1,576 results
Search Results
2. Selected Papers of Frederick Mosteller
- Author
-
Bradstreet, Thomas E.
- Subjects
Selected Papers of Frederick Mosteller (Book) -- Book reviews ,Books -- Book reviews ,Mathematics - Published
- 2008
3. Essays in Econometrics: Collected Papers of Clive W. J. Granger (Vols. 1 and 2).*
- Author
-
Embrechts, Paul A.L.
- Subjects
Essays in Econometrics: Collected Papers of Clive W. J. Granger (Vols. 1 and 2).* (Book) -- Book reviews ,Books -- Book reviews ,Mathematics - Abstract
Essays in Econometrics: Collected Papers of Clive W. J. Granger (Vols. 1 and 2).* Eric GHYSELS, Norman R. SWANSON, and Mark W. WATSON (Eds.). New York: Cambridge University Press, 2001. [...]
- Published
- 2004
4. Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics
- Author
-
Kafadar, Karen
- Subjects
Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics (Book) -- Book reviews ,Books -- Book reviews ,Mathematics - Abstract
This festschrift in honor of Professor Le Cam's 70th birthday attests to the wide-ranging impact of his work in probability theory, specifically on convergence and contiguity of probability measures, superefficiency, [...]
- Published
- 1997
5. Review Papers: Recent Developments in Nonparametric Density Estimation
- Author
-
Alan Julian Izenman
- Subjects
Statistics and Probability ,Statistics::Theory ,Restricted maximum likelihood ,Nonparametric statistics ,Estimator ,Density estimation ,Nonparametric regression ,Statistics::Machine Learning ,Histogram ,Kernel (statistics) ,Pattern recognition (psychology) ,Statistics ,Econometrics ,Statistics::Methodology ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject. The early density estimation methods, such as the histogram, kernel estimators, and orthogonal series estimators are still very popular, and recent research on them is described. Different types of restricted maximum likelihood density estimators, including order-restricted estimators, maximum penalized likelihood estimators, and sieve estimators, are discussed, where re...
- Published
- 1991
6. On the Choice of Plotting Positions on Probability Paper
- Author
-
Bradford F. Kimball
- Subjects
Statistics and Probability ,Distribution (number theory) ,Stress (linguistics) ,medicine ,Graph paper ,Sample (statistics) ,Statistics, Probability and Uncertainty ,medicine.symptom ,Type (model theory) ,Algorithm ,Mathematics ,Confusion - Abstract
This article is an attempt to throw more light on the problem of choosing plotting positions for the frequencies related to ordered sample values. The problem is particularly pertinent where special-scale graph paper is used such that a straight line indicates conformance of data to type of distribution assumed to apply. Such graph paper is often briefly referred to as “probability paper.” The types of distributions here considered are the normal and the extreme-value distribution of Type I, with the accent on the extreme-value case. Various methods of determining plotting positions have been put forward and there is confusion of thought in judging what plotting convention is optimum. An optimum criterion proposed by Chernoff and Lieberman has received wide attention. Blom in a recent book develops further criteria [2]. To clarify the problem the author has analyzed the purposes to be served in plotting data on probability paper. With a specific concept of the purpose to be served in mind, it bec...
- Published
- 1960
7. The Uses and Usefulness of Binomial Probability Paper
- Author
-
John W. Tukey and Frederick Mosteller
- Subjects
Paper ,Statistics and Probability ,Biometry ,Binomial approximation ,Statistics as Topic ,Negative binomial distribution ,Continuity correction ,Binomial test ,Binomial distribution ,Statistics ,Humans ,Applied mathematics ,Central binomial coefficient ,Statistics, Probability and Uncertainty ,Binomial proportion confidence interval ,Probability ,Count data ,Mathematics - Abstract
This article describes certain uses of Binomial Probability Paper. This graph paper was designed to facilitate the employment of R. A. Fisher's inverse sine transformation for proportions. The transformation itself is designed to adjust binomially distributed data so that the variance will not depend on the true value of the proportion p, but only on the sample size n. In addition, binomial data so transformed more closely approximate normality than the raw data. The usefulness of plotting binomial data in rectangular coordinates, using a square-root scale for the number observed in each category, was first pointed out by Fisher and Mather [10]. The graph paper under discussion 1 is specially ruled to make this mode of plotting both simple and rapid. A graduated quadrant makes the angular transformation (p = cos2 φ or p = sin2 φ) easily available at the same time. Most tests of counted data can be made quickly, easily and with what is usually adequate accuracy with this paper. Some 22 examples ar...
