Download or read book Nonparametric Inference on Quantile Marginal Effects written by David M. Kaplan and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Marginal Nonparametric Inference for Waiting Times in Multistage Models written by Douglas J. Lorenz and published by . This book was released on 2011 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Marginal inference for waiting times in multi-stage time-to-event models is complicated by right censoring of observations as well as the prior history of events in the model. In general, complications arise due to the evolution of the censoring process in so called "calendar time", contrasted with the evolution of the waiting time process conditional upon entry into a given stage. Developments in inference for survival data under dependent censoring have been extended to the multi-stage framework, and non parametric estimators for the cumulative hazard function and survival function for waiting times analogous of the classical Nelson-Aalen and Kaplan-Meier estimators for survival data have been developed. These estimators were derived under the principle of weighting the basic at-risk and event counting processes by the inverse probability of censoring. We extend this concept to K-sample hypothesis testing and non parametric regression, and define test statistics and regression coefficient estimators analogous to the log-rank test and Aalen's nonparametric linear regression estimators for survival data. We examine the asymptotic distribution of these statistics, and justify their use via simulation studies and analyses of real data sets.

Download or read book A Simple Nonparametric Approach for Estimation and Inference of Conditional Quantile Functions written by Zheng Fang and published by . This book was released on 2018 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy-to-implement, and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. The Monte Carlo simulations show that our new estimator compares well with the checkfunction-based estimator in terms of estimation mean squared error (MSE), and the bootstrap confidence bands give adequate coverage probabilities. An empirical example considering a dataset from Canadian high school graduate earnings illustrates that the proposed method delivers a more reasonable quantile estimate than the check-function counterpart.

Download or read book Recent Developments in Nonparametric Inference and Probability written by and published by IMS. This book was released on 2006 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

Download or read book An Introduction to the Advanced Theory of Nonparametric Econometrics written by Jeffrey S. Racine and published by Cambridge University Press. This book was released on 2019-06-27 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides theory, open source R implementations, and the latest tools for reproducible nonparametric econometric research.

Download or read book Fractional Order Statistic Approximation for Nonparametric Conditional Quantile Inference written by Matt Goldman and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes written by Victor Chernozhukov and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a method to construct simultaneous confidence bands for quantile and quantile effect functions for possibly discrete or mixed discrete-continuous random variables. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling strategies and does not depend on the sampling schemes. It is based upon projection of simultaneous confidence bands for distribution functions. We apply our method to analyze the distributional impact of insurance coverage on health care utilization and to provide a distributional decomposition of the racial test score gap. Our analysis generates new interesting findings, and complements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering standard inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.

Download or read book All of Statistics written by Larry Wasserman and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

Download or read book Contributions to Semiparametric Inference and Its Applications written by Seong Ho Lee and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation focuses on developing statistical methods for semiparametric inference and its applications. Semiparametric theory provides statistical tools that are flexible and robust to model misspecification. Utilizing the theory, this work proposes robust estimation approaches that are applicable to several scenarios with mild conditions, and establishes their asymptotic properties for inference. Chapter 1 provides a brief review of the literature related to this work. It first introduces the concept of semiparametric models and the efficiency bound. It further discusses two nonparametric techniques employed in the following chapters, kernel regression and B-spline approximation. The chapter then addresses the concept of dataset shift. In Chapter 2, novel estimators of causal effects for categorical and continuous treatments are proposed by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent for causal contrasts and asymptotically normal, when either the model explaining the treatment assignment is correctly specified, or the correct set of bases for the outcome models has been chosen and the assignment model is sufficiently rich. Asymptotic results are complemented with simulations illustrating the finite sample properties. A data analysis suggests a nonlinear effect of BMI on self-reported health decline among the elderly. In Chapter 3, we consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze non-labor income data and discover a new interesting predictor. In Chapter 4, we propose a procedure to select the best training subsample for a classification model. Identifying patient's disease status from electronic health records (EHR) is a frequently encountered task in EHR related research. However, assessing patient's phenotype is costly and labor intensive, hence a proper selection of EHR as a training set is desired. We propose a procedure to tailor the training subsample for a classification model minimizing its mean squared error (MSE). We provide theoretical justification on its optimality in terms of MSE. The performance gain from our method is illustrated through simulation and a real data example, and is found often satisfactory under criteria beyond mean squared error. In Chapter 5, we study label shift assumption and propose robust estimators for quantities of interest. In studies ranging from clinical medicine to policy research, the quantity of interest is often sought for a population from which only partial data is available, based on complete data from a related but different population. In this work, we consider this setting under the so-called label shift assumption. We propose an estimation procedure that only needs standard nonparametric techniques to approximate a conditional expectation, while by no means needs estimates for other model components. We develop the large sample theory for the proposed estimator, and examine its finite-sample performance through simulation studies, as well as an application to the MIMIC-III database.

