Showing papers in "Communications in Statistics-theory and Methods in 1984"
TL;DR: In this paper, a Ridge type estimator is proposed that will have smaller total mean squared error than the maximum likelihood estimator under certain conditions, and empirical study results are presented that evaluate this estimator for different sample sizes and degrees of multicollinearity.
Abstract: It is found that multicollinearity among the independent variables in logistic regression inflates the variances of the maximum likelihood estimator. A Ridge type estimator is proposed that will have smaller total mean squared error than the maximum likelihood estimator under certain conditions. Empirical study results are presented that evaluate this estimator for different sample sizes and degrees of multicollinearity.
211 citations
TL;DR: In this article, a simple and effective method of modifying a kernel regression estimate near the boundary is proposed to ensure that the bias and variance near boundary are of the same order of magnitude as in the interior.
Abstract: We present a simple and effective method of modifying a kernel regression estimate near the boundary. The modification ensures that the bias and variance near the boundary are of the same order of magnitude as in the interior.
204 citations
TL;DR: The g and h family of distributions, introduced by J.W. Tukey, is generated by a single transformation of the standard normal which allows for symmetry and heavier tails.
Abstract: The g and h family of distributions, introduced by J.W. Tukey, is generated by a single transformation of the standard normal which allows for symmetry and heavier tails. Selected percentage points are tabulated, and a closed-form solution for the moments, when they exist, is found. A comparison is made with the Pearson system of distributions. The g and h distributions cover most of the Pearson family to an adequate approximation, when the first four moments exist, and also generate a variety of other types of distributions. Selected distributions graphically illustrate the great variety of possible shapes.
151 citations
TL;DR: In this article, the authors considered the modal position (i-1)/(n-1) and the mean position i/(n+1) [the latter proposed by Weibull (1939a,b), and chose the latter.
Abstract: Probability paper was used as early as 1896, and was mentioned in the literature more than 30 times before 1950, mainly by hydrologists, most of whom used the plotting position (i-0.5)/n proposed by Hazen (1914). Gumbel (1942a) considered the modal position (i-1)/(n-1) and the mean position i/(n+1) [the latter proposed by Weibull (1939a,b)], and chose the latter. Lebedev (1952) and others proposed the use of (i-0.3)/(n+0.4), which is approximately the median position advocated by Johnson (1951). Blom (1958) sug-gested (i-α)/(n-2α+1), where a is a constant (usually 0 ≤ α ≤ 1), which includes all of the above plotting positions as special cases. Moreover, by proper choice of α, one can approximate F[E(xi)], the position proposed by Kimball (1946), for any distri-bution of interest. Gumbel (1954) stated five postulates which plotting positions should satisfy. Chernoff & Lieberman (1954) discussed the optimum choice of plotting positions in various situ-ations. It is clear that the optimum plotting position d...
95 citations
TL;DR: The Breslow estimator, a shrinkage version of the Kaplan-Meier estimator as mentioned in this paper, nearly always has the smaller mean square error (MSE) whenever the truesurvival probability is at least 0.20, but has considerably larger MSE when the survival probability is near zero.
Abstract: Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.
94 citations
TL;DR: In this article, a class of estimators, including ordinary least squares, ordinary ridge regression, and principal components regression, are examined, and it is demonstrated that gains exist from jointly utilizing the PCR and ORR techniques.
Abstract: In this paper we examine a class of estimators which includes ordinary least squares, ordinary ridge regression, and principal components regression. It is demonstrated that gains exist from jointly utilizing the PCR and ORR techniques.A money demand example is utilized to illustrate alternative estimators.
91 citations
TL;DR: This article examined the effect of imputation variance on the precision of the mean, and proposed four procedures for sampling the respondents that reduce this additional variance, including selection of respondents through selection of respc,ndents by sampling without replacement and by stratified sampling.
Abstract: Imputation methods that assign a selection of respondents’ values for missing i tern nonresponses give rise to an addd,tional source of sampling variation, which we term imputation varLance , We examine the effect of imputation variance on the precision of the mean, and propose four procedures for sampling the rEespondents that reduce this additional variance. Two of the procedures employ improved sample designs through selection of respc,ndents by sampling without replacement and by stratified sampl;lng. The other two increase the sample base by the use of multiple imputations.
76 citations
TL;DR: In this paper, the density estimators from censored data that have been obtained to date are outlined and all known results concerning nonparametric hazard rate estimation from censored samples are also briefly mentioned.
