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A Non Iterative Method For Fitting The Single Index Quantile Regression Model With Uncensored And Censored Data
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Book Synopsis A Non-iterative Method for Fitting the Single Index Quantile Regression Model with Uncensored and Censored Data by : Eliana Christou
Download or read book A Non-iterative Method for Fitting the Single Index Quantile Regression Model with Uncensored and Censored Data written by Eliana Christou and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. Linear and nonlinear QR models have been studied extensively, while recent research focuses on the single index quantile regression (SIQR) model. Compared to the single index mean regression (SIMR) problem, the fitting and the asymptotic theory of the SIQR model are more complicated due to the lack of closed form expressions for estimators of conditional quantiles. Consequently, existing methods are necessarily iterative. We propose a non-iterative estimation algorithm, and derive the asymptotic distribution of the proposed estimator under heteroscedasticity. For identifiability, we use a parametrization that sets the first coefficient to 1 instead of the typical condition which restricts the norm of the parametric component. This distinction is more than simply cosmetic as it affects, in a critical way, the correspondence between the estimator derived and the asymptotic theory. The ubiquity of high dimensional data has led to a number of variable selection methods for linear/nonlinear QR models and, recently, for the SIQR model. We propose a new algorithm for simultaneous variable selection and parameter estimation applicable also for heteroscedastic data. The proposed algorithm, which is non-iterative, consists of two steps. Step 1 performs an initial variable selection method. Step 2 uses the results of Step 1 to obtain better estimation of the conditional quantiles and, using them, to perform simultaneous variable selection and estimation of the parametric component of the SIQR model. It is shown that the initial variable selection method of Step 1 consistently estimates the relevant variables, and that the estimated parametric component derived in Step 2 satisfies the oracle property. Furthermore, QR is particularly relevant for the analysis of censored survival data as an alternative to proportional hazards and the accelerated failure time models. Such data occur frequently in biostatistics, environmental sciences, social sciences and econometrics. There is a large body of work for linear/nonlinear QR models for censored data, but it is only recently that the SIQR model has received some attention. However, the only existing method for fitting the SIQR model uses an iterative algorithm and no asymptotic theory for the resulting estimator of the Euclidean parameter is given. We propose a new non-iterative estimation algorithm, and derive the asymptotic distribution of the proposed estimator under heteroscedasticity.
Book Synopsis Advances in Contemporary Statistics and Econometrics by : Abdelaati Daouia
Download or read book Advances in Contemporary Statistics and Econometrics written by Abdelaati Daouia and published by Springer Nature. This book was released on 2021-06-14 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.
Book Synopsis Non-parametric Quantile Regression for Censored Data by : Stanislav Volgushev
Download or read book Non-parametric Quantile Regression for Censored Data written by Stanislav Volgushev and published by . This book was released on 2009 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Censored Quantile Regression with Auxiliary Information by : Chithran Vadaverkkot Vasudevan
Download or read book Censored Quantile Regression with Auxiliary Information written by Chithran Vadaverkkot Vasudevan and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In Survival analysis, it is vital to understand the effect of the covariates on the survival time. Commonly studied models are the Cox [1972] proportional hazards model and the accelerated failure time model. These methods mainly focus on one characteristic of the survival time. In reality, the association between the response and risk factors is not homogeneous always. This leads to the use of quantile regression [Koenker and Basset, 1978] models, which provide a global description of the association. In quantile regression modeling of the survival data, the problem of estimating the regression coefficients for extreme quantiles can be affected by severe censoring [Portnoy, 2003], especially when the sample size is small. In epidemiological studies, however, there are often times when only a subset of the whole study cohort is accurately observed. The rest of the cohort has only some auxiliary covariate available. The naive use of the auxiliary covariate in the model without the accurately measured covariate could lead to biased estimates. To deal with this problem in censored quantile regression, we propose a regression calibration based method when there is a linear relationship between the auxiliary covariate and the accurately measured covariate. When the relationship is non-linear, we propose a non-parametric kernel smoothing technique. We also propose an empirical likelihood [Owen, 1998, 2001] based weighted censored quantile regression to improve the efficiency of the censored quantile regression estimation by utilizing the auxiliary information about the target population parameters available through scientific facts/previous studies. The proposed estimators are consistent and have asymptotically Gaussian distributions. The efficiency gain compared to the existing methods is remarkable. These methods provide the possibilities of looking into extreme quantiles of the survival distribution. We also applied our proposed methods in real case examples.
