Download or read book Efficient Estimation of the Error Distribution Function in Heteroskedastic Nonparametric Regression with Missing Data written by Justin Chown and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Error Density and Distribution Function Estimation in Nonparametric Regression Models written by Fuxia Cheng and published by . This book was released on 2002 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity written by Oliver B. Linton and published by . This book was released on 2016 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the efficient estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. The effect of weighting on nonparametric regressions is examined, and cases when efficiency gain can be achieved via weighting is investigated. We show that in many popular nonparametric regression models our method has lower asymptotic variance than the usual unweighted procedures. A Monte Carlo investigation is conducted and confirms the efficiency gain over conventional nonparametric regression estimators in finite samples. We use our method in several common applications concerning stock returns.

Download or read book Efficient Estimation of Nonparametric Regression in the Presence of Dynamic Heteroskedasticity written by Oliver Linton and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Missing and Modified Data in Nonparametric Estimation written by Sam Efromovich and published by CRC Press. This book was released on 2018-03-12 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonparametric Regression With the Scale Depending on Auxiliary Covariates and Missing Data written by Tian Jiang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric curve estimation is a powerful statistical methodology which allows estimation of curves with no assumption about their shape. It provides useful insight into the nature of data and may guide further inference for specific parametric models. Considered statistical problem is a nonparametric heteroscedastic regression with auxiliary covariates and missing data. In this regression a univariate component is of the primary interest while the scale function is allowed to be dependent on both the predictor and auxiliary covariates. Missing mechanism is the missing at random (MAR), and two settings with missing responses or missing predictors are considered. The assumed MAR means that the probability of missing may depend on observed variables but not on missing variables. Developed asymptotic theory shows how the heteroscedasticity and MAR mechanism affect the constant of minimax convergence under the mean integrated squared error criterion. Further, it is shown that a procedure ignoring the scale function is not efficient and does not attain a sharp constant in the minimax lower bound. Models of missing responses and predictors are considered separately because their theory and methodology are different. For the case of missing responses, a sharp minimax and data-driven procedure is developed which is based on estimation of an unknown nuisance scale function. The estimator adapts to the MAR response mechanism and unknown smoothness of an underlying regression function. Further, efficiency is still preserved for a more general additive model with auxiliary covariates. A model with MAR predictors is dramatically more involved, and here classic regression estimators are no longer even consistent. For a model with MAR predictors a novel data-driven estimator is suggested which takes into account a scale function. This estimator is adaptive and matches performance of an oracle that knows all underlying nuisance functions. The asymptotic theory is extended to the case of a general additive model as well. The theory and methodology are tested using Monte Carlo simulation studies and real examples. The results favor the proposed methodology and support practical feasibility of the proposed methods for heteroscedastic regressions with missing data.

Download or read book Efficient Nonparametric and Semiparametric Regression Methods with Application in Case Control Studies written by Shahina Rahman and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression Analysis is one of the most important tools of statistics which is widely used in other scientific fields for projection and modeling of association between two variables. Nowadays with modern computing techniques and super high performance devices, regression analysis on multiple dimensions has become an important issue. Our task is to address the issue of modeling with no assumption on the mean and the variance structure and further with no assumption on the error distribution. In other words, we focus on developing robust semiparametric and nonparamteric regression problems. In modern genetic epidemiological association studies, it is often important to investigate the relationships among the potential covariates related to disease in case-control data, a study known as "Secondary Analysis". First we focus to model the association between the potential covariates in univariate dimension nonparametrically. Then we focus to model the association in mulivariate set up by assuming a convenient and popular multivariate semiparametric model, known as Single-Index Model. The secondary analysis of case-control studies is particularly challenging due to multiple reasons (a) the case-control sample is not a random sample, (b) the logistic intercept is practically not identifiable and (c) misspecification of error distribution leads to inconsistent results. For rare disease, controls (individual free of disease) are typically used for valid estimation. However, numerous publication are done to utilize the entire case-control sample (including the diseased individual) to increase the efficiency. Previous work in this context has either specified a fully parametric distribution for regression errors or specified a homoscedastic distribution for the regression errors or have assumed parametric forms on the regression mean. In the first chapter we focus on to predict an univariate covariate Y by another potential univariate covariate X neither by any parametric form on the mean function nor by any distributional assumption on error, hence addressing potential heteroscedasticity, a problem which has not been studied before. We develop a tilted Kernel based estimator which is a first attempt to model the mean function nonparametrically in secondary analysis. In the following chapters, we focus on i.i.d samples to model both the mean and variance function for predicting Y by multiple covariates X without assuming any form on the regression mean. In particular we model Y by a single-index model m(X^T [Lowercase theta symbol]), where [Lowercase theta symbol] is a single-index vector and m is unspecified. We also model the variance function by another flexible single index model. We develop a practical and readily applicable Bayesian methodology based on penalized spline and Markov Chain Monte Carlo (MCMC) both in i.i.d set up and in case-control set up. For efficient estimation, we model the error distribution by a Dirichlet process mixture models of Normals (DPMM). In numerical examples, we illustrate the finite sample performance of the posterior estimates for both i.i.d and for case-control set up. For single-index set up, in i.i.d case only one existing work based on local linear kernel method addresses modeling of the variance function. We found that our method based on DPMM vastly outperforms the other existing method in terms of mean square efficiency and computation stability. We develop the single-index modeling in secondary analysis to introduce flexible mean and variance function modeling in case-control studies, a problem which has not been studies before. We showed that our method is almost 2 times efficient than using only controls, which is typically used for many cases. We use the real data example from NIH-AARP study on breast cancer, from Colon Cancer Study on red meat consumption and from National Morbidity Air Pollution Study to illustrate the computational efficiency and stability of our methods. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155719

