Showing papers in "Journal of the American Statistical Association in 1965"
8,224 citations
TL;DR: A survey technique for improving the reliability of responses to sensitive interview questions is described, which permits the respondent to answer "yes" or "no" to a question without the interviewer knowing what information is being conveyed by the respondent.
Abstract: For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain questions. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. In this paper it is argued that such bias is potentially removable through allowing the interviewee to maintain privacy through the device of randomizing his response. A randomized response method for estimating a population proportion is presented as an example. Unbiased maximum likelihood estimates are obtained and their mean square errors are compared with the mean square errors of conventional estimates under various assumptions about the underlying population.
2,929 citations
1,149 citations
1,057 citations
763 citations
TL;DR: In this paper, a modified up-and-down method for sensitivity testing is presented with maximum likelihood estimates of LD50 tabulated for all sample sequences for nominal sample size N ≤ 6.
Abstract: A modified up-and-down method for sensitivity testing (all-or-none assays) is presented with maximum likelihood estimates of LD50 tabulated for all sample sequences for nominal sample size N ≤ 6. Approximate estimates for larger sample sizes are given. The design uses sequentially determined test levels and sequentially determined sample sizes. The estimates have mean square error approximately independent of the chosen starting level of the test sequence and the spacing between test levels. The actual sample size rarely exceeds the nominal sample size by more than two for moderately well chosen starting levels. Examples of the use of the method are given for two analyses of variance designs.
759 citations
TL;DR: In this paper, a regression of a dependent variable upon the proportions of families in the classes of the marginal income and education distributions for 1950 census tracts in the city of Chicago led to the estimation of "beta coefficient profiles" for television receiver and refrigerator ownership, for central heating system usage, and for a measure of dwelling unit overcrowding.
Abstract: Regression upon principal components of the percentage points of the income and education distributions for 1950 census tracts in the city of Chicago led to the estimation of “beta coefficient profiles” for television receiver and refrigerator ownership, for central heating system usage, and for a measure of dwelling unit overcrowding. The betas are standardized coefficients of regression of a dependent variable upon the proportions of families in the classes of the marginal income and education distributions. They measure the relative contribution of families in these classes to the over-all per cent saturation of the dependent variable in the tract. The coefficients were estimated by techniques developed in the first portion of the paper; estimation by classical regression methods would have been impossible because of multicollinearity. The empirical results are in substantial agreement with findings from regressions of the dependent variables upon the mean values of income and education, and t...
725 citations
TL;DR: In this article, two exact tests for testing the hypothesis that the residuals from a least square regression are homoscedastic are presented, one parametric and using the F-statistic, and the other nonparametric and uses the number of peaks in the ordered sequence of unsigned residuals.
Abstract: Two exact tests are presented for testing the hypothesis that the residuals from a least squares regression are homoscedastic. The results can be used to test the hypothesis that a linear [ratio] model explains the relationship between variables as opposed to the alternative that the ratio [linear] specification is correct. The first test is parametric and uses the F-statistic. The second test is nonparametric and uses the number of peaks in the ordered sequence of unsigned residuals. In conclusion, the results of some experimental calculations of the powers of the tests are discussed.
645 citations
TL;DR: In this article, a method is given of constructing a one-parameter class of bivariate distributions from given margins, which contains the known boundary distributions and the member corresponding to independent random variables.
Abstract: By developing an analogy with the measure of association in a fourfold contingency table, a method is given of constructing a one-parameter class of bivariate distributions from given margins. This class contains the known boundary distributions and the member corresponding to independent random variables. The class resulting from standard normal margins is compared with the standard normal bivariate distribution, and it is found that the two joint distributions and the two conditional distributions each agree tolerably well. Estimation of the parameter is illustrated by an example showing a computational advantage of this class of distributions.
469 citations
414 citations
TL;DR: In this article, the distribution and density functions of the ratio of two normal random variables were studied in terms of the vivariate normal distribution and the Nicholson's V function, both of which have been extensively studied and for which tables and computational procedures are readily available.
Abstract: The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio (u 1+ ¨˙ +un )/(v 1+ ¨˙ +vm ) where the u's and v's are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed.
TL;DR: In this paper, the probability of E(n|N|N; p) for n>N/2 in terms of simple tabulated quantities was shown. But the probability was not shown for n ≥ n/2.
Abstract: N points are independently drawn from the uniform distribution on (0, 1). Denote by E(n|N; p), the event: There exists a subinterval of (0, 1) of length p that contains at least n out of the N points. We find the probability, P(n|N; p), of E(n|N; p) for n>N/2 in terms of simple tabulated quantities.