Book Synopsis Survival Analysis Using S by : Mara Tableman
Download or read book Survival Analysis Using S written by Mara Tableman and published by CRC Press. This book was released on 2003-07-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival Analysis Using S: Analysis of Time-to-Event Data is designed as a text for a one-semester or one-quarter course in survival analysis for upper-level or graduate students in statistics, biostatistics, and epidemiology. Prerequisites are a standard pre-calculus first course in probability and statistics, and a course in applied linear regression models. No prior knowledge of S or R is assumed. A wide choice of exercises is included, some intended for more advanced students with a first course in mathematical statistics. The authors emphasize parametric log-linear models, while also detailing nonparametric procedures along with model building and data diagnostics. Medical and public health researchers will find the discussion of cut point analysis with bootstrap validation, competing risks and the cumulative incidence estimator, and the analysis of left-truncated and right-censored data invaluable. The bootstrap procedure checks robustness of cut point analysis and determines cut point(s). In a chapter written by Stephen Portnoy, censored regression quantiles - a new nonparametric regression methodology (2003) - is developed to identify important forms of population heterogeneity and to detect departures from traditional Cox models. By generalizing the Kaplan-Meier estimator to regression models for conditional quantiles, this methods provides a valuable complement to traditional Cox proportional hazards approaches.
Book Synopsis Composite Quantile Regression for the Single-Index Model by : Yan Fan
Download or read book Composite Quantile Regression for the Single-Index Model written by Yan Fan and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. When it comes to nonparametric specifications of the conditional quantile (or more generally tail) curve one faces, as in mean regression, a dimensionality problem. We propose a projection based single index model specification. For very high dimensional regressors X one faces yet another dimensionality problem and needs to balance precision vs. dimension. Such a balance may be achieved by combining semiparametric ideas with variable selection techniques.
Book Synopsis Survival Analysis by : John P. Klein
Download or read book Survival Analysis written by John P. Klein and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making complex methods more accessible to applied researchers without an advanced mathematical background, the authors present the essence of new techniques available, as well as classical techniques, and apply them to data. Practical suggestions for implementing the various methods are set off in a series of practical notes at the end of each section, while technical details of the derivation of the techniques are sketched in the technical notes. This book will thus be useful for investigators who need to analyse censored or truncated life time data, and as a textbook for a graduate course in survival analysis, the only prerequisite being a standard course in statistical methodology.
Book Synopsis Quantile Regression With Censored Data by :
Download or read book Quantile Regression With Censored Data written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Composite Quantile Regression for the Single-Index Model by : Yan Fan
Download or read book Composite Quantile Regression for the Single-Index Model written by Yan Fan and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Simple 3-Step Censored Quantile Regression and Extramarital Affairs by : Victor Chernozhukov
Download or read book Simple 3-Step Censored Quantile Regression and Extramarital Affairs written by Victor Chernozhukov and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors, with desirable finite sample properties and small bias. The envelope restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models, including normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The main empirical example involves a very large data-set on extramarital affairs, with high 68 percent censoring. We estimate 45-90 percent conditional quantiles. Effects of covariates are not representable as location-shifts. Less religious women, with fewer children, and higher status, tend to engage into the matters relatively more than their opposites, especially at the extremes. Marriage longevity effect is positive at moderately high quantiles and negative at high quantiles. Education and marriage happiness effects are negative, especially at the extremes. We also briefly consider the survival quantile regression on the Stanford heart transplant data. We estimate the age and prior surgery effects across survival quantiles.