Download or read book Applied Nonparametric Econometrics written by Daniel J. Henderson and published by Cambridge University Press. This book was released on 2015-01-12 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

Download or read book Asymptotic Statistics written by Petr Mandl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: In particular up-to-date-information is presented in detection of systematic changes, in series of observation, in robust regression analysis, in numerical empirical processes and in related areas of actuarial sciences.

Download or read book Nonparametric Inference on Monotone Functions with Applications to Observational Studies written by Theodore Westling and published by . This book was released on 2018 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study general strategies for constructing nonparametric monotone function estimators in two broad statistical settings. In the first setting, a sensible initial estimator of the monotone function of interest is available, but may fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid in the domain. We demonstrate that this corrected estimator is always at least as good in supremum norm as the initial estimator, and provide conditions under which the two estimators are asymptotically equivalent. In the second setting, a sensible estimator of the primitive of the function of interest is available. In this setting, estimators considered in the literature have often been of so-called Grenander type, being representable as the left derivative of the greatest convex minorant of the primitive estimator. We provide general conditions for consistency and pointwise convergence in distribution of a class of generalized Grenander-type estimators. This broad class allows the minorization operation to be performed on a data-dependent transformation of the domain. We use our general results from the second setting to perform a detailed study of generalized Grenander-type estimation of a monotone covariate-adjusted regression curve, which describes the effect of a continuous exposure on an outcome while adjusting for potential confounders. In particular, we show how our results can be used to conduct doubly-robust inference for this parameter.

Download or read book Methods and Theory for Nonparametric Inference In High dimensional Settings written by Yunhua Xiang and published by . This book was released on 2021 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation addresses nonparametric estimation and inference problems of graphical modeling, linear association assessment, and matrix completion. First, we introduce a flexible framework for nonparametric graphical modeling. We propose three nonparametric measures of conditional dependence, which have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This parameter is always explicitly defined even when the true relationship is nonlinear and is equivalent with the regression coefficient under a linear model space. Thus, its estimator can be a more robust alternative to the standard model-based techniques to estimate the coefficients of a linear model. In the final project, we theoretically show that nuclear-norm penalization used for recovering low-rank matrices, remains effective even when the underlying matrices are generated by a low-dimensional non-linear manifold. The convergence rate can be expressed as a function of the size of the matrix, as well as the smoothness and dimension of the manifold, which is minimax optimal (up to a log term).

Download or read book New Theory and Methods for High Order Accurate Inference on Quantile Treatment Effects and Conditional Quantiles written by David M. Kaplan and published by . This book was released on 2013 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concerns methods for inference on quantiles in various models. Methods that are asymptotically justified may still be quite inaccurate in finite samples. To improve the state of the art, I explore different theoretical approaches for achieving higher-order accuracy: fractional order statistic theory based on exact finite-sample distributions in Chapters 1 and 2, and Edgeworth expansions and fixed-smoothing asymptotics in Chapter 3. For each of the different practical methods proposed, I examine accuracy via precise theoretical results as well as simulations. The family of methods using interpolated duals of exact-analytic L-statistics (IDEAL) covers unconditional (one-sample and two-sample treatment/control, Ch. 1) and nonparametric conditional (Ch. 2) models, and it offers improvements over the existing literature in terms of accuracy, robustness, and/or computation time. The Edgeworth-based method improves upon related prior methods and is a good alternative for quantiles too far into the tails for IDEAL to handle.

Download or read book Journal of Statistical Planning and Inference written by North-Holland Publishing Company and published by . This book was released on 1998 with total page 1188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka