Some Properties of the Least Squares Estimator in Regression Analysis when the Independent Variables are Stochastic PDF Download
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Author: P. K. Bhattacharya (Mathematician)
Publisher:
ISBN:
Category : Matrices
Languages : en
Pages : 32
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Book Description
For the linear regression of y on x observations the loss in estimating the true regression function by another function is considered as a loss function. For the loss function, it is shown under certain conditions that if the class of estimates which are linear in y's and have bounded risk is non-empty, then the estimate obtained by the method of least squares belongs to this class and has uniformly minimum risk in this class. A necessary and sufficient condition on the distribution function of x observations is obtained for this class to be non-empty, which unfortunately is not easy to verify in particular cases and is violated in a ver simple situation. owever, by a sequential modification of the sampling scheme, this condition may always be satisfied at the cost of an arbitrarily small increase in the expected sa ple size. I T IS ALSO SHOWN UNDER CERTAIN FURTHER C NDITIONS ON THE FAMILY OF ADMISSIBLE DISTRIB TIONS THAT THE LEAST SQUARES ESTIMATOR IS MINIMAX IN THE CLASS OF ALL ESTIMATORS. (Author).
Author: P. K. Bhattacharya (Mathematician)
Publisher:
ISBN:
Category : Matrices
Languages : en
Pages : 32
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Book Description
For the linear regression of y on x observations the loss in estimating the true regression function by another function is considered as a loss function. For the loss function, it is shown under certain conditions that if the class of estimates which are linear in y's and have bounded risk is non-empty, then the estimate obtained by the method of least squares belongs to this class and has uniformly minimum risk in this class. A necessary and sufficient condition on the distribution function of x observations is obtained for this class to be non-empty, which unfortunately is not easy to verify in particular cases and is violated in a ver simple situation. owever, by a sequential modification of the sampling scheme, this condition may always be satisfied at the cost of an arbitrarily small increase in the expected sa ple size. I T IS ALSO SHOWN UNDER CERTAIN FURTHER C NDITIONS ON THE FAMILY OF ADMISSIBLE DISTRIB TIONS THAT THE LEAST SQUARES ESTIMATOR IS MINIMAX IN THE CLASS OF ALL ESTIMATORS. (Author).
Author: Alexander Holmes
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 1801
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Book Description
Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.
Author: R. Carter Hill
Publisher: John Wiley & Sons
ISBN: 1118452275
Category : Business & Economics
Languages : en
Pages : 1808
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Book Description
Principles of Econometrics, Fifth Edition, is an introductory book for undergraduate students in economics and finance, as well as first-year graduate students in a variety of fields that include economics, finance, accounting, marketing, public policy, sociology, law, and political science. Students will gain a working knowledge of basic econometrics so they can apply modeling, estimation, inference, and forecasting techniques when working with real-world economic problems. Readers will also gain an understanding of econometrics that allows them to critically evaluate the results of others’ economic research and modeling, and that will serve as a foundation for further study of the field. This new edition of the highly-regarded econometrics text includes major revisions that both reorganize the content and present students with plentiful opportunities to practice what they have read in the form of chapter-end exercises.
Author:
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ISBN:
Category : Weights and measures
Languages : en
Pages : 574
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Author:
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ISBN:
Category : Health surveys
Languages : en
Pages : 524
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Author: Richard A. Johnson
Publisher: John Wiley & Sons
ISBN: 0470409274
Category : Mathematics
Languages : en
Pages : 712
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Book Description
Johnson provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters have been updated with real-world data to make the material more relevant. The revised pedagogy will help them contextualize statistical concepts and procedures. The numerous examples clearly demonstrate the important points of the methods. New What Will We Learn opening paragraphs set the stage for the material being discussed. Using Statistics Wisely boxes summarize key lessons. In addition, Statistics in Context sections give business professionals an understanding of applications in which a statistical approach to variation is needed.
Author: Christiaan Heij
Publisher: OUP Oxford
ISBN: 0191608408
Category : Business & Economics
Languages : en
Pages : 1132
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Book Description
Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
Author: Brian L. Joiner
Publisher:
ISBN:
Category : Annals of mathematical statistics
Languages : en
Pages : 512
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Book Description
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Author: Eugene Demidenko
Publisher: John Wiley & Sons
ISBN: 0471726133
Category : Mathematics
Languages : en
Pages : 732
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Book Description
A rigorous, self-contained examination of mixed model theory and application Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. Paying special attention to algorithms and their implementations, the book discusses: Modeling of complex clustered or longitudinal data Modeling data with multiple sources of variation Modeling biological variety and heterogeneity Mixed model as a compromise between the frequentist and Bayesian approaches Mixed model for the penalized log-likelihood Healthy Akaike Information Criterion (HAIC) How to cope with parameter multidimensionality How to solve ill-posed problems including image reconstruction problems Modeling of ensemble shapes and images Statistics of image processing Major results and points of discussion at the end of each chapter along with "Summary Points" sections make this reference not only comprehensive but also highly accessible for professionals and students alike in a broad range of fields such as cancer research, computer science, engineering, and industry.
Author: United States. Air Force. Office of Aerospace Research
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 794
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Book Description