Abstract: Nonparametric estimation of the probability density function f° of a lifetime distribution based on arbitrarily right-censor-ed observations from f° has been studied extensively in recent years. In this paper the density estimators from censored data that have been obtained to date are outlined. Histogram, kernel-type, maximum likelihood, series-type, and Bayesian nonparametric estimators are included. Since estimation of the hazard rate function can be considered as giving a density estimate, all known results concerning nonparametric hazard rate estimation from censored samples are also briefly mentioned.
65 citations
TL;DR: In this article, a continuous multivariate exponential distribution is introduced which can model a full range of correlation structures and attains the Frechet bounds in the bivariate case, is easy to simulate, arises as a model for reliability and failure due to shocks, and is analogous to the multivariate normal distribution.
Abstract: A continuous multivariate exponential distribution is introduced which can model a full range of correlation structures and attains the Frechet bounds in the bivariate case, is easy to simulate, arises as a model for reliability and failure due to shocks, and is analogous to the multivariate normal distribution. Two examples are given in which it models data satisfactorily
65 citations
TL;DR: In this paper, the authors describe decision making procedures as they exist in most clinical trials, review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.
Abstract: In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.
63 citations
TL;DR: In this paper, an asymptotic distribution theory for the state estimate from a Kalman filter in the absence of the usual Gaussian assumption is presented, where the stability properties of the state transition matrix play a key role in the distribution theory.
Abstract: An asymptotic distribution theory for the state estimate from a Kalman filter in the absence of the usual Gaussian assumption is presented It is found that the stability properties of the state transition matrix playa key role in the distribution theory Specifically, when the state equation is neutrally stable (ie, borderline stable-unstable) the state estimate is asymptotically normal when the random terms in the model have arbitrary distributions This case includes the popular random walk state equation However, when the state equation is either stable or unstable, at least some of the random terms in the model must be normally distributed beyond some finite time before the state estimate is asymptotically normal
TL;DR: The literature pertaining to splines in regression analysis is reviewed in this paper, where the concepts of fixed and variable knot spline regression are developed and corresponding inferential procedures are considered.
Abstract: The literature pertaining to splines in regression analysis is reviewed. Spline regression is motivated as a simple extension of the basic polynomial regression model. Using this framework, the concepts of fixed and variable knot spline regression are developed and corresponding inferential procedures are considered. Smoothing splines are also seen to be an extension of polynomial regression and various optimality properties, as well as inferential and diagnostic methods, for these types of splines are discussed.
TL;DR: In this article, general methods not dependent on the sequential nature of time are considered for estimating the parameters of Gaussian processes, and an example is given in which a variable is measured at locations in time or space the observed data can be regarded as incomplete, the missing data sites completing a regular pattern such as a rectangular grid.
Abstract: In many situations in which a variable is measured at locations in time or space the observed data can be regarded as incomplete, the missing data sites perhaps completing a regular pattern such as a rectangular grid. In this paper general methods not dependent on the sequential nature of time are considered for estimating the parameters of Gaussian processes. An example is given.
TL;DR: In this article, the authors present several methods for full, partial, and practical adaptation of selector statistics that are measures of skewness, peakedness, and tailweight, primarily in estimating loca-tion in some single-sample situations.
Abstract: We present several methods for full, partial, and practical adaptation. Selector statistics that are measures of skewness, peakedness, and tailweight are used, primarily in estimating loca-tion in some single-sample situations. We note several practical adaptive techniques in current use, including illustrations in-volving stepwise regression, analysis of variance, ridge regres-sion, and splines. We suggest some areas in which future develop-ment of adaptive methods is needed:density estimation; M, R, and L estimation in regression; and dependent data. There is also a need to develop better selector statistics.
TL;DR: In this paper, the authors reviewed the experience of several recent clinical trials and showed that the decision process to terminate a trial early is very complex and many factors must be taken into account.
Abstract: Monitoring interim accumulating data in a clinical trial for evidence of therapeutic benefit or toxicity is a frequent policy, usually carried out by an independent scientific committee. While statistical methodology has been developed to assess the significance of these interim analyses, such methods should not be viewed as absolute rules but only serve as useful guides. The decision process to terminate a trial early is very complex and many factors must be taken into account. The complexity of this decision process is illustrated by reviewing the experience of several recent clinical trials.
TL;DR: A derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks are presented and a general likelihood function is obtained.
