Showing papers in "Journal of the American Statistical Association in 1973"
1,655 citations
TL;DR: Every multivariate observation is visualized as a computer-drawn face that makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data.
Abstract: A novel method of representing multivariate data is presented. Each point in k-dimensional space, k≤18, is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data. Other graphical representations are described briefly.
1,356 citations
TL;DR: The Law of Large Numbers Probability Convergence and the Law of large numbers Probability Distributions Information Decision Theory Theory of Estimators Point Estimation in Practice Interval Estimation Test of Hypotheses Goodness of Fit Tests as mentioned in this paper.
Abstract: Basic Concepts in Probability Convergence and the Law of Large Numbers Probability Distributions Information Decision Theory Theory of Estimators Point Estimation in Practice Interval Estimation Test of Hypotheses Goodness-of-Fit Tests.
1,135 citations
TL;DR: In this paper, the positive part version of Stein's estimator is one member of a class of "good" rules that have Bayesian properties and also dominate the MLE, and other members of this class are also useful in various situations.
Abstract: Stein's estimator for k normal means is known to dominate the MLE if k ≥ 3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of “good” rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more complicated estimation problems, and conclude with results from empirical linear Bayes rules in non-normal cases.
948 citations
768 citations
TL;DR: In this article, computer simulation techniques were used to study the Type I and Type III error rates and the correct decision rates for ten pairwise multiple comparison procedures, and the results indicated that Scheffe's test, Tukey's test and the Student-Newman-Keuls test are less appropriate than either the least significant difference with the restriction that the analysis of variance F value be significant at α =.05, two Bayesian modifications of the smallest significant difference, or Duncan's multiple range test.
Abstract: Computer simulation techniques were used to study the Type I and Type III error rates and the correct decision rates for ten pairwise multiple comparison procedures. Results indicated that Scheffe's test, Tukey's test, and the Student-Newman-Keuls test are less appropriate than either the least significant difference with the restriction that the analysis of variance F value be significant at α = .05, two Bayesian modifications of the least significant difference, or Duncan's multiple range test. Because of its ease of application, many researchers may prefer the restricted least significant difference.
655 citations
TL;DR: A simple model of the effects of time on memory is described, where the effect of forgetting and telescoping where the event is remembered as occurring more recently than it did is combined.
Abstract: This article describes a simple model of the effects of time on memory. The model combines the effects of forgetting and telescoping where the event is remembered as occurring more recently than it did. The model is tested on behavior data for which validation information are available. The use of records and of aided recall are shown to have opposite effects on memory errors. Records reduce telescoping effects, but not errors of omission. Aided recall reduces omissions, but does not reduce and may even increase telescoping. The article also includes a discussion of other characteristics of the interview and the respondent that affect memory.
439 citations
TL;DR: In this article, two linear models with error structure of the nested type are considered and transformations are presented by which uncorrelated errors with constant variances are obtained, where the transformed observations are differences between the original observations and multiples of averages of subsets of the observations.
Abstract: Two linear models with error structure of the nested type are considered. Transformations are presented by which uncorrelated errors with constant variances are obtained. The transformed observations are differences between the original observations and multiples of averages of subsets of the observations. The transformations permit the calculation of the generalized least-squares estimators and their covariance matrices by ordinary least-squares regression. Regression-type estimators are presented for use when the variance components are unknown. Sufficient conditions are presented under which the estimated generalized least-squares estimator is unbiased and asymptotically equivalent to the generalized least-squares estimator.
327 citations
TL;DR: In this paper, the studentized Tukey procedures (Ext-T) were used to estimate all linear combinations of a set of means for an unbalanced AOV fixed effects model.
Abstract: Under fairly general conditions the studentized range can be used to approximately simultaneously estimate all linear combinations of a set of means for an unbalanced AOV fixed effects model. These new methods are called extended Tukey procedures (Ext-T). Comparisons are made with the Scheffe (S) procedures. It is recommended generally that the (Ext-T) procedures be used if primary interest is in pairwise comparisons of the means and if the unbalance is not severe.
303 citations
TL;DR: In this paper, the univariate skewness and kurtosis statistics, and b 2, and The W statistic proposed by Shapiro and Wilk are generalized to test a hypothesis of multivariate normality by use of S.N. Roy's union-intersection principle.
