Topic

# Mathematical statistics

About: Mathematical statistics is a research topic. Over the lifetime, 3191 publications have been published within this topic receiving 293043 citations. The topic is also known as: Probabilities. Mathematical statistics.

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01 Jan 1987

TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.

Abstract: Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse.Large-Sample Inference Based on Maximum Likelihood Estimates.Bayes and Multiple Imputation.PART III: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA: APPLICATIONS TO SOME COMMON MODELS.Multivariate Normal Examples, Ignoring the Missing-Data Mechanism.Models for Robust Estimation.Models for Partially Classified Contingency Tables, Ignoring the Missing-Data Mechanism.Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missing-Data Mechanism.Nonignorable Missing-Data Models.References.Author Index.Subject Index.

18,201 citations

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03 Feb 1984

TL;DR: This paper presents the results of a series of experiments conducted in farmers' fields in the Czech Republic over a period of three years to investigate the effects of agricultural pesticides on animal welfare and human health.

Abstract: Elements of Experimentation. Single-Factor Experiments. Two-Factor Experiments. Three-or More-Factor Experiments. Comparison Between Treatment Means. Analysis of Multiobservation Data. Problem Data. Analysis of Data from a Series of Experiments. Regression and Correlation Analysis. Covariance Analysis. Chi-Square Test. Soil Heterogeneity. Competition Effects. Mechanical Errors. Sampling in Experimental Plots. Experiments in Farmers' Fields. Presentation of Experimental Results. Appendices. Index.

13,377 citations

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01 Jan 1965TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.

Abstract: Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation. Large Sample Theory and Methods. Theory of Statistical Inference. Multivariate Analysis. Publications of the Author. Author Index. Subject Index.

8,300 citations

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01 Mar 1990

TL;DR: In this paper, a theory and practice for the estimation of functions from noisy data on functionals is developed, where convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework.

Abstract: This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.

6,120 citations

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06 Aug 1999

TL;DR: In this article, the authors present a regression analysis with time series data using OLS asymptotics and a simple regression model in Matrix Algebra, which is based on the linear regression model.

Abstract: 1. The Nature of Econometrics and Economic Data. Part I: REGRESSION ANALYSIS WITH CROSS-SECTIONAL DATA. 2. The Simple Regression Model. 3. Multiple Regression Analysis: Estimation. 4. Multiple Regression Analysis: Inference. 5. Multiple Regression Analysis: OLS Asymptotics. 6. Multiple Regression Analysis: Further Issues. 7. Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables. 8. Heteroskedasticity. 9. More on Specification and Data Problems. Part II: REGRESSION ANALYSIS WITH TIME SERIES DATA. 10. Basic Regression Analysis with Time Series Data. 11. Further Issues in Using OLS with Time Series Data. 12. Serial Correlation and Heteroskedasticity in Time Series Regressions. Part III: ADVANCED TOPICS. 13. Pooling Cross Sections across Time: Simple Panel Data Methods. 14. Advanced Panel Data Methods. 15. Instrumental Variables Estimation and Two Stage Least Squares. 16. Simultaneous Equations Models. 17. Limited Dependent Variable Models and Sample Selection Corrections. 18. Advanced Time Series Topics. 19. Carrying out an Empirical Project. APPENDICES. Appendix A: Basic Mathematical Tools. Appendix B: Fundamentals of Probability. Appendix C: Fundamentals of Mathematical Statistics. Appendix D: Summary of Matrix Algebra. Appendix E: The Linear Regression Model in Matrix Form. Appendix F: Answers to Chapter Questions. Appendix G: Statistical Tables. References. Glossary. Index.

6,120 citations