations of it, is studied for various cases, including those of choosing between the Weibull and lognormal distributions, between the Lognormal and gamma distributions, and between the gamma and Weiball distributions, as well as choosing one of the three.
Abstract: A method for selecting a distributional model for a random variable, given a random sample of observations of it, is studied for various cases. The problems considered include those of choosing between the Weibull and lognormal distributions, between the lognormal and gamma distributions, and between the gamma and Weibull distributions, as well as choosing one of the three. Simulation studies were performed to estimate probabilities of correct selection for the method when it is applied to these problems
TL;DR: In this paper, the authors developed a "robust" statistic T2 R, based on Tiku's (1967, 1980) MML estimators of location and scale parameters, for testing an assumed meam vector of a symmetric multivariate distribution.
Abstract: We develop a ‘robust’ statistic T2 R, based on Tiku's (1967, 1980) MML (modified maximum likelihood) estimators of location and scale parameters, for testing an assumed meam vector of a symmetric multivariate distribution. We show that T2 R is one the whole considerably more powerful than the prominenet Hotelling T2 statistics. We also develop a robust statistic T2 D for testing that two multivariate distributions (skew or symmetric) are identical; T2 D seems to be usually more powerful than nonparametric statistics. The only assumption we make is that the marginal distributions are of the type (1/σk)f((x-μk)/σk) and the means and variances of these marginal distributions exist.
TL;DR: In this article, the one-way ANOVA model with common variance was considered and the Simultaneous Confidence Intervals (SCI) for monotone contrasts in the means were derived and compared to alternative intervals gene-rated by Williams (1977)
Abstract: The one-way ANOVA model with common variance is considered. Simultaneous confidence Intervals (SCI) for monotone contrasts in the means are derived and compared to alternative intervals gene¬rated by Williams (1977)
TL;DR: In this paper, further distributions arising from models of errors in inspection and grading of samples from finite, possibly stratified lots are obtained, and the effects of errors on the advantages of these techniques assessed.
Abstract: Continuing the studies of Johnson et al (1980) and Johnson and Kotz (1981), further distributions arising from models of errors in inspection and grading of samples from finite, possibly stratified lots are obtained. Screening, and hierarchal screening forms of inspection are also considered, and the effects of errors on the advantages of these techniques assessed.
TL;DR: In this paper, the joint distribution of a linear and-a quadratic form and two Quadratic forms are obtained when the sample is taken from a mixture of two p-co»ponent multivariate normal distributions with mean JJ.
Abstract: In this paper, the joint distribution of (a) a linear and-a quadratic form, and (b) two quadratic forms are obtained when the sample is taken from a mixture of two p-co»ponent multivariate normal distributions with mean JJ. and JJ« respectively and common covarlaece matrix Z # Also the distribution of Hotelling's t2-statistic is obtained when irji- + (1-ir)^ - j) t where w f O^i^l f Is the mixing proportion (contamination, 1-w). Actual values of a (level of significance) when nominal level a Is 0»05 are computed for some particolar combination of parameters* These results show that the si2e of the test can differ greatly even for a contan-ination as small as 0,05 if the Mahalanobis (square) distance Is large and/or the sample size Is large