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.

Download or read book Missing and Modified Data in Nonparametric Estimation written by Sam Efromovich and published by Chapman & Hall/CRC. This book was released on 2018 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Efromovichis 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. s 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 Efromovichis 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. 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.

Download or read book Efficient Estimation of Regression Coefficients with Missing Data written by Clint Allen Cummins and published by . This book was released on 1989 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Nonparametric Regression Estimation in a Correlated errors Model written by David Brian Holiday and published by . This book was released on 1986 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Efficient and Robust Estimation in Semiparametric Linear Regression Models with Missing Data written by Alex Catane Bajamonde and published by . This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Logistic Regression with Missing Values in the Covariates written by Werner Vach and published by . This book was released on 1994 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Design and Efficient Estimation in Regression Analysis with Missing Data in Two phase Studies microform written by Yang Zhao and published by Library and Archives Canada = Bibliothèque et Archives Canada. This book was released on 2005 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book METHODOLOGIES FOR MISSING DATA WITH RANGE REGRESSIONS written by Kevin E. Stoll and published by . This book was released on 2019 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primary focus of this dissertation is to draw inferences about a response variable that is subject to being missing using large samples. When some response variables are missing and the missing behavior is dependent on the response variable, simply using the sample mean of the non-missing responses to estimate the population mean is biased in general. There are, however, historical mean estimators that can circumvent the bias. Examples include the inverse propensity weighted, regression, double-robust, stratification, and empirical likelihood estimators. In order to obtain an appropriate estimate on the targeted population mean, these methods place greater weight on non-missing observations likely to be missing. We review the historical estimators, and we propose new estimators and methodologies for mean estimation and beyond. The consistency of each estimator primarily depends on the existence of non-missing covariates, the missing at random assumption, and a correctly specified model relating the covariates to the missing behavior or response, each of which is discussed. Among our proposals lie new double-robust estimators which obtain lower variance than historical methods when the regression or propensity function is known and yield competitive performances when regression and propensity functions are estimated. Additionally, we detail bootstrap approaches which enable researchers to efficiently draw inferences beyond mean estimation.Furthermore, we rework range regression for missing response variables, but also develop nonparametric range regression which models the average rank versus each bin. We argue the average rank to be superior to the median and mean for measuring trends among the bins particularly when researchers seek distributional superiority or when the sample mean is not guaranteed to converge, e.g. under Cauchy response. In doing so, we define ascendancy, a measure of pairwise distributional superiority. Then, we interpret the relationship between the average rank and the ascendancy of a conditional response over a benchmark random variable which is distributed by a mixture of the cumulative distribution functions of the underlying populations; the relationship is made apparent through an alternative calculation of the average rank that we find. Bootstrap approaches enabling researchers to fit nonparametric range and range regression under missing response variables are provided.

Download or read book Efficient Estimation of the Regression Parameter in a Heteroscedastic Regression Model where Heteroscedasticity is Modeled as a Function of the Mean Response written by Jeffrey Scott Forrester and published by . This book was released on 2001 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semiparametrically Efficient Estimation of the Average Linear Regression Function written by Bryan S. Graham and published by . This book was released on 2018 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: ELet Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment control variables. Here X may include (combinations of) continuous, discrete, and/or non-mutually exclusive "treatments". Consider the linear regression of Y onto X in a subpopulation homogenous in W = w (formally a conditional linear predictor). Let b0 (w) be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average b0 = E[b0 (W)]. When X is binary-valued (multi-valued) our procedure recovers the (a vector of) average treatment effect(s). When X is continuously-valued, or consists of multiple non-exclusive treatments, our estimand coincides with the average partial effect (APE) of X on Y when the underlying potential response function is linear in X, but otherwise heterogenous across agents. When the potential response function takes a general nonlinear/heterogenous form, and X is continuously-valued, our procedure recovers a weighted average of the gradient of this response across individuals and values of X. We provide a simple, and semiparametrically efficient, method of covariate adjustment for settings with complicated treatment regimes. Our method generalizes familiar methods of covariate adjustment used for program evaluation as well as methods of semiparametric regression (e.g., the partially linear regression model).