- Published
- 1949
8. A Note on Chernoff and Lieberman's Generalized Probability Paper
- Author
-
G. W. Cran
- Subjects
Statistics and Probability ,Combinatorics ,Percentile ,Distribution (mathematics) ,Estimator ,Applied mathematics ,Graph paper ,Statistics, Probability and Uncertainty ,Invariant (mathematics) ,Scale parameter ,Plot (graphics) ,Mathematics - Abstract
The determination of plotting positions on probability graph paper so that the associated weighted least squares estimators of the scale parameter and the percentiles of a continuous distribution have certain properties is discussed. Necessary and sufficient conditions are given for an invariant optimal plot for percentile estimation. Also discussed is the derivation of ordered plotting positions.
- Published
- 1975
9. Celebrating Statistics: Papers in Honour of Sir David Cox on His 80th Birthday
- Author
-
Hall, Daniel B.
- Subjects
Oxford University Press (Oxford, England) ,Book publishing -- Statistics ,Mathematics - Published
- 2006
10. E.T. Jaynes; papers on probability, statistics, and statistical physics
- Author
-
Rodriguez, Carlos C.
- Subjects
E.T. Jaynes; Papers on Probability, Statistics, and Statistical Physics (Book) -- Book reviews ,Books -- Book reviews ,Mathematics - Published
- 1985
11. Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics
- Author
-
Grace L. Yang, Erik Torgersen, Karen Kafadar, and David Polland
- Subjects
Statistics and Probability ,Probability and statistics ,Statistics, Probability and Uncertainty ,Mathematical economics ,Mathematics - Published
- 1997
12. Use of Normal Probability Paper
- Author
-
Herman Chernoff and Gerald J. Lieberman
- Subjects
Statistics and Probability ,Inverse-chi-squared distribution ,Half-normal distribution ,Q-function ,Student's t-distribution ,Skew normal distribution ,Cumulative distribution function ,Statistics ,Applied mathematics ,Statistics, Probability and Uncertainty ,Rankit ,Folded normal distribution ,Mathematics - Abstract
Normal probability paper is so designed that the cumulative distribution function of a normally distributed chance variable appears as a straight line. It is a common practice to plot the observations of a sample on this paper to obtain a graphical check for normality or to obtain a graphical estimate of the mean and variance of the population. Textbooks, however, are not very specific about methods for plotting, for, although the ordered observations are plotted along the abscissa, some uncertainties about the corresponding ordinates are left unresolved. The purpose of this paper is to indicate, with a special example, that any graphical technique should depend to a large extent on the purpose for which the graph is drawn. In particular, it presents tables covering sample sizes up to 10, for selecting the ordinates on normal probability paper so as to obtain “optimum” graphical estimates of the mean ζ and the standard deviation σ of a normal distribution. The somewhat more complicated problem of...
- Published
- 1954
13. Optimum Sample Size for a Problem in Choosing the Population with the Largest Mean: Some Comments on Somerville's Paper
- Author
-
J. B. Ofosu
- Subjects
Statistics and Probability ,education.field_of_study ,Sample size determination ,Statistics ,Population ,Econometrics ,Statistics, Probability and Uncertainty ,education ,Mathematics - Published
- 1974
14. Contributions to Survey Sampling and Applied Statistics: Papers in Honor of H. O. Hartley
- Author
-
Herbert A. David and Ronald R. Regal
- Subjects
Statistics and Probability ,Honor ,Statistics ,Survey sampling ,Statistics, Probability and Uncertainty ,Mathematics - Published
- 1980
15. Collected Papers of R. A. Fisher: Volume I, 1912-24, and Volume II, 1925-31
- Author
-
M. H. D. and J. H. Bennett
- Subjects
Statistics and Probability ,business.industry ,Statistics, Probability and Uncertainty ,Nuclear medicine ,business ,Volume (compression) ,Mathematics - Published
- 1974
16. Experimental Design: Selected Papers of Frank Yates
- Author
-
Frank Yates and Oscar Kempthorne
- Subjects
Statistics and Probability ,Statistics, Probability and Uncertainty ,Mathematics - Published
- 1972
17. Selected Papers in Statistics and Probability
- Author
-
W. A. W., Abraham Wald, T. W. Anderson, H. Cramer, H. A. Freeman, J. L. Hodges, E. L. Lehmann, A. M. Mood, and C. M. Stein
- Subjects
Statistics and Probability ,Statistics ,Probability and statistics ,Statistics, Probability and Uncertainty ,Mathematics - Published
- 1955
18. A Note on Griffin's Paper 'Graphic Computation of Tau as a Coefficient of Disarray'
- Author
-
S. M. Shah
- Subjects
Statistics and Probability ,Combinatorics ,Ranking ,Computation ,Griffin ,Value (computer science) ,Table (database) ,Statistics, Probability and Uncertainty ,Natural order ,Numbering ,Mathematics - Abstract
tau. It consists of computing "the number of intersections resulting from connecting the two rankings of each member by lines, one ranking having been put in natural order, " and computing tau from the number of intersections. In the case of ties in both rankings, Griffin suggests the construction of four graphs, for each of which the number of intersections is computed. Tau is then computed from the sum of the four sets of intersections. The purpose of this note is to suggest that only two of the four graphs are necessary, say those in which the differences in ranking from that given by the natural order are minimized in both sets, and then maximized in both sets. If one doubles the total number of intersections found in these two graphs, the values of 4s, required for the computation of tau, can be found. That this is sufficienit can be seen by numbering the columns in the table at the top of page 447 and noting that the sum of the entries in columns 1 and 4 equals the sum in columns 1 and 2. If one wishes to check the value obtained, the computation may be repeated using the other pair of graphs.
