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Constrained Statistical Inference
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Book Synopsis Constrained Statistical Inference by : Mervyn J. Silvapulle
Download or read book Constrained Statistical Inference written by Mervyn J. Silvapulle and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of fields, focusing on sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality-constrained inference problems that do not fit well in the contemplated unified framework, providing a meaningful way for readers to comprehend methodological resolutions. Chapter coverage includes: Population means and isotonic regression Inequality-constrained tests on normal means Tests in general parametric models Likelihood and alternatives Analysis of categorical data Inference on monotone density function, unimodal density function, shape constraints, and DMRL functions Bayesian perspectives, including Stein’s Paradox, shrinkage estimation, and decision theory
Book Synopsis Constrained Statistical Inference by : Pranab Kumar Sen
Download or read book Constrained Statistical Inference written by Pranab Kumar Sen and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constrained Statistical Inference in Regression by : Thelge Buddika Peiris
Download or read book Constrained Statistical Inference in Regression written by Thelge Buddika Peiris and published by . This book was released on 2014 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
Book Synopsis Constrained Statistical Inference in Regression by : Thelge Buddika Peiris (‡e author)
Download or read book Constrained Statistical Inference in Regression written by Thelge Buddika Peiris (‡e author) and published by . This book was released on 2014 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
Book Synopsis Constrained Statistical Inference by : David K. Ruch
Download or read book Constrained Statistical Inference written by David K. Ruch and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction -- 2. Comparison of population means and isotonic regression -- 3. Tests on multivariate normal mean -- 4. Tests in general parametric models -- 5. Likelihood and alternatives -- 6. Analysis of categorical data -- 7. Beyond parametrics -- 8. Bayesian perspectives -- 9. Miscellaneous topics
Book Synopsis Constrained Statistical Inference in Generalized Linear, and Mixed Models with Incomplete Data by : Karelyn Alexandrea Davis
Download or read book Constrained Statistical Inference in Generalized Linear, and Mixed Models with Incomplete Data written by Karelyn Alexandrea Davis and published by . This book was released on 2011 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Inference Under Inequality Constraints by : Richard Dykstra
Download or read book Statistical Inference Under Inequality Constraints written by Richard Dykstra and published by . This book was released on 2002 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constrained Statistical Inference when Target and Sample Populations Differ by : Huijun Yi
Download or read book Constrained Statistical Inference when Target and Sample Populations Differ written by Huijun Yi and published by . This book was released on 2014 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: When analyzing an I x J contingency table, there are situations where sampling is taken from a sampled population that differs from the target population. Clearly the resulting estimators are typically biased. In this dissertation, four adjusting methods for estimating the cell probabilities under inequality constrains, namely, raking (RAKE), maximum likelihood under random sampling (MLRS), minimum chi-squared (MCSQ), and least squares (LSQ) are developed for particular models relating the target and sampled populations.Considering the difficulty of solving primal problem due to large dimensions, we use the Khun-Tucker conditions to exploit the duality for each method. Extensive simulation is performed to provide a systematic comparison between adjusting methods. The comparisons are also made by using a measure of information loss because of biased sampling.We apply four methods to the second National Health and Nutrition Examination Survey data under reasonable constraints. Not only the performance of four methods are compared in the example, but also how different constraints affect the quality of estimation is inspected. We emphasize that a sampling is taken from a sample population that differs from a target population. In the absence of knowledge of target population, a prior distribution can be considered as describing the initial knowledge about the target population. In the dissertation we also discuss Bayesian analysis with the use of a proper prior to measure missing information.