Abstract: Boag (1949) and Berkson and Gage (1952) proposed a mixture model for the analysis of survival time data when aproportion of treated patients are cured. This paper presents a derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks. The assumptions underlying the model are stated and discussed and a general likelihood function is obtained. Use of the model is illustrated ith data from the Stanford Heart Transplant Program.
TL;DR: In this paper, a method of constructing maps through spatial discrimination is given, which depends basically on the assumption of local spatial continuity, and a factorized covariance matrix, given an autocovariance function, which leads to a deeper insight into the pioneering work of Switzer (1980).
Abstract: A method of constructing maps through spatial discrimination is given. The discrimination depends basically on the assumption of local spatial continuity, and a factorized covariance matrix. Given an autocovariance function, this formulation in particular, leads to a deeper insight into the pioneering work of Switzer (1980). Certain windows for the maps are examined, and choice of window size is discussed in relation to the classification error when the variables are dependent versus independent. When a training data is given, we give a method of estimating the parameters in the model. Some numerical examples are also given.
TL;DR: In this article, the authors proposed a method to estimate the unknown mean by a testimator that is based upon the result of a test of the hypothesis if H0 is accepted based on the first sample of size n1, where the weighing factor k is a function of the test statistic for testing H0.
Abstract: Let X be distributed normally with unknown mean μ and known variance σ2. Further, it is assumed that prior knowledge about μ is available in the form of an initial estimate μ0 of μ. It A is proposed to estimate the unknown mean by a testimator that is based upon the result of a test of the hypothesis If H0 is accepted based on the first sample of size n1 we take where the weighing factor k is a function of the test statistic for testing H0. However, if H0 is rejected, we obtain a second sample of size n2, and take . Choosing an expression for the mean square error of is derived and comparisons are made with variance of a single sample mean. The case when the variance σ2 is unknown is also considered.
TL;DR: In this paper, a review of goodness-of-fit tests for one and two parameter exponential models using both complete and censored samples is presented, with special attention given to both the omnibus or general alternative and to specialized alter-natives such as the class of distributions with increasing failure rates.
Abstract: Developments since 1960 in goodness-of-fit tests for the one and two parameter exponential models using both complete and censored samples are reviewed. Special attention is given to both the omnibus or general alternative and to specialized alter-natives such as the class of distributions with increasing failure rates. The use of transformations in developing tests is also discussed.
TL;DR: In this paper, a brief overview of the ethics of interim analysis of accumulating data and the complexity of decision making for early termination is given and some discussion as to why they have not been adopted.
Abstract: This manuscript gives a brief overview of the ethics of interim analysis of accumulating data and the complexity of decision making for early termination. A review of previously proposed sequential methods for data monitoring is given and some discussion as to why they have not been adopted. Finally, attention is focused on two recent concepts, group sequential boundaries and stochastic curtailment, which have promise in their applicability and utility.
TL;DR: In this paper, the authors investigated the relationship between the size of the 1inear trend test in proportions Cochran, 1954; Armitage, 1955 and the design of the chronic animal bioassays used as cancer screens.
Abstract: This paper investigates the relationship between the size of the 1inear trend test in proportions Cochran, 1954; Armitage, 1955 and the design of the chronic animal bioassays used as cancer screens. The results indicate that an improper design choice can cause the true size of the test to deviate from its nominal value. These results extend to modifications of the test, including versions which correct for differential survival and continuity.
TL;DR: In this paper, a modification of the Kruskal-Wallis test statistic is proposed which is exactly distribution-free under the usual nonparanetric asswnption that the continuous populations are identical with any shape.
Abstract: The problem of testing the equality of the medians of several populations is considered. Standard distribution-free procedures for this problem require that the populations have the same shape in order to maintain their nominal significance level, ever asymptotically, under the null hypothesis of equal medians , A modification of the Kruskal-Wallis test statistic is proposed which is exactly distribution-free under the usual nonparanetric asswnption that the continuous populations are identical with any shape. It is asymptotically distribution-free when the Continuous populations are asswned to be syrmnetric with equal medians.
TL;DR: In this paper, the exact forms of the p.d.f. and the moments of the rth order statistics in a sample of size n from the Log-logistic (Ll ) distribution were derived.
Abstract: The aim of this paper is to derive the exact forms of the p.d.f. and the moments of the rth order statistics in a sample of size n from the Log-logistic (Ll ) distribution. Measures of skewness and kurtosis are tabulated. The recurrence relations between the moments of all order statistics and an expression of the covariance between any two order statistics, xi and xjand the distribution of the ratio of Xi to xj are derived.
