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Author : A. R. Rasekh
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (62 download)
Download or read book Ridge Estimation in Functional Errors in Variables Models written by A. R. Rasekh and published by . This book was released on 1995 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raymond J. Carroll
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (227 download)
Download or read book Comparisons Between Some Estimators in Functional Errors-in-Variables Regression Models written by Raymond J. Carroll and published by . This book was released on 198? with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report studies the functional errors-in-variables regression model. In the case of no equation error (all randomness due to measurement errors), the maximum likelihood estimator computed assuming normality is asymptotically better than the usual moments estimator, even if the errors are not normally distributed. For certain statistical problems such as randomized two group analysis of covariance, the least squares estimate is shown to be better than the aformentioned errors-in-variables methods for estimating certain important contrasts.
Author : Silvelyn Zwanzig
Publisher :
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (247 download)
Download or read book Estimation in Nonlinear Functional Error-in-variables Models written by Silvelyn Zwanzig and published by . This book was released on 2000 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. K. Md. Ehsanes Saleh
Publisher : John Wiley & Sons
ISBN 13 : 1118644611
Total Pages : 384 pages
Book Rating : 4.1/5 (186 download)
Download or read book Theory of Ridge Regression Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2019-02-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.
Author : Kirk M. Wolter
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (17 download)
Download or read book Estimation of Nonlinear Errors-in-variables Models written by Kirk M. Wolter and published by . This book was released on 2002 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: An estimator is presented for the coefficients of the quadratic functional relationship. The estimator is show to be asymptotically normally distributed as the sample size increases.
Author : Osval Antonio Montesinos López
Publisher : Springer Nature
ISBN 13 : 3030890104
Total Pages : 707 pages
Book Rating : 4.0/5 (38 download)
Download or read book Multivariate Statistical Machine Learning Methods for Genomic Prediction written by Osval Antonio Montesinos López and published by Springer Nature. This book was released on 2022-02-14 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.
Author : Edna Schechtman
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (13 download)
Download or read book A Robust Estimator of the Slope in the Functional Errors-in-variables Model written by Edna Schechtman and published by . This book was released on 1989 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most Maximum Likelihood Estimates for the slope in the errors-in-variables models without replications rely on artificial assumptions, e.g., known ratio of variances of the two error terms. When this ratio is known, these estimates will perform well. If the ratio is not known, an alternative estimator has to be used. The Median-Slope estimator, proposed in this paper, is one such alternative. No assumptions are made about the parameters or the underlying distribution, but the predictors, although unknown, are assumed to be fixed and ordered. The Median-Slope estimator has a high breakdown point and is shown, via simulation, to perform well, especially for heavy tailed distributions. Large sample properties are investigated and the estimator is applied to some real data set.
Author : Odile Pons
Publisher : World Scientific
ISBN 13 : 9811272859
Total Pages : 259 pages
Book Rating : 4.8/5 (112 download)
Download or read book Functional Estimation For Density, Regression Models And Processes (Second Edition) written by Odile Pons and published by World Scientific. This book was released on 2023-09-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.
Author : Fouad Sabry
Publisher : One Billion Knowledgeable
ISBN 13 :
Total Pages : 315 pages
Book Rating : 4.:/5 (661 download)
Download or read book Regression Analysis written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2024-02-04 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Regression Analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. The most common form of regression analysis is linear regression, in which one finds the line that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line that minimizes the sum of squared differences between the true data and that line. For specific mathematical reasons, this allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters or estimate the conditional expectation across a broader collection of non-linear models. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Regression analysis Chapter 2: Least squares Chapter 3: Gauss-Markov theorem Chapter 4: Nonlinear regression Chapter 5: Coefficient of determination Chapter 6: Instrumental variables estimation Chapter 7: Omitted-variable bias Chapter 8: Ordinary least squares Chapter 9: Residual sum of squares Chapter 10: Simple linear regression Chapter 11: Generalized least squares Chapter 12: Heteroskedasticity-consistent standard errors Chapter 13: Variance inflation factor Chapter 14: Non-linear least squares Chapter 15: Principal component regression Chapter 16: Lack-of-fit sum of squares Chapter 17: Leverage (statistics) Chapter 18: Polynomial regression Chapter 19: Errors-in-variables models Chapter 20: Linear least squares Chapter 21: Linear regression (II) Answering the public top questions about regression analysis. (III) Real world examples for the usage of regression analysis in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Regression Analysis.
