Showing papers in "Journal of the American Statistical Association in 1975"
TL;DR: Kerlinger and Pedhazur as discussed by the authors present the three main applied analytical models which derive from the general linear hypothesis-analysis of variance, regression, and analysis of covariance.
Abstract: One of the dilemmas facing those who teach sociological methods and statistics these days is how to present the three main applied analytical models which derive from the general linear hypothesis-analysis of variance, regression, and analysis of covariance. The reason for this dilemma is that whereas there now exist in the sociological literature a number of theoretical expositions integrating these various models, nowhere has there existed a reference or, for that matter, a set of references which provided the computational integration in sufficient clarity that the teacher could assign them to his class and be assured that the student would obtain a clear picture of how the three models were computationally interrelated and interchangeable. Kerlinger and Pedhazur have painstakingly provided such a resource. For those looking for such a text (or reference book), it is a teacher's delight! The authors provide one with a consistency of framework which opens in Part 1 (five chapters). Those chapters are a review of the foundations of multiple regression and can be easily read by students who have had an introductory course in statistics. The review is, however, more than just a rehash of regression theory and procedures, as the authors are also developing a framework for the later integration of analysis of variance, analysis of covariance, time series analysis, path analysis and multivariate analysis (multivariate analysis of variance, canonical regression, and discriminant analysis). Part 2, which consists of six chapters, is the focal point of the book. For example, chapters 5, 6, and 7 give an introduction to the use of dummy coding to achieve the same results as one gets in one-way analysis of variance. Chapter 8 extends the procedures to multiple categorical variables and how they can be handled in the multiple regression framework to achieve the same results one would obtain via ANOV computational procedures in factorial designs. Chapter 9 departs from this theme to open considerations of testing for linear and curvilinear regression when working with continu'ous variables. Chapter 10 weaves these considerations into those developed earlier regarding categorical variables and discusses regression procedures for handling both continuous and categorical regressors in the same equation. (I have found this to be a topic of great interest among sociology students who wonder how to use
4,811 citations
TL;DR: A recently devised method of prediction based on sample reuse techniques that is most useful in low structure data paradigms that involve minimal assumptions is presented.
Abstract: An account is given of a recently devised method of prediction based on sample reuse techniques. It is most useful in low structure data paradigms that involve minimal assumptions. A series of applications demonstrating the technique is presented.
2,278 citations
TL;DR: The effect of interventions on a given response variable in the presence of dependent noise structure is discussed and some properties of the maximum likelihood estimators of parameters measuring level changes are discussed.
Abstract: This article discusses the effect of interventions on a given response variable in the presence of dependent noise structure. Difference equation models are employed to represent the possible dynamic characteristics of both the interventions and the noise. Some properties of the maximum likelihood estimators of parameters measuring level changes are discussed. Two applications, one dealing with the photochemical smog data in Los Angeles and the other with changes in the consumer price index, are presented.
2,270 citations
TL;DR: In this paper, the authors consider a model in which one observes multiple indicators and multiple causes of a single latent variable and derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix.
Abstract: We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to psychometricians. We derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix. Two alternative “limited information” estimators are also considered and compared with the maximum-likelihood estimators in terms of efficiency.
1,453 citations
1,378 citations
TL;DR: In this paper, a simplified computational scheme is given and extended to mixed regressive-autoregressive models for spatial interaction, and the ML estimator is compared with several alternatives.
Abstract: Autoregressive models for spatial interaction have been proposed by several authors (Whittle [15] and Mead [11], for example). In the past, computational difficulties with the ML approach have led to the use of alternative estimators. In this article, a simplified computational scheme is given and extended to mixed regressive-autoregressive models. The ML estimator is compared with several alternatives.
1,308 citations
949 citations
TL;DR: In this article, the mean of a multivariate normal distribution having uniformly lower mean squared error than the sample mean is reviewed briefly in an empirical Bayes context and applied to predict baseball averages, to estimate toxomosis prevalence rates, and to estimate the exact size of Pearson's chi-square test with results from a computer simulation.
Abstract: In 1961, James and Stein exhibited an estimator of the mean of a multivariate normal distribution having uniformly lower mean squared error than the sample mean. This estimator is reviewed briefly in an empirical Bayes context. Stein's rule and its generalizations are then applied to predict baseball averages, to estimate toxomosis prevalence rates, and to estimate the exact size of Pearson's chi-square test with results from a computer simulation. In each of these examples, the mean square error of these rules is less than half that of the sample mean.
832 citations
TL;DR: This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and expensive and expensive process of manually cataloging and forecasting the distribution of distributions in a discrete-time manner.