- Published
- 1961
19. A SELECTION OF EARLY STATISTICAL PAPERS OF J. NEYMAN (Book).
- Author
-
Kempthorne, Oscar
- Subjects
- *
MATHEMATICS , *STATISTICS , *NONFICTION - Abstract
Reviews the book "A Selection of Early Statistical Papers of J. Neyman."
- Published
- 1970
- Full Text
- View/download PDF
20. The Selected Papers of E.S. Pearson (Book).
- Author
-
Johnson, Norman L.
- Subjects
- *
MATHEMATICS , *PERIODICAL editors , *NONFICTION - Abstract
Reviews the book "Selected Papers of E.S. Pearson."
- Published
- 1968
- Full Text
- View/download PDF
21. The Multiple-Partial Correlation Coefficient
- Author
-
Dudley J. Cowden
- Subjects
Statistics and Probability ,Population pressure ,GEORGE (programming language) ,Correlation coefficient ,Mathematics education ,Multiple correlation ,Subject (documents) ,Statistics, Probability and Uncertainty ,Mathematical economics ,Partial correlation ,Mathematics ,Unpublished paper - Abstract
A partial correlation coefficient which is also a multiple correlation coefficient is discussed. Its relationship with other well-known coefficients is explained. Computational methods for computing the estimating equation and the correlation coefficient are suggested. * The writer wishes to thank Professors Harold Hotelling, George E. Nicholson, and John H. Smith for critically reading the manuscript and offering valuable comments. Professor Hotelling indicated the method of computation which he had suggested in an unpublished paper (see note 5). Professor Smith called the writer's attention to some of the earlier references to the subject in the literature. Since the first draft of this paper was written (June, 1951), it has been learned that Professor C. Horace Hamilton, of the North Carolina State College of Agriculture and Engineering, has written an article entitled “Population Pressure and Other Factors Affecting Net Rural-Urban Migration,” in which the coefficient of multiple-partial corr...
- Published
- 1952
22. Graphic Computation ofR1.23
- Author
-
Frederick V. Waugh and Karl A. Fox
- Subjects
Statistics and Probability ,Algebra ,Theoretical computer science ,Computation ,Graph paper ,Multiple correlation ,Statistics, Probability and Uncertainty ,Object (computer science) ,Mathematics - Abstract
Lord recently published a nomograph “for calculating a multiple correlation coefficient (R 1.23) from the zero-order correlations (r 12, r 13, and r 23).” His paper reminded us that in 1947 we developed a graphic method of computing R 1.23. If the sole object is speed of computation, the advantage would doubtless lie with Lord's nomograph rather than with our graphic method. But we might claim two possible advantages to the method outlined in this paper. First, the computation can be carried out on ordinary graph paper. Second, we believe that our graphic method can help many students to understand the basic relationships between the zero-order correlations and the multiple-correlation coefficient.
- Published
- 1957
23. Linear Hypothesis Testing in Linear Models With High-Dimensional Responses
- Author
-
Runze Li and Changcheng Li
- Subjects
Statistics and Probability ,05 social sciences ,Linear model ,High dimensional ,Linear hypothesis ,01 natural sciences ,Article ,010104 statistics & probability ,0502 economics and business ,Linear regression ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Projection (set theory) ,050205 econometrics ,Mathematics - Abstract
In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this paper. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.
- Published
- 2021
24. TIES IN PAIRED-COMPARISON EXPERIMENTS: A GENERALIZATION OF THE BRADLEY-TERRY MODEL.
- Author
-
Rao, P. V. and Kupper, L. L.
- Subjects
- *
PROBABILITY theory , *MATHEMATICS , *BAYESIAN analysis , *PARAMETERS (Statistics) , *STATISTICS - Abstract
The Bradley-Terry model for a paired-comparison experiment with t treatments postulates a set of t 'true' treatment ratings π1, π2, ..., π1 such that π1 is ≥ 0, σpi;i = 1 and the probability for preferring treatment i to treatment j is π2 (π2 + πj)-1. Thus, according to this model, every comparison of two treatments results in a definite preference for one of the two. This is an unrealistic restriction since when there is no difference between the responses due to two treatments, any method of expressing preference for one over the other is somewhat arbitrary. This paper considers a modification of the Bradley-Terry model by introducing an additional parameter, called threshold parameter, into the model. This permits 'ties' in the model. The problem of estimation and tests of hypotheses for the parameters of the modified model is also dealt with in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