Book Synopsis Quantile Regression with Censored Data Using Generalized L1 Minimization by : Anna Lindgren
Download or read book Quantile Regression with Censored Data Using Generalized L1 Minimization written by Anna Lindgren and published by . This book was released on 1993 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Approaches for Quantile Regression by : Minzhao Liu
Download or read book New Approaches for Quantile Regression written by Minzhao Liu and published by . This book was released on 2014 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression is a powerful way to study the relationship between covariates and responses. Various approaches have been proposed to estimate quantile regression models. However, most existing methods still suffer from several difficulties: crossing fitted quantile lines and non-coherent models due to separate distributional assumptions for different quantiles. In addition, there is limited literature on multivariate quantile regression and quantile regression with non-ignorable missing data. This dissertation addresses these challenge by flexibly fitting quantile regression for univariate and multivariate data, using pattern mixture models for non-ignorable missingness, and providing simple computational algorithm. In Chapter 1, we provide background on quantile regression and introduce the existing frequentist and Bayesian methods. In Chapter 2, we adopt Polya tree priors to non-parametrically fit quantile regression for univariate responses. In Chapter 3, we propose algorithms to estimate marginal quantile regression parameters within pattern mixture models for longitudinal data with monotone non-ignorable missingness. And we propose nonparametric Bayesian methods for the pattern mixture models in Chapter 4.
Book Synopsis Simple Three-step Censored Quantile Regression and Extramartial Affairs by : Victor Chernozhukov
Download or read book Simple Three-step Censored Quantile Regression and Extramartial Affairs written by Victor Chernozhukov and published by . This book was released on 2001 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors, with desirable finite sample properties and small bias. The envelope restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models, including normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The main empirical example involves a very large data-set on extramarital affairs, with high 68 percent censoring. We estimate 45-90 percent conditional quantiles. Effects of covariates are not representable as location-shifts. Less religious women, with fewer children, and higher status, tend to engage into the matters relatively more than their opposites, especially at the extremes. Marriage longevity effect is positive at moderately high quantiles and negative at high quantiles. Education and marriage happiness effects are negative, especially at the extremes. We also briefly consider the survival quantile regression on the Stanford heart transplant data. We estimate the age and prior surgery effects across survival quantiles. Keywords: Quantile regression, median regression, censoring, duration, survival, classification, discriminant analysis. JEL Classifications: C14, C24, C41, C51, D13.
Book Synopsis A Simple Method for Regression Analysis with Censored Data by : Josef Schmee
Download or read book A Simple Method for Regression Analysis with Censored Data written by Josef Schmee and published by . This book was released on 1979 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems requiring regression analysis of censored data arise frequently in practice. For example, in accelerated testing one wishes to relate stress and average time to failure from data including unfailed units, i.e., censored observations. Maximum likelihood is one method for obtaining the desired estimates; in this paper, we propose an alternative approach. An initial least squares fit is obtained treating the censored values as failures. Then, based upon this initial fit, the expected failure time for each censored observation is estimated. These estimates are then used, instead of the censoring times, to obtain a revised least squares fit and new expected failure times are estimated for the censored values. These are then used in a further least squares fit. The procedure is iterated until convergence is achieved. This method is simpler to implement and explain to non-statisticians than maximum likelihood and appears to have good statistical and convergence properties. The method is illustrated by an example, and some simulation results are described. Variations and areas for further study also are discussed. (Author).
Book Synopsis Copula Theory and Its Applications by : Piotr Jaworski
Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
Book Synopsis Quantile Regression Analysis of Censored Data with Selection by : Victor Champonnois
Download or read book Quantile Regression Analysis of Censored Data with Selection written by Victor Champonnois and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonparametric Quantile Regression with Censored Data by : D. M. Dabrowska
Download or read book Nonparametric Quantile Regression with Censored Data written by D. M. Dabrowska and published by . This book was released on 1987 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