Abstract: Preface 1. Introduction 2. Predictive distributions 3. Decisive prediction 4. Informative prediction 5. Mean coverage tolerance prediction 6. Guaranteed coverage tolerance prediction 7. Other approaches to prediction 8. Sampling inspection 9. Regulation and optimisation 10. Calibration 11. Diagnosis 12. Treatment allocation Appendix Bibliography Author Index Subject Index Example and problem index.
778 citations
TL;DR: In this article, the asymptotic relative efficiency of the normal discrimination procedure and logistic regression is compared, and it is shown that the latter procedure is between one half and two thirds as effective as normal discrimination for statistically interesting values of the parameters.
Abstract: A random vector x arises from one of two multivariate normal distributions differing in mean but not covariance. A training set x 1, x 2, ··· x n of previous cases, along with their correct assignments, is known. These can be used to estimate Fisher's discriminant by maximum likelihood and then to assign x on the basis of the estimated discriminant, a method known as the normal discrimination procedure. Logistic regression does the same thing but with the estimation of Fisher's disriminant done conditionally on the observed values of x 1 x 2, ···, x n . This article computes the asymptotic relative efficiency of the two procedures. Typically, logistic regression is shown to be between one half and two thirds as effective as normal discrimination for statistically interesting values of the parameters.
547 citations
TL;DR: In this article, two analytic methods of specifying k are proposed and evaluated in terms of mean square error by Monte Carlo simulations, with three explanatory variables and determined by the largest eigenvalue of the correlation matrix.
Abstract: Consider the standard linear model . Ridge regression, as viewed here, defines a class of estimators of indexed by a scalar parameter k. Two analytic methods of specifying k are proposed and evaluated in terms of mean square error by Monte Carlo simulations. With three explanatory variables and determined by the largest eigenvalue of the correlation matrix, least squares is dominated by these estimators in all cases investigated; however, mixed results are obtained with determined by the smallest eigenvalue. These estimators compare favorably with other ridge-type estimators evaluated elsewhere for two explanatory variables.
TL;DR: It is argued that since man is a selective, sequential information processing system with limited capacity, he is ill-suited for assessing probability distributions, and the importance of task characteristics on judgmental performance is also emphasized.
Abstract: This article considers the implications of recent research on judgmental processes for the assessment of subjective probability distributions. It is argued that since man is a selective, sequential information processing system with limited capacity, he is ill-suited for assessing probability distributions. Various studies attesting to man's difficulties in acting as an “intuitive statistician” are summarized in support of this contention. The importance of task characteristics on judgmental performance is also emphasized. A critical survey of the probability assessment literature is provided and organized around five topics: (1) the “meaningfulness” of probability assessments; (2) methods of eliciting distributions; (3) feedback and evaluation of assessors; (4) differential ability of groups of assessors and (5) the problems of eliciting a single distribution from a group of assessors. Conclusions from the analysis with respect to future work include the need to capitalize on cognitive simplific...
TL;DR: In this article, simple one-step versions of Huber's (M) estimates for the linear model are introduced, and the large sample behavior of these procedures is examined under very mild regularity conditions.
Abstract: Simple “one-step” versions of Huber's (M) estimates for the linear model are introduced. Some relevant Monte Carlo results obtained in the Princeton project [1] are singled out and discussed. The large sample behavior of these procedures is examined under very mild regularity conditions.
TL;DR: In this article, a new kind of Bayesian motivated procedure is introduced which leads to a strongly consistent estimator for median effective dose in bioassay with a normal quantal response curve.
Abstract: This article is concerned with a generalization of the problem of estimation of median effective dose in bioassay with a normal quantal response curve. A new kind of Bayesian motivated procedure is introduced which leads to a strongly consistent estimator. The convergence is robust in that it holds for a bundle of sequences of design vectors—an important feature in a mental testing context where a specified design vector cannot be produced on demand.
TL;DR: In this paper, the power of multiple comparisons procedures for fixed maximal experimentwise levels was studied for fixed-maximal experimentwise level, and the authors generally recommend the Tukey technique for its elegant simplicity and existent confidence bounds, which is little below that of any other method.
Abstract: Powers of multiple comparisons procedures are studied for fixed maximal experimentwise levels. Analytical considerations show Tukey-Scheffe methods to have least power, Duncan's to be intermediate, Ryan's most powerful. (Newman-Keuls tests could preserve experimentwise levels only if modified radically and impractically.) Extensive Monte-Carlo trials show these power differences to be small, especially for range statistics. We therefore generally recommend the Tukey technique for its elegant simplicity and existent confidence bounds—its power is little below that of any other method. Simulation was for 3, 4 and 5 treatments: the conclusions might need modification for more treatments.