25. Comment.
- Author
-
Lindley, D. V. and Laviolette, Michael
- Subjects
- *
PROBABILITY theory , *FUZZY sets , *FUZZY logic , *FUZZY systems , *MATHEMATICS , *STATISTICS - Abstract
This article comments on a paper by Nozer D. Singpurwalla and Jane M. Booker which aimed to develop a line of argument that probability theory has a sufficiently rich structure tor incorporating fuzzy sets within its framework. According to the commenter, the paper provides a real advance in the understanding of fuzzy sets, by providing a sensible connection between membership functions and likelihood, and thereby probability. He says the paper's modification of the basic question is answered most convincingly. However, the answer raises an apparent conflict between the two calculi of fuzzy logic and probability. What is now needed is a second article to resolve this conflict. The commenter's conjecture is that the resolution will show that the rules of fuzzy logic are untenable. According to him, his principal reason behind the conjecture is that the rules of the probability calculus follow from simple, obvious assumptions, whereas those of the fuzzy calculus have been arbitrarily selected. He points out that this arbitrariness is fine for a pure mathematician. But, according to him, an applied mathematician, faced with the reality of uncertainty in the real world, must take into account that world and cannot ignore the basic assumptions about uncertainty that underlie the probability calculus and reflect basic truths about the world.
- Published
- 2004
- Full Text
- View/download PDF
26. Predictive Inference for Locally Stationary Time Series With an Application to Climate Data
- Author
-
Srinjoy Das and Dimitris N. Politis
- Subjects
FOS: Computer and information sciences ,Statistics and Probability ,Series (mathematics) ,05 social sciences ,Prediction interval ,Linear prediction ,01 natural sciences ,Methodology (stat.ME) ,010104 statistics & probability ,Predictive inference ,13. Climate action ,0502 economics and business ,Kernel smoother ,General regression ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Statistics - Methodology ,050205 econometrics ,Mathematics - Abstract
The Model-free Prediction Principle of Politis (2015) has been successfully applied to general regression problems, as well as problems involving stationary time series. However, with long time series, e.g. annual temperature measurements spanning over 100 years or daily financial returns spanning several years, it may be unrealistic to assume stationarity throughout the span of the dataset. In the paper at hand, we show how Model-free Prediction can be applied to handle time series that are only locally stationary, i.e., they can be assumed to be as stationary only over short time-windows. Surprisingly there is little literature on point prediction for general locally stationary time series even in model-based setups and there is no literature on the construction of prediction intervals of locally stationary time series. We attempt to fill this gap here as well. Both one-step-ahead point predictors and prediction intervals are constructed, and the performance of model-free is compared to model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, model-free and model-based, are novel in the context of time-series that are locally (but not globally) stationary. We also demonstrate the application of our Model-based and Model-free prediction methods to speleothem climate data which exhibits local stationarity and show that our best model-free point prediction results outperform that obtained with the RAMPFIT algorithm previously used for analysis of this data.
- Published
- 2020
27. Robust data-driven inference for density-weighted average derivatives
- Author
-
Cattaneo, Matias D., Crump, Richard K., and Jansson, Michael
- Subjects
Derivatives (Financial instruments) -- Forecasts and trends ,Robust statistics -- Usage ,Market trend/market analysis ,Mathematics - Abstract
This paper presents a novel data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density-weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth-dependent robust inference procedures proposed by Cattaneo, Crump, and Jansson (2009) are coupled with this new data-driven bandwidth selector. The resulting robust data-driven confidence intervals compare favorably to the alternative procedures available in the literature. The online supplemental material to this paper contains further results from the simulation study. KEY WORDS: Averaged derivative; Bandwidth selection; Robust inference; Small bandwidth asymptotics.
- Published
- 2010
28. Empirical likelihood in missing data problems
- Author
-
Qin, Jing, Zhang, Biao, and Leung, Denis H.Y.
- Subjects
Estimation theory -- Usage ,Combinatorial probabilities -- Usage ,Geometric probabilities -- Usage ,Probabilities -- Usage ,Mathematics - Abstract
Missing data is a ubiquitous problem in medical and social sciences. It is well known that inferences based only on the complete data may not only lose efficiency, but may also lead to biased results if the data is not missing completely at random (MCAR). The inverse-probability weighting method proposed by Horvitz and Thompson (1952) is a popular alternative when the data is not MCAR. The Horvitz-Thompson method, however, is sensitive to the inverse weights and may suffer from loss of efficiency. In this paper, we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters. One important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations. The proposed method can achieve semiparametric efficiency if the probability of missingness is correctly specified. Simulation results show that the proposed method has better finite sample performance than its competitors. Supplemental materials for this paper, including proofs of the main theoretical results and the R code used for the NHANES example, are available online on the journal website. KEY WORDS: Empirical likelihood; Estimating functions; Missing data: Surrogate end point.