Abstract: The univariate skewness and kurtosis statistics, and b 2, and The W statistic proposed by Shapiro and Wilk are generalized to test a hypothesis of multivariate normality by use of S.N. Roy's union-intersection principle. These generalized statistics are invariant with respect to nonsingular matrix multiplication and vector addition. Two univariate test statistics, Kolmogorov-Smirnov and Cramer-Von Mises, are used to test whether transformed vector observations follow a χ2 distribution. The significance points, and powers against selected alternatives, of these five test statistics are obtained by Monte Carlo methods. These studies showed that adequate powers may be achieved for small sample sizes.
294 citations
TL;DR: In this paper, the authors considered the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels and showed how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting.
Abstract: The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley's theorem is stated to extend the Modified Gauss-Newton method to this problem.
TL;DR: In this paper, an iterative technique is proposed for the absolute deviations regression of data, which is based on any standard least squares curve fitting algorithm, and the resulting regression procedure is computationally simple, requires less storage and is faster than the linear programming algorithm.
Abstract: An iterative technique is proposed for the absolute deviations regression of data. At the heart of the technique is any standard least squares curve fitting algorithm. Hence, the resulting regression procedure is computationally simple, requires less storage and is faster than the linear programming algorithm recently proposed as a solution to this problem. Problems associated with non-unique solutions in least absolute deviations regression are also discussed.
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TL;DR: One-at-a-time experiments are always done when the experimental system is set up to produce single results or pairs of results as discussed by the authors, but may give biased estimates when random error is small compared to main effects expected.
Abstract: One-at-a-time experiments are always done when the experimental system is set up to produce single results or pairs of results. When random error is small compared to main effects expected, such experiments are economical, but may give biased estimates. These biases can usually be described by two-factor interactions (2fi). Minimal augmentations of standard one-at-a-time sequences are given, first to separate main effects from 2fi, then to estimate each 2fi separately. Each new datum produces one or more new estimates.
TL;DR: In this article, a least-squares prediction approach is applied to finite population sampling theory, focusing on characteristics of particular samples rather than on plans for choosing samples, and random sampling is considered in the light of these results.
Abstract: This is an application of a least-squares prediction approach to finite population sampling theory. One way in which this approach differs from the conventional one is its focus on characteristics of particular samples rather than on plans for choosing samples. Here we study samples in which many superpopulation models lead to the same optimal (BLU) estimator. Random sampling is considered in the light of these results.
TL;DR: In this paper, a sequence of covariance structure procedures for estimating variance components under more general assumptions than are provided in the typical mixed-model analysis of variance is presented. But the analysis is limited to simulated data and to an empirical example.
Abstract: This article demonstrates the usefulness of analysis of covariance structure procedures for estimating variance components under more general assumptions than are provided in the typical mixed-model analysis of variance. A sequence of eight models is presented based on varying degrees of restrictive assumptions. Maximum likelihood procedures are employed in the estimation of the parameters of the models. The procedures are applied to simulated data and to an empirical example which shows the necessity of the more general assumptions.
TL;DR: In this paper, a method for estimating means and associated inference procedures in a single sample and one-way classification has been developed by a least squares approach in which estimates of the heterogeneity variances are obtained by moments and used in weighting.
Abstract: Data which appear to be binomial proportions sometimes exhibit heterogeneity which results in greater variation than would be expected under the binomial distribution. Methods for estimating means and associated inference procedures in a single sample and one-way classification have been developed by a least squares approach in which estimates of the heterogeneity variances are obtained by moments and used in weighting. Monte Carlo studies of the performance of this technique in moderate and small samples indicate that (1) these empirical weighting estimates have high efficiency relative to exact least squares estimates; (2) the variance estimators are nearly unbiased; (3) the resulting inference procedures are usually adequate for practical application.
TL;DR: In this article, structural change occurs at given points through jump discontinuities in the third derivative of a continuous piecewise cubic estimating function, and testing procedures are developed for detecting structural change as well as linear or quadratic segments.
Abstract: Spline theory and piecewise regression theory are integrated to provide a framework in which structural change is viewed as occurring in a smooth fashion. Specifically, structural change occurs at given points through jump discontinuities in the third derivative of a continuous piecewise cubic estimating function. Testing procedures are developed for detecting structural change as well as linear or quadratic segments. Finally, the techniques developed are illustrated empirically in a learning-by-doing model.
TL;DR: In this article, the authors discuss possible problems associated with the Almon lag technique, caused by misspecification of the length of the lag or the degree of the polynomial.
Abstract: This article discusses possible problems associated with the Almon lag technique, caused by misspecification of the length of the lag or the degree of the polynomial. It is argued that the choice of the lag length is particularly treacherous. Finally, two studies of the relative importance of fiscal and monetary policy are reexamined, and it is shown how insufficient attention to these problems has significantly affected their conclusions.