TL;DR: In this paper, the authors investigated the likelihood ratio method for confidence interval estimation of survival or life-time probabilities for censored data, which depends on a constrained product-limit estimator for the survival function.
Abstract: The likelihood ratio method for confidence interval estimation of survival or life-time probabilities is investigated for censored data. This approach depends on a constrained product-limit estimator for the survival function. The likelihood method is compared with two alternative methods based on normal approximations to the product-limit estimator for several cases of uncensored and randomly censored samples. The methods are generalized for the ratio of two survival probabilities.
TL;DR: The concept of power for monotone invariant clustering procedures is developed via the possible partitions of objects at each iteration level in the obtained hierarchy in this article, and the probability of rejecting the randomness hypothesis is obtained empirically for the possible types of partitions of the n objects employed.
Abstract: The concept of power for monotone invariant clustering procedures is developed via the possible partitions of objects at each iteration level in the obtained hierarchy. At a given level, the probability of rejecting the randomness hypothesis is obtained empirically for the possible types of partitions of the n objects employed. The results indicate that the power of a particular hierarchical clustering procedure is a function of the type of partition. The additional problem of estimating a “true” partition at a certain level of a hierarchy is discussed briefly.
TL;DR: This paper proposed a new family of compound Poisson distributions as a model for word frequency counts, which was applied to a variety of data over the entire length of the observed word distributions.
Abstract: In the past, several attempts were made to represent word frequency counts by statistical distribution laws. Of the models suggested, none was singularly successful when applied to a variety of data over the entire length of the observed word distributions. In this article, a new family of compound Poisson distributions [9, 10] is proposed as a model for word frequency counts. Twenty observed distributions quoted in the literature were fitted and the results look most encouraging.
TL;DR: A method is proposed for estimating the likelihood ratio classification rule in practical situations and assessing its performance, and its performance is compared with that of some other classification rules.
Abstract: The likelihood ratio classification rule is derived from the location model, applicable when the data contains both binary and continuous variables. A method is proposed for estimating the rule in practical situations and assessing its performance. Losses incurred by the estimation procedure are investigated, and use of Fisher's linear discriminant function on such data is studied for the case of known population parameters. Finally, the proposed rule is applied to some data sets, and its performance is compared with that of some other classification rules.
TL;DR: In this article, an estimator of heteroscedastic variances in the Gauss-Markov linear model where E(e) = 0 and with σ i 2 and unknown is described.
Abstract: We describe an estimator of heteroscedastic variances in the Gauss-Markov linear model where E(e) = 0 and with σ i 2 and unknown. It may be thought of as an approximation to the MINQUE method which results in computational economy, positive estimates, and decreased mean square error. Properties of this almost unbiased estimator are stated. It is compared with other estimators, and extensions to more general models are discussed.
TL;DR: In this article, the existence of bias, its effect on both ratio estimates and composite estimates, and a comparison of the estimated mean-square errors of ratio and composite estimate are illustrated with data from the Current Population Survey.
Abstract: Evidence is available from many different kinds of surveys that repeated interviewing of the same persons can frequently change response patterns. For many characteristics, estimates from different panels relating to the same time period do not have the same expected value. In panel surveys, estimation techniques frequently take advantage of the correlation between observations on identical persons over time. The existence of a bias, its effect on both ratio estimates and composite estimates, and a comparison of the estimated mean-square errors of ratio and composite estimates are illustrated with data from the Current Population Survey.
TL;DR: In this paper, an iterative reclassification procedure based on the n 1 + n 3 + M observations is proposed and found asymptotically optimal when M → ∞ and n 1 and n 2 are moderately large.
Abstract: The construction of a suitable rule of allocation in the two-population discrimination problem is considered in the case where there are initially available from the populations II1, II2, n 1, n 2 observations and M unclassified observations. An iterative reclassification procedure based on the n 1 + n 3 + M observations is proposed and found asymptotically optimal when M → ∞ and n 1 and n 2 are moderately large. The case of finite M is evaluated by a Monte Carlo experiment which suggests that the proposed procedure, after only one iteration, gives a rule with smaller average risk than the usual rule based on just the n 1 + n 2 classified observations.
TL;DR: In this article, the coefficient vectors are treated as random drawings from a continuous multivariate distribution, and an approximate Bayesian solution is proposed to solve the problem of discontinuous shifts in regression regimes at unknown points in the data series.
Abstract: Quandt [20] analyzed the problem of discontinuous shifts in regression regimes at unknown points in the data series. We note that Quandt's statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method based on a proper prior distribution of the unknown parameters yields sensible results. However, the exact evaluation of the posterior distribution is unusually burdensome and cannot be simplified even in large samples. To avoid this difficulty, we suggest an alternative formulation and provide an approximate Bayesian solution. In this alternative formulation, the coefficient vectors are treated as random drawings from a continuous multivariate distribution.