- Published
- 2009
29. Learn from thy neighbor: parallel-chain and regional adaptive MCMC
- Author
-
Craiu, Radu V., Rosenthal, Jeffrey, and Yang, Chao
- Subjects
Markov processes -- Usage ,Algorithms -- Usage ,Monte Carlo method -- Usage ,Algorithm ,Mathematics - Abstract
Starting with the seminal paper of Haario, Saksman, and Tamminen (Haario, Saksman. and Tamminen 2001), a substantial amount of work has been done to validate adaptive Markov chain Monte Carlo algorithms. In this paper we focus on two practical aspects of adaptive Metropolis samplers. First, we draw attention to the deficient performance of standard adaptation when the target distribution is multimodal. We propose a parallel chain adaptation strategy that incorporates multiple Markov chains which are run in parallel. Second, we note that the current adaptive MCMC paradigm implicitly assumes that the adaptation is uniformly efficient on all regions of the state space. However, in many practical instances, different 'optimal' kernels are needed in different regions of the state space. We propose here a regional adaptation algorithm in which we account for possible errors made in defining the adaptation regions. This corresponds to the more realistic case in which one does not know exactly the optimal regions for adaptation. The methods focus on the random walk Metropolis sampling algorithm but their scope is much wider. We provide theoretical justification for the two adaptive approaches using the existent theory build for adaptive Markov chain Monte Carlo. We illustrate the performance of the methods using simulations and analyze a mixture model for real data using an algorithm that combines the two approaches. KEY WORDS: Adaptive Markov chain Monte Carlo; Metropolis sampling; Parallel chains; Random walk Metropolis sampling; Regional adaptation.
- Published
- 2009
30. Comment.
- Author
-
Wu, Colin O. and Huang, Jianhua Z.
- Subjects
- *
MATHEMATICAL functions , *MATHEMATICAL models , *ESTIMATION theory , *COMPLEX numbers , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Comments on a paper which developed a model for clustered functional data through a hierarchical nonparametric mixed-effects structure. Types of data that constitute clustered functional data; Features of the general nonparametric approach; Estimation methods.
- Published
- 2003
- Full Text
- View/download PDF
31. Practical small-sample asymptotics for regression problems
- Author
-
Strawderman Robert L., Casella, George, and Wells, Martin T.
- Subjects
Regression analysis -- Research ,Asymptotic expansions -- Analysis ,Mathematics - Abstract
A general method for estimating the distribution of a solution to an estimating equation defined through as sum of independent random variables is proposed. Suggested expansions are valid for the distribution of approximated parameters from general regression models and are not different from saddlepoint approximations in the case of iid random variables. A main advantage of the proposed methodology is that in requires on the conditional cumulant-generating function to be specified., 1. INTRODUCTION Daniels's (1954) seminal paper on saddlepoint approximations in statistics spawned a great deal of research in the general area of small-sample asymptotic approximations. His original paper concentrated primarily [...]
- Published
- 1996
32. Use of nested orthogonal contrasts in analyzing rank data
- Author
-
Marden, John I.
- Subjects
Decision-making -- Analysis ,Mathematical models -- Analysis ,Standard deviations -- Analysis ,Mathematics - Abstract
A data set consisting of 143 rankings of 10 occupations from a survey of Goldberg has been analyzed in a number of recent papers. The purpose of this paper is to use so-called 'nested orthogonal contrasts' of the occupations to gain further insight into the data. A contrast is a comparison of subsets of the occupations based on their relative ranks; contrasts are orthogonal if the comparisons they represent are not confounded. Various models based on sets of orthogonal contrasts-including contingency table models, models analogous to those of Fligner and Verducci, and latent class models--are applied to the data. It is found that there are three main groups of occupations based on overall prestige, and within each group are distinctions between managerial and technical occupations. KEY WORDS: Contingency tables; Discordant pairs; Kendall's tau; Mallows's [pi] model; Orthogonal contrasts; Permutations; Rank statistics., 1. BACKGROUND One question on a survey of engineering graduates discussed by Goldberg (1976) asked people to rank m = 10 occupations according to their perceived social prestige, with 1 [...]
- Published
- 1992
33. Some Estimators of a Population Total From Simple Random Samples Containing Large Units.
- Author
-
Hidiroglou, Michael A. and Srinath, Kadaba P.
- Subjects
- *
ESTIMATION theory , *OUTLIERS (Statistics) , *POPULATION statistics , *DATA editing , *STATISTICAL sampling , *MATHEMATICAL statistics , *NUMERICAL analysis , *MATHEMATICS - Abstract
The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators. A numerical study of these estimators is also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1981
- Full Text
- View/download PDF
34. Developments in Multiple Comparisons 1966--1976.
- Author
-
Millier, Rupert G. and Jr.