TL;DR: In this paper, the principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution, and the maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the assumption.
Abstract: The principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution. The maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the Poisson assumption. Computationally, both of these estimation procedures are equivalent to a properly weighted least squares analysis. Approximate tests of the assumed Poisson variation and “goodness of fit” of the data to the model are proposed. Applications of the estimation procedure to linear and nonlinear regression models are discussed, and numerical examples are presented.
TL;DR: In this article, two asymptotically robust tests for equality of variances in the k-sample case are discussed: a simple X 2 test and a test based on the jack-knife procedure.
Abstract: Two asymptotically robust tests for equality of variances in the k-sample case are discussed: a simple X 2 test and a test based on the jack-knife procedure. Some Monte Carlo experiments suggest that these tests are reasonably robust for moderately small samples, are more powerful than Box's grouping test and perform similarly to Bartlett's test in the normal case.
TL;DR: The gamma-Poisson form of the negative binomial distribution (NBD) model generally gives a good fit to many aspects of repeat-buying behavior for a wide range of frequently bought branded consumer goods.
Abstract: The gamma-Poisson form of the negative binomial distribution (NBD) model generally gives a good fit to many aspects of repeat-buying behavior for a wide range of frequently bought branded consumer goods. Nonetheless, empirical evidence suggests that purchasing a particular brand-size in successive equal time-periods tends to be more regular than Poisson. An alternative model is therefore examined in which inter-purchase times for a given consumer are described by an Erlang distribution rather than by the negative exponential distribution implicit in the Poisson assumption of the NBD model. But it is found that the NBD model is robust to this kind of departure. Because of its greater simplicity, the NBD model therefore seems preferable for practical use.
TL;DR: In this paper, a new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator (the vector of observed proportions).
Abstract: A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is moderate. The general superiority of p* over in large sparse multinomials is thus revealed. The novel asymptotic framework may also provide insight in other multinomial problems.
TL;DR: The authors reviewed the history of robust estimation, emphasizing the period 1885-1920 and the work of Newcomb, Edgeworth, Sheppard, and Daniell, and paid particular attention to lines of development which have excited recent interest, including linear functions of order statistics and mixtures of normal densities as models for heavy-tailed populations.
Abstract: This article reviews some of the history of robust estimation, emphasizing the period 1885–1920 and the work of Newcomb, Edgeworth, Sheppard, and Daniell. Particular attention is paid to lines of development which have excited recent interest, including linear functions of order statistics and mixtures of normal densities as models for heavy-tailed populations.
TL;DR: In this paper, five procedures for binary classification with binary variables and small samples are discussed and evaluated, including linear and quadratic discriminative discriminator, based on first and second order approximation to multinomial probabilities.
Abstract: Five procedures for discrimination with binary variables and small samples are discussed and evaluated. Two procedures are specific for binary variables and are based on first and second order approximations to multinomial probabilities. The third procedure, based on the full multinomial model, is completely general. The fourth and fifth procedures are the linear and quadratic discriminants. Evaluation is in terms of mean actual error and mean correlation between observed and true log likelihood ratios determined by Monte Carlo sampling. The concept of a “reversal” in log likelihood ratios is introduced to explain the results.
TL;DR: In this paper, an explicit definition of a (k, r)-cluster is proposed and exact distributional results are derived under a non-metric hypothesis for the case k = 1.
Abstract: An explicit definition of a (k, r)-cluster is proposed. Each (k, r)-cluster has the property that each of its elements is within a distance r of at least k other elements of the same cluster and the entire set can be linked by a chain of links each less than or equal to r. Some exact distributional results are derived under a nonmetric hypothesis for the case k = 1. An example is given to illustrate the use of probability theory in identifying significant clustering structures in terms of compactness and isolation.
TL;DR: In this article, a regression model where the variance of the dependent variable is proportional to the square of its expectation is considered, and the asymptotic efficiency of the weighted least squares estimator as compared to the maximum likelihood estimator for the cases when the dependent variables follow a normal, lognormal, or gamma distribution is analyzed.
Abstract: In this article we consider a regression model where the variance of the dependent variable is proportional to the square of its expectation. First, we obtain the asymptotic efficiency of the weighted least squares estimator as compared to the maximum likelihood estimator for the cases when the dependent variable follows a normal, lognormal, or Gamma distribution. Second, we derive a test of whether the dependent variable follows a lognormal or a Gamma distribution. An example is worked out for the purpose of illustration.