Consistent Estimation Using Data from More Than One Sample
Consistent Estimation Using Data from More Than One Sample

Author: William T. Dickens

Publisher:

Published: 1984

Total Pages: 66

ISBN-13:

DOWNLOAD EBOOK

This paper considers the estimation of linear models when group average data from more than one sample is used. Conditions under which OL8 coefficient estimates are consistent are identified. The standard OL8 covariance estimate is shown to be inconsistent and a consistent estimator is proposed. Finally, since the conditions under which OL8 is consistent are quite restrictive, several estimators which are consistent in many cases where OL8 is not are developed. The large sample distribution properties and an estimator for the asymptotic covariance matrix for the most general of these alternative estimators is also presented. One important application of these findings is to estimating compensating wage differences. Past authors, beginning with Thaler and Rosen (1976) have argued that finer classification schemes would reduce errors-in-variable bias. The analysis presented here suggests that the opposite is true if finer classification results in fewer observations per classification. This could explain why authors using the broader (industry) classification schemes have found larger compensating differences and suggests that these estimates may be closer to the true values.

Statistical Inference: Theory of Estimation
Statistical Inference: Theory of Estimation

Author: Prakash S. Chougule

Publisher: Blue Rose Publishers

Published: 2022-01-24

Total Pages: 271

ISBN-13:

DOWNLOAD EBOOK

The book “Statistical Inference: Theory of Estimation” aims to help the student in gaining knowledge about Statistical Inference. This book contains five chapters like Point estimation, Likelihood function and Sufficiency, Cramer Rao Inequality, methods of estimation and Interval estimation. Every chapter has been divided into several headings and sub headings to offer clarity and conciseness. The authors have tried his best to simplify units and are written in very simple and lucid language. so that the reader can get an intuitive understanding the contains of the book. The number of examples included in the book will really make the study very easy and yet efficient. The question bank of simple and relative exercise included lot of multiple choice questions at the end of each chapter is given which helps the students to evaluate themselves. The book will particularly help students of B.Sc. and M.Sc. statistics classes.

Missing and Modified Data in Nonparametric Estimation
Missing and Modified Data in Nonparametric Estimation

Author: Sam Efromovich

Publisher: CRC Press

Published: 2018-03-12

Total Pages: 867

ISBN-13: 135167983X

DOWNLOAD EBOOK

This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.

Data Science
Data Science

Author: C. Raju

Publisher: Penguin Random House India Private Limited

Published: 2023-08-21

Total Pages: 135

ISBN-13: 9357082220

DOWNLOAD EBOOK

Data science is a perfect blend of 10 per cent maths, 20 per cent statistics, 30 per cent common sense and 40 per cent applied knowledge. While you can learn maths and statistics, you need to accumulate certain experience for common sense to kick in and apply what you have learnt. This introductory book on data science builds upon an individual's innate knowledge and arms you with the tools to use this interdisciplinary academic field in everyday scenarios. With straightforward real-world examples and applications, it takes you on a path that may seem daunting but is made simple through Professor Raju's easy manner. It endows you with a holistic and flawless understanding of the fundamental principles required to build a solid foundation in data science.

Introductory Regression Analysis
Introductory Regression Analysis

Author: Allen Webster

Publisher: Routledge

Published: 2013-03-05

Total Pages: 488

ISBN-13: 1136593098

DOWNLOAD EBOOK

Regression analysis is arguably the single most powerful and widely applicable tool in any effective examination of common business issues. Every day, decision-makers face problems that require constructive actions with significant consequences, and regression procedures can prove a meaningful and valuable asset in the decision-making process. This text is designed to help students achieve a full understanding of regression and the many ways it can be used. Taking into consideration current statistical technology, Introductory Regression Analysis focuses on the use and interpretation of software, while also demonstrating the logic, reasoning, and calculations that lie behind any statistical analysis. Furthermore, the text emphasizes the application of regression tools to real-life business concerns. This multilayered, yet pragmatic approach fully equips students to derive the benefit and meaning of a regression analysis. This text is designed to serve in a second undergraduate course in statistics, focusing on regression and its component features. The material presented in this text will build from a foundation of the principles of data analysis. Although previous exposure to statistical concepts would prove helpful, all the material needed for an examination of regression analysis is presented here in a clear and complete form.

Lectures on Probability Theory and Mathematical Statistics - 3rd Edition
Lectures on Probability Theory and Mathematical Statistics - 3rd Edition

Author: Marco Taboga

Publisher: Createspace Independent Publishing Platform

Published: 2017-12-08

Total Pages: 670

ISBN-13: 9781981369195

DOWNLOAD EBOOK

The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

Sampling Strategies for Natural Resources and the Environment
Sampling Strategies for Natural Resources and the Environment

Author: Timothy G. Gregoire

Publisher: CRC Press

Published: 2007-07-12

Total Pages: 480

ISBN-13: 1584883707

DOWNLOAD EBOOK

Written by renowned experts in the field, Sampling Strategies for Natural Resources and the Environment covers the sampling techniques used in ecology, forestry, environmental science, and natural resources. The book presents methods to estimate aggregate characteristics on a per unit area basis as well as on an elemental basis. In addition to common sampling designs such as simple random sampling and list sampling, the authors explore more specialized designs for sampling vegetation, including randomized branch sampling and 3P sampling. One of the book's unique features is the emphasis on areal sampling designs, including plot/quadrat sampling, Bitterlich sampling, line intersect sampling, and several lesser known designs. The book also provides comprehensive solutions to the problem of edge effect. Another distinguishing aspect is the inclusion of sampling designs for continuums, focusing on the methods of Monte Carlo integration. By presenting a conceptual understanding of each sampling design and estimation procedure as well as mathematical derivations and proofs in the chapter appendices, this text promotes a deep understanding of the underpinnings of sampling theory, estimation, and inference. Moreover, it will help you reliably sample natural populations and continuums.

Decision Sciences
Decision Sciences

Author: Raghu Nandan Sengupta

Publisher: CRC Press

Published: 2016-11-30

Total Pages: 1042

ISBN-13: 1482282569

DOWNLOAD EBOOK

This handbook is an endeavour to cover many current, relevant, and essential topics related to decision sciences in a scientific manner. Using this handbook, graduate students, researchers, as well as practitioners from engineering, statistics, sociology, economics, etc. will find a new and refreshing paradigm shift as to how these topics can be put to use beneficially. Starting from the basics to advanced concepts, authors hope to make the readers well aware of the different theoretical and practical ideas, which are the focus of study in decision sciences nowadays. It includes an excellent bibliography/reference/journal list, information about a variety of datasets, illustrated pseudo-codes, and discussion of future trends in research. Covering topics ranging from optimization, networks and games, multi-objective optimization, inventory theory, statistical methods, artificial neural networks, times series analysis, simulation modeling, decision support system, data envelopment analysis, queueing theory, etc., this reference book is an attempt to make this area more meaningful for varied readers. Noteworthy features of this handbook are in-depth coverage of different topics, solved practical examples, unique datasets for a variety of examples in the areas of decision sciences, in-depth analysis of problems through colored charts, 3D diagrams, and discussions about software.