- Subjects
- *
STATISTICAL correlation , *MULTIPLE comparisons (Statistics) , *BIBLIOGRAPHY , *MATHEMATICAL statistics , *INFORMATION resources , *STATISTICS , *MATHEMATICS - Abstract
This article contains a bibliography of papers on multiple comparisons between 1966 and 1976. A. discussion of some of the more important developments during this period precedes the bibliography. [ABSTRACT FROM AUTHOR]
- Published
- 1977
- Full Text
- View/download PDF
35. Ideal Multiple-choice Items.
- Author
-
Weitzman, R. A.
- Subjects
- *
MULTIPLE choice examinations , *MULTIPLE comparisons (Statistics) , *EXAMINATIONS , *MATHEMATICAL analysis , *PROBABILITY measures , *MATHEMATICS , *MATHEMATICAL economics , *LOGIC ,QUESTIONS & answers - Abstract
A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
36. MULTIVARIATE MAXIMA AND MINIMA WITH MATRIX DERIVATIVES.
- Author
-
Tracy, Derrick S. and Dwyer, Paul S.
- Subjects
- *
MATRICES (Mathematics) , *MAXIMA & minima , *MATHEMATICS , *KRONECKER products , *TENSOR products , *PROBLEM solving - Abstract
The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
37. FIRST AND SECOND MOMENTS OF THE RANDOMIZATION TEST IN TWO-ASSOCIATE PBIB DESIGNS.
- Author
-
Cléroux, Robert
- Subjects
- *
MOMENTS method (Statistics) , *MATHEMATICS , *STATISTICS , *DISTRIBUTION (Probability theory) , *THEORY , *APPROXIMATION theory , *ERROR , *THEORY of knowledge , *PROBLEM solving - Abstract
In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment +error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
38. A SOLUTION TO THE PROBLEM OF LINKING MULTIVARIATE DOCUMENTS.
- Author
-
Du Bois Jr., N. S. D'Andrea
- Subjects
- *
DOCUMENTATION , *MULTIVARIATE analysis , *PUBLIC health , *CLINICAL medicine , *MATHEMATICS , *THEORY , *HEALTH , *MEDICAL care - Abstract
In many scientific investigations, it is desired to bring together, or link, two or more documents which represent the same individual, even though these documents do not contain a unique identifier and were derived from different sources. In medical and public health research and elsewhere, this problem is known as the document linkage problem. This paper considers some aspects of classifying pairs of documents into one of two populations when their items are identifying information, where each item of information can take on three distinct values correct, incorrect or missing. Section I identifies three document linkage problems. Sections 2 and 3 deal with the mathematical formulation of the multivariate document linkage problem. Section 4 gives the classification procedure and Section 5 deals with the application of the theory to a problem in the field of public health. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
39. FORECASTING SHORT-TERM ECONOMIC CHANGE.
- Author
-
Moore, Geoffrey H.
- Subjects
- *
STATISTICIANS , *ECONOMIC forecasting , *ECONOMISTS , *STATISTICS , *MATHEMATICAL statistics , *MATHEMATICS - Abstract
Economic statisticians do not enjoy an untarnished reputation for accurate forecasting. We have managed, over the years, to come up with some memorable failures. While we have also had our share of successes, they are not as well remembered nor as numerous as we should like. Recently, however, we have begun to pay more attention to the record, and a substantial body of evidence on forecasting performance has accumulated. In this paper I propose to review this record, try to arrive at a balanced appraisal, and offer some suggestions for improvement. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
40. ON SOME INVARIANT CRITERIA FOR GROUPING DATA.
- Author
-
Friedman, H. P. and Rubin, J.
- Subjects
- *
CLUSTER analysis (Statistics) , *STATISTICAL correlation , *RANDOM variables , *SPATIAL analysis (Statistics) , *MULTIVARIATE analysis , *MATHEMATICS , *MATHEMATICAL optimization - Abstract
This paper deals with methods of "cluster analysis". In particular we attack the problem of exploring the structure of multivariate data in search of "clusters". The approach taken is to use a computer procedure to obtain the "best" partition of n objects into g groups. A number of mathematical criteria for "best" are discussed and related to statistical theory. A procedure for optimizing the criteria is outlined. Some of the criteria are compared with respect to their behavior on actual data. Results of data analysis are presented and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
41. PROBABILITY SAMPLING WITH QUOTAS.
- Author
-
Sudman, Seymour
- Subjects
- *
STATISTICAL sampling , *PROBABILITY measures , *PROBABILITY theory , *STATISTICS , *MATHEMATICS , *INTERVIEWING , *AGE & employment - Abstract
This paper describes certain quota sampling procedures and attempts to show that they are very close to traditional probability sampling. Quotas are shown to depend on availability for interviewing and evidence is presented to show that sex, age, and employment status are reasonable predictors of availability. Quota sampling methods are not unbiased but data are presented which suggest that the bias is generally of the order of 3 to 5 per cent. It is shown, however, that the cost differentials between these quota samples and call-back samples are small. The major advantage of this new procedure may well be the speed with which interviewing may be completed during crises such as the Kennedy assassination. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
42. MISSING OBSERVATIONS IN MULTIVARIATE STATISTICS .
- Author
-
Afifi, A. A. and Elashoff, R. M.