Book Synopsis Efficient Statistical Inference Under Sampling and Computational Constraints by : Ankit Pensia
Download or read book Efficient Statistical Inference Under Sampling and Computational Constraints written by Ankit Pensia and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical inference has a long history of established algorithms with theoretical guarantees, but modern machine learning applications impose new statistical and computational constraints. These constraints include constraints on sampling such as poor quality datasets that deviate from idealized assumptions and constraints on computational resources such as time, memory, communication bandwidth, and privacy. These constraints can lead to a significant decrease in the performance of classical inference techniques, calling for new algorithmic solutions. In this thesis, we focus on fundamental statistical inference tasks such as mean estimation, linear regression, and hypothesis testing in the presence of aforementioned constraints. The first part of the thesis focuses on statistical constraints on sampling and the challenges posed by real-world datasets that often do not conform to idealized assumptions. Many such datasets contain heavy tails, arbitrary outliers, and heterogeneity as opposed to the idealistic assumption of i.i.d. (sub-)Gaussian data. We develop practical statistical inference algorithms for mean estimation and linear regression with provable guarantees that are robust to these deviations. We achieve these results by developing algorithms that work under minimal structures on the data and proving that these structures hold with exponential probability, even under heavy-tailed data. In regimes where the existence of efficient algorithms is unknown, we give concrete evidence that efficient algorithms might indeed not exist by showing average-case computational lower bounds for a restricted family of algorithms. The second part of the thesis focuses on computational constraints and the need to optimize algorithms for limited memory, communication bandwidth, and privacy in large-scale, distributed machine learning pipelines (in addition to optimizing for runtime). We begin by considering the space complexity of efficient algorithms for high-dimensional robust statistics, where we develop the first streaming algorithms with near-optimal space complexity. Finally, we consider simple hypothesis testing under communication bandwidth and local privacy constraints, where we characterize the minmax optimal sample complexity and develop computationally-efficient algorithms.
Book Synopsis Modes of Parametric Statistical Inference by : Seymour Geisser
Download or read book Modes of Parametric Statistical Inference written by Seymour Geisser and published by John Wiley & Sons. This book was released on 2006-01-27 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating investigation into the foundations of statistical inference This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses. The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference: * Frequentist * Likelihood * Fiducial * Bayesian The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development. The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.
Book Synopsis Emprical Likelihood and Constrained Statistical Inference for Some Moment Inequality Models by : Rami Tabri
Download or read book Emprical Likelihood and Constrained Statistical Inference for Some Moment Inequality Models written by Rami Tabri and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The principal purpose of this thesis is to extend empirical likelihood (EL) based procedures to some statistical models defined by unconditional moment inequalities. We develop EL procedures for two such models in the thesis. In the first type of model, the underlying probability distribution is the (infinite-dimensional) parameter of interest, and is defined by a continuum of moment inequalities indexed by a general class of estimating functions. We develop the EL estimation theory using a feasible-value-function approach, and demonstrate the uniform consistency of the estimator over the set of underlying distributions in the model. Furthermore, for large sample sizes, we prove that it has smaller mean integrated squared error than the estimator that ignores the information in the moment inequality conditions. We also develop computational algorithms for this estimator, and demonstrate its properties in Monte Carlo simulation experiments for the case of infinite-order stochastic dominance. The second type of moment inequality model concerns stochastic dominance (SD) orderings between two income distributions. We develop asymptotic and bootstrap empirical likelihood-ratio tests for the null hypothesis that a given unidirectional strong SD ordering between the income distributions holds. These distributions are discrete with finite support, and, therefore, the SD conditions are framed as sets of linear inequality constraints on the vector of SD curve ordinates. Testing for strong SD requires that we consider as the null model one that allows at most one pair of these ordinates to be equal at an interior point of their support. Finally, we study the performance of these tests in Monte Carlo simulations." --
Book Synopsis Order Restricted Statistical Inference by : Tim Robertson
Download or read book Order Restricted Statistical Inference written by Tim Robertson and published by John Wiley & Sons Incorporated. This book was released on 1988 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work attempts to provide a comprehensive treatment of the topic of statistical inference under inequality constraints, in which much of the theory is based on the principles ofr maximum likelihood estimation and likelihood ratio tests.