TL;DR: In this article, the authors derived the predictive density function for the multivariate normal regression model and showed how it can be used in the analysis of several problems, such as illustrative investment problems.
Abstract: In this paper we review the derivation of the predictive density function for the normal multiple regression model, state and prove a general theorem on optimal point prediction, and show how the predictive density can be employed in the analysis of an illustrative investment problem. Then we derive the predictive density function for the multivariate normal regression model and indicate how it can be used in the analysis of several problems.
TL;DR: In this article, the T-element column vector of values taken by the dependent variable is used to estimate the parameter vector of the equation, where y is the T element column vector and u a column of T disturbance.
Abstract: Classical regression analysis is concerned with the estimation of the parameter vector\(beta \)of the equation\(y = X\beta + u\)(1.1)where y is the T-element column vector of values taken by the dependent variable, X the \(TxA\) matrix of values taken by the A independent variables, \(beta \) a column of A parameters, and u a column of T disturbance.
TL;DR: In this paper, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Abstract: Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential Equations V: Dependence on Initial Conditions and Parameters VI: Total and Partial Differential Equations VII: The Poincare-Bendixson Theory VIII: Plane Stationary Points IX: Invariant Manifolds and Linearizations X: Perturbed Linear Systems XI: Linear Second Order Equations XII: Use of Implicity Function and Fixed Point Theorems XIII: Dichotomies for Solutions of Linear Equations XIV: Miscellany on Monotomy Hints for Exercises References Index.
TL;DR: In this paper, the estimation of variance components in the one-way model from a subjective Bayesian point of view is considered, and the situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail.
Abstract: The estimation of variance components in the one-way model is considered from a subjective Bayesian point of view. The situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail. Exact and approximate posterior distributions are obtained in both the balanced and unbalanced case. Common sense aspects of the problem are emphasized, and some contrasts with other approaches. For example, Bayesianly speaking, a large negative unbiased estimate of the between variance component indicates an uninformative experiment in which the effective likelihood for that variance component is extremely flat, instead of strong evidence that the variance component is nearly zero.
TL;DR: In this paper, four ratio estimators are compared with respect to bias, efficiency, approach to normality and computational convenience: simple, Quenouille's, Beale's and modified ratio estimator.
Abstract: In this article, four ratio estimators designated as simple, Quenouille's, Beale's and modified ratio estimators are compared with respect to bias, efficiency, approach to normality and computational convenience. They are shown to be asymptotically minimum variance bound estimators. Some additional ratio estimators are discussed briefly and compared with these. Quenouille's, Beale's, and modified ratio estimators are found to be more attractive than the alternatives compared.
TL;DR: In this paper, a table of critical values of the Wilcoxon Signed Rank Statistic is presented for N = 4(1)100 pairs of observations at one-tail probability levels of.00005,.0005,,.0025,.005,.005,.025,.050,.025).150, and.20.05).45.
Abstract: A table of critical values of the Wilcoxon Signed Rank Statistic is presented for N = 4(1)100 pairs of observations at one-tail probability levels of .00005, .0005, .0025, .005 (.005) .025, .050 (.025) .150, and .20 (.05) .45. Probabilities were computed accurately to at least 6 digits, regardless of the location of the decimal point. Therefore, all critical values are correct as tabled. Normal approximation probabilities were found to be biased, too small at the .05 level but too large at the .005 and .0005 probability levels. Approximation errors were less than 10% for all N > 35 for the .05, .025, and .005 one-tail probability levels; but this degree of accuracy was not achieved at the .0005 level for N = 100.
TL;DR: In this paper, a multivariate generalization of the inverted beta distribution is presented, and two asymptotic formulae for approximating the related probability integral are developed and illustrated with numerical examples.
Abstract: In this paper we obtain a multivariate generalization of the inverted beta distribution. Properties of this distribution and its connection with the multivariate Student-t distribution are discussed. Two asymptotic formulae for approximating the related probability integral are developed and illustrated with numerical examples. Application of this distribution to a problem in Bayesian inference is given.
TL;DR: In this article, a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems is presented, which is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p th and bottom r th fractions of the combined sample.
Abstract: This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p th and bottom r th fractions of the combined sample. The percentile modified tests for scale are quite effective. When p = r = 1/8 (i.e., we score only the extreme quarter of the combined sample) the A.R.E. of the test to the F test is .85.
TL;DR: The authors compared the Pearson Chi-square and Kolmogorov good-ness-of-fit tests with respect to validity under the following conditions: (1) the independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are "small"; i.e., not greater than 50.
Abstract: This paper compares the Pearson Chi-Square and Kolmogorov good-ness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are “small”; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test.