- Subjects
- *
MULTIVARIATE analysis , *MATHEMATICAL statistics , *STATISTICS , *ANALYSIS of variance , *MATHEMATICAL variables , *MATHEMATICS , *REGRESSION analysis , *ESTIMATION theory - Abstract
In this paper we review the literature on the problem of handling multivariate data with observations missing on some or all of the variables under study. We examine the ways that statisticians have devised to estimate means, variances, correlations and linear regression functions from such data and refer to specific computer programs for carrying out the estimation. We show how the estimation problems can be simplified if the missing data follows certain patterns. Finally, we outline the statistical properties of the various estimators. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
43. CONFIDENCE BANDS OF UNIFORM AND PROPORTIONAL WIDTH FOR LINEAR MODELS.
- Author
-
Bowden, David C. and Graybill, Franklin A.
- Subjects
- *
LINEAR statistical models , *MATHEMATICAL models , *MATHEMATICAL statistics , *STATISTICS , *MATHEMATICS - Abstract
In this paper confidence bands are given for simple linear model. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
44. OPTIMUM ALLOCATION OF SAMPLING UNITS TO STRATA WHEN THERE ARE R RESPONSES OF INTEREST.
- Author
-
Folks, John Leroy and Antle, Charles E.
- Subjects
- *
MATHEMATICAL variables , *STATISTICAL sampling , *MATHEMATICAL functions , *MATHEMATICS , *SAMPLE size (Statistics) , *STATISTICS - Abstract
A common problem in many areas is to achieve a combination of control variables which will simultaneously maximize all of the responses which are functions of the control variables. The fact that in general we can not simultaneously maximize all of the responses has led to the formulation of compromise solutions to this vector maximum problem. A point in the control variable space is better than a second point if each response at the first point is greater than or equal to the corresponding response at the second point. If a point is such that there is no better point, it is said to be admissible, or efficient. A set of points is complete if given any point not in the set there is a point in the set which is better. In this paper this formulation is used to consider the allocation of sample size to several strata when there are several characteristics of interest. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
45. APPLICATIONS OF PROBABILITY THEORY IN CRIMINALISTICS.
- Author
-
Kingston, Charles R.
- Subjects
- *
CRIMINAL investigation , *DISTRIBUTION (Probability theory) , *PROBABILITY theory , *FORENSIC sciences , *RANDOM variables , *LEGAL evidence , *MATHEMATICAL variables , *MATHEMATICS - Abstract
This paper considers some problems in the probabilistic analysis of physical evidence in criminal investigations. Two basic assumptions are made: (1) That the number of persons or objects possessing a particular set of properties can be considered as a random variable, and (2) that it is possible to estimate the probability function of this random variable. Two models (one with and one without the assumption that the suspect is a random selection from the set of possible suspects) which arc applicable to the evaluation of partial transfer evidence--an important category of physical evidence that is found in most criminal investigations--are developed. A detailed analysis of the models and an example are presented for the case when the estimated probability distribution is binomial with an expected value less than 1. As the expected value becomes smaller, the assumption of randomness in the selection of the suspect becomes immaterial to the evaluation of the evidential significance. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
46. A Few Remarks on "Fixed-Width Output Analysis for Markov Chain Monte Carlo" by Jones et al.
- Author
-
Bednorz, Witold and Łatuszyński, Krzysztof
- Subjects
MARKOV processes ,STATISTICS ,MATHEMATICS ,STOCHASTIC processes - Abstract
Our aim is to relax assumptions and simplify proofs in results given by Jones, Haran, Caffo, and Neath in the recent paper "Fixed-Width Output Analysis for Markov Chain Monte Carlo." [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
47. Spherical Regression Models Using Projective Linear Transformations
- Author
-
Eric Klassen, Wei Wu, Anuj Srivastava, and Michael Rosenthal
- Subjects
Statistics and Probability ,Unit sphere ,Statistics::Theory ,Regression analysis ,Geometry ,Linear map ,Linear predictor function ,Statistics::Methodology ,Applied mathematics ,Projective linear group ,Statistics, Probability and Uncertainty ,Rotation (mathematics) ,Random variable ,Mathematics ,Variable (mathematics) - Abstract
This article studies the problem of modeling relationship between two spherical (or directional) random variables in a regression setup. Here the predictor and the response variables are constrained to be on a unit sphere and, due to this nonlinear condition, the standard Euclidean regression models do not apply. Several past papers have studied this problem, termed spherical regression, by modeling the response variable with a von Mises-Fisher (VMF) density with the mean given by a rotation of the predictor variable. The few papers that go beyond rigid rotations are limited to one- or two-dimensional spheres. This article extends the mean transformations to a larger group—the projective linear group of transformations—on unit spheres of arbitrary dimensions, while keeping the VMF density to model the noise. It develops a Newton–Raphson algorithm on the special linear group for estimating the MLE of regression parameter and establishes its asymptotic properties when the sample-size becomes large. Through ...
- Published
- 2014
48. Adaptive Thresholding for Sparse Covariance Matrix Estimation
- Author
-
Weidong Liu and T. Tony Cai
- Subjects
Statistics and Probability ,FOS: Computer and information sciences ,Mathematical optimization ,62H12, 62F12 ,Covariance matrix ,05 social sciences ,Matrix norm ,Contrast (statistics) ,Estimator ,Covariance ,01 natural sciences ,Thresholding ,Methodology (stat.ME) ,010104 statistics & probability ,Rate of convergence ,0502 economics and business ,DNA microarray experiment ,0101 mathematics ,Statistics, Probability and Uncertainty ,Algorithm ,Statistics - Methodology ,050205 econometrics ,Mathematics - Abstract
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be sub-optimal over the same parameter spaces. Support recovery is also discussed. The adaptive thresholding estimators are easy to implement. Numerical performance of the estimators is studied using both simulated and real data. Simulation results show that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumors microarray experiment. A supplement to this paper which contains additional technical proofs is available online., Comment: To appear in Journal of the American Statistical Association
- Published
- 2011
49. Robust Data-Driven Inference for Density-Weighted Average Derivatives
- Author
-
Richard K. Crump, Michael Jansson, and Matias D. Cattaneo
- Subjects
Statistics and Probability ,Mathematical optimization ,Mean squared error ,Bandwidth (signal processing) ,Monte Carlo method ,Robust statistics ,Estimator ,Inference ,Confidence interval ,Bandwidth (computing) ,Variety (universal algebra) ,Statistics, Probability and Uncertainty ,Algorithm ,Weighted arithmetic mean ,Mathematics - Abstract
This paper presents a novel data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density-weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth-dependent robust inference procedures proposed by Cattaneo, Crump, and Jansson (2009) are coupled with this new data-driven bandwidth selector. The resulting robust data-driven confidence intervals compare favorably to the alternative procedures available in the literature. The online supplemental material to this paper contains further results from the simulation study.
- Published
- 2010
50. Comment
- Author
-
Armin Schwartzman
- Subjects
Statistics and Probability ,Normalization (statistics) ,False discovery rate ,Statistics ,Multiple comparisons problem ,Null distribution ,Econometrics ,Statistics, Probability and Uncertainty ,Standard normal table ,Mixture model ,Empirical distribution function ,Mathematics ,Statistical hypothesis testing - Abstract
In a series of recent articles, Bradley Efron has pointed out that in large-scale multiple testing problems, the observed distribution of the test statistics often does not match the theoretical null distribution (Efron, 2004, 2007a,b, 2008). The correction, which he termed “empirical null”, has been a subject of controversy in the statistical community. In Efron (2007a), he made the case that, even when the theoretical model is correct, the observed distribution of the test statistics can look different from the theoretical null distribution simply because of correlation between the test statistics. Efron’s present article represents an important step forward in the understanding of this problem. As opposed to previous papers, where the the effect of correlation was treated within the context of multiple testing problems and false discovery rates, Efron’s present article breaks through the confusion by separating these two concepts and focusing on the core issue, which is the behavior of a large collection of correlated normal variables. Only then, as applications, he presents the implications for false discovery rate analysis when the correlated normal variables are z-scores in a large-scale multiple testing problem. I think this separation is crucial and helps get us nearer a new theory of inference for high-dimensional data. In what follows, I present my own interpretation of Efron’s results on how correlation affects the empirical distribution of normal variables. As a shortcut, I work in the countinous domain directly rather than with histogram bins and avoid the inclusion of unnecessary constraints such as normalization, which applies very specifically to microarray data. For simplicity, I assume all the variables are standard normal rather than belonging to a mixture model, but may have an arbitrary correlation structure. Using these results, I hope to answer the question raised in Efron (2007a) of whether large-scale correlation can substantially widen the observed histogram, as in Figure 1 in that paper and Efron’s current one. The theoretical arguments below indicate that this is unlikely. On the contrary, large-scale correlation has to be mostly positive in order to satisfy positive definite contraints, and as a result, correlation will most likely narrow and shift the observed histogram rather than widen it. An important implication is that a wide histogram may be an indication of the presence of true signal, rather than an artifact of correlation. Having a model for the observed distribution under correlation, I will suggest a new way of fitting an empirical null, which may be more appropriate in cases where the observed widening is larger than could be explained by correlation alone. I will conclude commenting briefly on the possibility of performing this kind of analysis with χ2 variates rather than normal. I will try to keep the notation close to that of Efron, but some discrepancies in notation will be inevitable.
- Published
- 2010
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.