Book Synopsis Empirical Likelihood and Bootstrap Inference with Constraints by : Chunlin Wang
Download or read book Empirical Likelihood and Bootstrap Inference with Constraints written by Chunlin Wang and published by . This book was released on 2017 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical likelihood and the bootstrap play influential roles in contemporary statistics. This thesis studies two distinct statistical inference problems, referred to as Part I and Part II, related to the empirical likelihood and bootstrap, respectively. Part I of this thesis concerns making statistical inferences on multiple groups of samples that contain excess zero observations. A unique feature of the target populations is that the distribution of each group is characterized by a non-standard mixture of a singular distribution at zero and a skewed nonnegative component. In Part I of this thesis, we propose modelling the nonnegative components using a semiparametric, multiple-sample, density ratio model (DRM). Under this semiparametric setup, we can efficiently utilize information from the combined samples even with unspecified underlying distributions. We first study the question of testing homogeneity of multiple nonnegative distributions when there is an excess of zeros in the data, under the proposed semiparametric setup. We develop a new empirical likelihood ratio (ELR) test for homogeneity and show that this ELR has a $\chi^2$-type limiting distribution under the homogeneous null hypothesis. A nonparametric bootstrap procedure is proposed to calibrate the finite-sample distribution of the ELR. The consistency of this bootstrap procedure is established under both the null and alternative hypotheses. Simulation studies show that the bootstrap ELR test has an accurate nominal type I error, is robust to changes of underlying distributions, is competitive to, and sometimes more powerful than, several popular one- and two-part tests. A real data example is used to illustrate the advantages of the proposed test. We next investigate the problem of comparing the means of multiple nonnegative distributions, with excess zero observations, under the proposed semiparametric setup. We develop a unified inference framework based on our new ELR statistic, and show that this ELR has a $\chi^2$-type limiting distribution under a general null hypothesis. This allows us to construct a new test for mean equality. Simulation results show favourable performance of the proposed ELR test compared with other existing tests for mean equality, especially when the correctly specified basis function in the DRM is the logarithm function. A real data set is analyzed to illustrate the advantages of the proposed method. In Part II of this thesis, we investigate the asymptotic behaviour of, the commonly used, bootstrap percentile confidence intervals when the parameters are subject to inequality constraints. We concentrate on the important one- and two-sample problems with data generated from distributions in the natural exponential family. Our attention is focused on quantifying asymptotic coverage probabilities of the percentile confidence intervals based on bootstrapping maximum likelihood estimators. We propose a novel local framework to study the subtle asymptotic behaviour of bootstrap percentile confidence intervals when the true parameter values are close to the boundary. Under this framework, we discover that when the true parameter is on, or close to, the restriction boundary, the local asymptotic coverage probabilities can always exceed the nominal level in the one-sample case; however, they can be, surprisingly, both under and over the nominal level in the two-sample case. The results provide theoretical justification and guidance on applying the bootstrap percentile method to constrained inference problems. The two individual parts of this thesis are connected by being referred to as {\em constrained statistical inference}. Specifically, in Part I, the semiparametric density ratio model uses an exponential tilting constraint, which is a type of equality constraint, on the parameter space. In Part II, we deal with inequality constraints, such as a boundary or ordering constraints, on the parameter space. For both parts, an important regularity condition in traditional likelihood inference, that parameters should be interior points of the parameter space, is violated. Therefore, the respective inference procedures involve non-standard asymptotics that create new technical challenges.
Book Synopsis Principles of Statistical Inference by : D. R. Cox
Download or read book Principles of Statistical Inference written by D. R. Cox and published by Cambridge University Press. This book was released on 2006-08-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.
Book Synopsis From Statistical Physics to Statistical Inference and Back by : P. Grassberger
Download or read book From Statistical Physics to Statistical Inference and Back written by P. Grassberger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.
Book Synopsis Advances in Info-Metrics by : Min Chen
Download or read book Advances in Info-Metrics written by Min Chen and published by Oxford University Press, USA. This book was released on 2020 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Info-metrics is a framework for rational inference on the basis of limited, or insufficient, information. It is the science of modeling, reasoning, and drawing inferences under conditions of noisy and insufficient information. Info-metrics has its roots in information theory (Shannon, 1948), Bernoulli's and Laplace's principle of insufficient reason (Bernoulli, 1713) and its offspring the principle of maximum entropy (Jaynes, 1957). It is an interdisciplinary framework situated at the intersection of information theory, statistical inference, and decision-making under uncertainty. Within a constrained optimization setup, info-metrics provides a simple way for modeling and understanding all types of systems and problems. It is a framework for processing the available information with minimal reliance on assumptions and information that cannot be validated. Quite often a model cannot be validated with finite data. Examples include biological, social and behavioral models, as well as models of cognition and knowledge. The info-metrics framework extends naturally for tackling these types of common problems"--
Book Synopsis Inference Control in Statistical Databases by : Josep Domingo-Ferrer
Download or read book Inference Control in Statistical Databases written by Josep Domingo-Ferrer and published by Springer. This book was released on 2003-08-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inference control in statistical databases, also known as statistical disclosure limitation or statistical confidentiality, is about finding tradeoffs to the tension between the increasing societal need for accurate statistical data and the legal and ethical obligation to protect privacy of individuals and enterprises which are the source of data for producing statistics. Techniques used by intruders to make inferences compromising privacy increasingly draw on data mining, record linkage, knowledge discovery, and data analysis and thus statistical inference control becomes an integral part of computer science. This coherent state-of-the-art survey presents some of the most recent work in the field. The papers presented together with an introduction are organized in topical sections on tabular data protection, microdata protection, and software and user case studies.