TL;DR: It is found that relatively small imperfections in the matching process can lead to substantial bias in estimating the relationship between response errors and “true” values.
Abstract: When response errors are studied by means of record checks, the possibility exists that matching errors are made in relating responses to the corresponding record data. Two simple models are developed for matching errors, and the implications of such matching errors on various measures of response errors are studied. The models are applied to the data from a record check study, and it is found that relatively small imperfections in the matching process can lead to substantial bias in estimating the relationship between response errors and “true” values.
TL;DR: In this article, a method is proposed of using information on several variates to improve the precision of estimators of population totals, means, etc., and it is shown that the variances of difference estimators are comparable to those of ratio estimators.
Abstract: Usually auxiliary information based on just one variate is used to improve the precision of estimators of population totals, means, etc. In this paper a method is proposed of using information on several variates to achieve higher precision. The technique of difference estimation is employed throughout. It is shown that the variances of difference estimators are comparable to those of ratio estimators. The results are extended to double sampling procedures and sampling over two occasions.
TL;DR: In this paper, the power of Student t-distribution tests is discussed and the noncentrality parameters are given to 5 decimal places for tests which have Type I error equal to 0.90.
Abstract: Tables are given which correspond to the power of various tests which use the Student t-distribution. Noncentrality parameters are given to 5 decimal places for tests which have Type I error equal to 0.050, 0.025, 0.010 and 0.005. Type II errors are covered as follows: 0.01, 0.05, 0.10 (0.10) 0.90. One-sided and two-sided tests are discussed.
TL;DR: In this paper, a Bayes solution is provided for an estimation problem involving a sample from a multivariate normal population having an arbitrary unknown covariance matrix, but a vector mean whose components are all equal.
Abstract: A Bayes solution is supplied for an estimation problem involving a sample from a multivariate normal population having an arbitrary unknown covariance matrix, but a vector mean whose components are all equal. Assuming that a particular unnormed prior density is a convenient expression for displaying prior ignorance, it is then demonstrated that a posterior interval for this common mean can be based on Student's t distribution. If prior information can be conveniently represented by a natural conjugate prior density, the posterior interval will also depend on Student's t. An extension is made to the case of estimating the constant difference between two parallel profiles.
TL;DR: In this article, an attempt has been made to investigate the adequacy of certain suggested approximations by computing the exact distributions for some particular cases, and these exact distributions have been compared with approximate distributions.
Abstract: Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-side...
IBM1
TL;DR: In this paper, the concept of expected significance level (esl) is defined and its basic properties are presented in Section 2 and the relationship between esl and the familiar criterion of power is discussed.
Abstract: After a brief motivating discussion, of approaches to significance tests in Section 1, the concept of expected significance level (esl) is defined and its basic properties are presented in Section 2. Section 3 discusses the relationship between esl and the familiar criterion of power. While a complete description of power for each size α is more informative than esl, it is argued that esl is often a reasonable compromise between high ideals and practicability. Section 4 gives two estimation methods for Monte Carlo simulation of esl and shows how to estimate variances and covariances for the second of these methods. The first method leads to the familiar Wilcoxon two-sample statistic which is clearly a sample analogue of esl. The second and more apposite method leads to a modification of the Wilcoxon statistic.
TL;DR: In this article, the Neyman stratified allocation result generalizes when it is formally assumed that there is prior information concerning the unknown stratum means, expressed in the form of a multivariate normal prior distribution.
Abstract: The question of how the well-known Neyman stratified allocation result generalizes when it is formally assumed that there is prior information concerning the unknown stratum means is dealt with here. This prior information is taken to be expressible in the form of a multivariate normal prior distribution. Several methods of assessing prior distributions are discussed. The allocation for stratified sampling is shown to be a special case of a more general allocation problem. A computational algorithm is presented for this more general problem of finding the allocation of sampling effort which minimizes the posterior variance of any given linear combination of unknown normal process means subject to a budget constraint. A feature of the solution is that for limited budgets one may rely solely on his prior information concerning some strata, sampling only in a subset of the strata. Finally, several applications are briefly described including a “non-Bayesian” solution to a particular problem of alloc...
TL;DR: In this article, an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical inference and prediction, e.g., one observation from a two-parameter normal model is not sufficient to permit inference about the variance but two observations are.
Abstract: In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical inference and prediction—e.g., one observation from a two-parameter normal model is not (in our special sense) sufficient to permit inference about the variance but two observations are. In essence, the procedure stipulates that prior indifference distributions be improper but become proper after an appropriate minimal sample. With some limitation on the family of priors considered, this procedure permits unique specification of indifference for the more commonly encountered statistical models. Furthermore, these specification...