TL;DR: In this article, the problem of admissible maximum likelihood estimators for for the parameters is discussed and a necessary and sufficient condition is derived for which unique admissible estimators exist.
Abstract: The generalized Poisson distribution;containing two parameters and studied by many researchers; describes the distribution of busy periods under a queueing system and has very interesting properties; The probabilities for successive classes depend upon the previous occurrences; The problem of admissible maximum likelihood estimators for for the parameters Is discussed and a necessary and sufficient condition is derived for which unique admissible maximum likelihood estimators exist; The first; order terms in the biases; variances and the covariance of these maximum likelihood estimators are obtained.
TL;DR: Magda as mentioned in this paper proved the universal optimality of circular balanced uniform designs over a subclass of the possible designs, and strengthened this result to optimality over the set of all designs with the same number of experimental units, periods and treatments.
Abstract: Magda (1980) introduced a model for repeated measurements designs with a circular structure of the residual effects. He proved the universal optimality of circular balanced uniform designs over a subclass of the possible designs. We strengthen his result to optimality over the set of all designs with the same number of experimental units, periods and treatments.
TL;DR: In this article, a statistical procedure to test that a life distribution is exponential against the native that it is continuous new better than used in expectation is presented, and the test is shown to be consistent and asymptotic relative efficiency resul ts are obtained against the competitor developed earlier by Hollander and Proschan for certain families of alternatives.
Abstract: We present a statistical procedure to test that a life distribution is exponential against the al ternative that it is continuous new better than used in expectation. The test is shown to be consistent and asymptotic relative efficiency resul ts are obtained against the competitor developed earlier by Hollander and Proschan [2], for certain families of alternatives.
TL;DR: Stochastic approximation procedures are sequential estimation methods which provide estimates for the point at which a general regression function attains a given value as mentioned in this paper. But their application to the problem of estimating the median effective does in bioassay and to estimating the maximally tolerated does in phase I clinical trials is discussed.
Abstract: Stochastic approximation procedures are sequential estimation methods which provide estimates for the point at which a general regression function attains a given value. The application of such methods to the problem of estimating the median effective does in bioassay and to the problem of estimating the maximally tolerated does in phase I clinical trials is discussed. it is argued that these methods could be very useful in practice.
TL;DR: This article reviewed statistical tests and procedures which aid the experimenter in deterrmining lack of fit or functional misspecification associated with the deterministic portion of a proposed linear regression model.
Abstract: Assessment of the adequacy of a proposed linear regression model is necessarily subjective. However, the following three criteria may warrant investigation whether the distributional assumptions for the stochastic portion of the model are satisfied, whether the predictive capability of the model is satisfactory, and whether the deterministic portion of the model is adejuate in a statistical sense. The first two criteria have been reviewed in the literature to some extent. This paper reviews statistical tests and procedures which aid the experimenter in deterrmining lack of fit or functional misspecification associated with the deterministic portion of a proposed linear regression model.
TL;DR: A flexible sequential approach to the design of clinical trials is discussed herein, based on a “confidence sequence” viewpoint instead of the rigid stopping and terminal decision rules in conventional sequential testing theory.
Abstract: A flexible sequential approach to the design of clinical trials is discussed herein. This approach is based on a “confidence sequence” viewpoint instead of the rigid stopping and terminal decision rules in conventional sequential testing theory. By using an appropriate confidence sequence, one can always ensure a prescribed degree of scientific rigor (confidence) in establishing the drug to be effective. Moreover, one also has the option of terminating the trial early when there is already enough statistical evidence for concluding that the drug is effective, or when the drug shows uniorseen harmful effects, or when the data predict that there is little chance of arriving at a definitive conclusion in favor of the drug by the scheduled end of the trial. We discuss how these and other ethical and economic considerations can be readily incorporated into the stopping criteria of the trial.
TL;DR: In this paper, a Consistent Adjusted Least Squares (CALS) estimator is proposed for a single equation errors-in-variables model and its asymptotic distribution is given.
Abstract: A single equation errors-in-variables model is considered. Exact restrictions on the parameters in the model are assumed to be available such that the model is just-identified. A Consistent Adjusted Least Squares (CALS) estimator for this model is proposed and its asymptotic distribution is given. Special cases are given as illustrations. CALS is identical to the Method of Moments (MM), and to Maximum Likelihood (ML) under the structural interpretation. Under the functional interpretation it is identical to ML in cases where the latter method is consistent.