TL;DR: This model, using methods already developed for the study of quasi-independence in contingency tables, is shown how to test whether the model fits the observed data, estimate the proportion of intrinsically scalable (and unscalable) individuals, and estimate the distribution of the intrinsically scalable individuals among the d different scale types.
Abstract: To analyze the “scalability” of the observed response patterns for a set of m dichotomous items, we introduce a model in which a given individual in the population is either “intrinsically scalable” or “intrinsically unscalable” (with respect to the m items), and there are d different types of “intrinsically scalable” individuals. With this model, using methods already developed for the study of quasi-independence in contingency tables, we show how to (a) test whether the model fits the observed data, (b) estimate the proportion of intrinsically scalable (and unscalable) individuals, and (c) estimate the distribution of the intrinsically scalable individuals among the d different scale types.
TL;DR: In this article, an adaptive distribution-free test is proposed for the two-sample location problem, where the data are used to assess the tailweight and skewness of the underlying distributions, leading to the selection and then application, with the same data, of one of several common rank tests for shift, such as the Mann-Whitney-Wilcoxon test.
Abstract: An adaptive distribution-free test is proposed for the two-sample location problem First, the data are used to assess the tailweight and skewness of the underlying distributions This leads to the selection and then application, with the same data, of one of several common rank tests for shift, such as the Mann-Whitney-Wilcoxon test The preliminary selection is made in a way that insures the testing procedure is distribution-free A Monte Carlo study shows that the adaptive test has excellent power over a wide class of distributions and is preferable to certain prominent nonadaptive tests
TL;DR: The most stringent bounds on P [m] and P 1 are more stringent than corresponding bounds presented in the literature, for most systems.
Abstract: Analysis of dependent probability systems of a moderate to large finite number (m) of events must often be based solely on the partial system information given by S 1, the sum of the probabilities of occurrence of the m individuaf events; and S 2, the sum of the probabilities of occurrence of each of the ( m 2) pairs of events. This information is used to develop the most stringent upper and lower bounds on the aggregated probabilities P [n], the probability of occurrence of exactly n events (n = 0, 1, …, m); and on P 1, the probability of occurrence of one or more of the m events. The most stringent bounds on P [m] and P 1 are more stringent than corresponding bounds presented in the literature, for most systems.
TL;DR: In this article, the effects of reasonable and actual levels of misclassification in the 2 × 2 table on bias in the difference between two proportions and on the bias in relative odds as well as on the distributions of these statistics are examined.
Abstract: It is shown elsewhere [15] that the false negative and false positive rates associated with medical screening techniques do not follow any general or simple models; and that the usual assumptions made for analytical purposes are violated. The effects of reasonable and actual levels of misclassification in the 2 × 2 table on the bias in the difference between two proportions and on the bias in relative odds as well as on the distributions of these statistics are examined. The false positive rates, and in particular the difference between them, in the two sample problem are responsible for most of the bias resulting from misclassification.
TL;DR: In this paper, it is shown that Bayesian confidence intervals and tests may be obtained by using Student's t and χ2 distributions. But the MSE of the Bayesian estimates were uniformly smaller than those of the ML estimate.
Abstract: Some aspects of Bayesian methods of inference relative to switching regression models are analyzed. It is shown that Bayesian confidence intervals and tests may be obtained by using Student's t and χ2 distributions. Mean biases and MSE of some Bayesian estimates are compared by Monte Carlo methods with those of the ML estimate. The MSE of the Bayesian estimates were uniformly smaller than those of the ML estimate. An experiment designed by Quandt [11] is also analyzed.
TL;DR: In this paper, the authors investigated the distribution of the vector (X 1,n−i1*, X 2,n-i2*, ···, Xm,n −im*) not depending on n.
Abstract: Let (X 1j , X 2j , ···, Xmj ), j = 1, 2, ···, n, be a sample of size n on an m-dimensional vector (X 1, X 2, ···, Xm ), m ≥ 2. Let the order statistics of the rth component be denoted by X r,1* ≤ X r,2* ≤ ··· ≤ X r,n *. In this article we investigate the distribution of the vector (X 1,n−i1*, X 2,n–i2*, ···, Xm,n–im *) for (i 1, i 2, ···, im ) not depending on n. The major emphasis is on asymptotic theory and a general formula is given for the asymptotic distribution of the vector above when each ij = 0. Necessary and sufficient condition is also given for the asymptotic independence of the components of the vector investigated. This extends results known for m = 2. In Section 4 examples are given for illustration.