Author : A. R. Rasekh
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (62 download)
Download or read book Residuals in Functional Errors in Variables Models with Unequally Replicated Observations written by A. R. Rasekh and published by . This book was released on 1995 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavlo Stetsenko
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (857 download)
Download or read book Estimation of Errors-in-variables Models with No Auxiliary Data written by Pavlo Stetsenko and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers estimation in the context of regression models where some of the regressors are measured with errors. The regression model is identified under the assumption of strict exogeneity in the regression equation and classical errors. The structural model is equivalent to a certain infinite set of moment conditions, which allows me to construct a CGMM (continuous GMM) estimator for the parameters of the model. Alternatively, I also construct a finite-dimensional GMM by selecting a subset of moment conditions. Both frameworks are discussed in the paper, as they need to be augmented in order to allow for complex-valued moments. Monte-Carlo simulations show that my proposed estimation technique is several times better in terms of MSE than the alternatives proposed in the earlier literature.
Author : Michael H. Kutner
Publisher : McGraw-Hill/Irwin
ISBN 13 : 9780072386882
Total Pages : 1396 pages
Book Rating : 4.3/5 (868 download)
Download or read book Applied Linear Statistical Models written by Michael H. Kutner and published by McGraw-Hill/Irwin. This book was released on 2005 with total page 1396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
Author : Abdolrahman Rasekh
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (61 download)
Download or read book Diagnostic Methods in the Functional Errors in Variables Models written by Abdolrahman Rasekh and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marco Taboga
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781981369195
Total Pages : 670 pages
Book Rating : 4.3/5 (691 download)
Download or read book Lectures on Probability Theory and Mathematical Statistics - 3rd Edition written by Marco Taboga and published by Createspace Independent Publishing Platform. This book was released on 2017-12-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Yongming Qu
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (517 download)
Download or read book Estimation for the Nonlinear Errors-in-variables Model written by Yongming Qu and published by . This book was released on 2002 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of the parameters of the functional nonlinear measurement error model is considered. A simulation bias adjusted (SIMBA) estimation procedure is presented. In the SIMBA procedure, internal Monte Carlo simulation based on the sample data is used to adjust a naive estimator, such as the ordinary least squares estimator, for bias. Let the measurement error variance [(Sigma symbol followed by superscript 2 over subscript un)] be a sequence depending on the sample size n, and assume [Sigma symbol followed by superscript 2 over subscript un] [right pointing arrow] 0 as n [right pointing arrow] [Infinity symbol]. Under some regularity conditions, the order in probability convergence rate for the SIMBA estimator is max [(Sigma symbol followed by superscript 4 over subscript un, n superscript -1/2)], while the order in probability convergence rate for the ordinary least squares estimator is max [(Sigma symbol followed by superscript 2 over subscript un, n superscript -1/2)]. Monte Carlo simulation is conducted to test the performance of SIMBA for four models: linear model, quadratic model, cosine model and logistic model. Monte Carlo simulation shows that the SIMBA estimation procedure outperforms or is comparable to methods such as simulation extrapolation, regression calibration and adjusted least squares. An example application of SIMBA estimation for the logistic regression model with errors in variables is given. In the example, the relation between minerals from dietary intake and the supplement use for people over 50 is studied. The data are from the two surveys: the Third National Health and Nutrition Examination Survey and the related Supplemental Nutrition Survey. One interesting result is that people whose dietary intake of minerals is high are more likely to take supplements.
Author : Paul P. Gallo
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.:/5 (256 download)
Download or read book Properties of Estimators of Errors-in-variables Regression Models written by Paul P. Gallo and published by . This book was released on 1982 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Feng Zhang
Publisher : Stanford University
ISBN 13 :
Total Pages : 91 pages
Book Rating : 4.F/5 ( download)
Download or read book Cross-validation and Regression Analysis in High-dimensional Sparse Linear Models written by Feng Zhang and published by Stanford University. This book was released on 2011 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern scientific research often involves experiments with at most hundreds of subjects but with tens of thousands of variables for every subject. The challenge of high dimensionality has reshaped statistical thinking and modeling. Variable selection plays a pivotal role in the high-dimensional data analysis, and the combination of sparsity and accuracy is crucial for statistical theory and practical applications. Regularization methods are attractive for tackling these sparsity and accuracy issues. The first part of this thesis studies two regularization methods. First, we consider the orthogonal greedy algorithm (OGA) used in conjunction with a high-dimensional information criterion introduced by Ing& Lai (2011). Although it has been shown to have excellent performance for weakly sparse regression models, one does not know a priori in practice that the actual model is weakly sparse, and we address this problem by developing a new cross-validation approach. OGA can be viewed as L0 regularization for weakly sparse regression models. When such sparsity fails, as revealed by the cross-validation analysis, we propose to use a new way to combine L1 and L2 penalties, which we show to have important advantages over previous regularization methods. The second part of the thesis develops a Monte Carlo Cross-Validation (MCCV) method to estimate the distribution of out-of-sample prediction errors when a training sample is used to build a regression model for prediction. Asymptotic theory and simulation studies show that the proposed MCCV method mimics the actual (but unknown) prediction error distribution even when the number of regressors exceeds the sample size. Therefore MCCV provides a useful tool for comparing the predictive performance of different regularization methods for real (rather than simulated) data sets.
