Download or read book Quantile Function Methods with Applications to Robust Estimation written by Lai Wei and published by . This book was released on 2013 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation of the population quantiles is of great interest in a broad spectrum of theories, methods and applications of parametric, robust and exploratory statistical analyses. In this dissertation, we investigate the limitations of traditional quantile function estimation methods. The lack of efficiency of sample quantile caused by the variability of individual order statistics leads us to form a weighted average of the order statistics, using an appropriate weight function, which we call the L-estimator in general. We propose a new class of quantile function estimators, namely, the semi-parametric tail extrapolated quantile estimator, which belongs to the class of L estimator and has excellent performance for estimating the extreme tails with finite sample sizes compared with other L-estimators, such as the Harrel-Davis estimator and the kernel quantile estimator. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of the confidence intervals of quantile estimators. The new class of quantile estimators is obtained by modification of traditional quantile estimators, and therefore, should be especially appealing to researchers in estimating the extreme tails. A natural estimator of the ``quantile function of a sample quantile'' is defined, which is accomplished by employing a quasi-quantile estimator with bandwidth function defined as the quantile function of a specific uniform fractional order statistic. Large sample expressions for the mean and variance of the new quasi-quantile estimator are developed to order O(n-2). Applications include nonparametric estimation of the moments of the uth sample quantile (0

Download or read book Robustness in Data Analysis written by Georgij Leonidovič Ševljakov and published by VSP. This book was released on 2002 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of mathematical statistics called robustness statistics deals with the stability of statistical inference under variations of accepted distribution models. Although robust statistics involves mathematically highly defined tools, robust methods exhibit a satisfactory behaviour in small samples, thus being quite useful in applications. This volume in the book series Modern Probability and Statistics addresses various topics in the field of robust statistics and data analysis, such as: a probability-free approach in data analysis; minimax variance estimators of location, scale, regression, autoregression and correlation; "L1-norm methods; adaptive, data reduction, bivariate boxplot, and multivariate outlier detection algorithms; applications in reliability, detection of signals, and analysis of the sudden cardiac death risk factors. The book contains new results related to robustness and data analysis technologies, including both theoretical aspects and practical needs of data processing, which have been relatively inaccessible as they were originally only published in Russian. This book will be of value and interest to researchers in mathematical statistics as well as to those using statistical methods.

Download or read book Robustness in Statistics written by Robert L. Launer and published by Academic Press. This book was released on 2014-05-12 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.

Download or read book A Density Quantile Function Perspective on Robust Estimation written by Emanuel Parzen and published by . This book was released on 1978 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides an overview to a new general approach to statistical data analysis and parameter estimation which could be called the quantile function approach. The aims of descriptive statistics (to graphically summarize and display the data) are obtained by Quantile-Box plots of the sample quantile function. The aims of goodness of fit are obtained by fitting smooth quantile functions to the sample quantile function. The aims of parameter estimation, especially robust estimation of location and scale parameters, are attained by regression analysis of the sample quantile function. (The goal of a statistician in analyzing a batch of data X1, ..., Xn should be both estimation of parameters and goodness of fit. By 'goodness of fit' is meant fitting of the observed sample probabilities by a smooth probability law.).

Download or read book Quantile Based Reliability Analysis written by N. Unnikrishnan Nair and published by Springer Science & Business Media. This book was released on 2013-08-24 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a fresh approach to reliability theory, an area that has gained increasing relevance in fields from statistics and engineering to demography and insurance. Its innovative use of quantile functions gives an analysis of lifetime data that is generally simpler, more robust, and more accurate than the traditional methods, and opens the door for further research in a wide variety of fields involving statistical analysis. In addition, the book can be used to good effect in the classroom as a text for advanced undergraduate and graduate courses in Reliability and Statistics.

Download or read book Robustness in Statistics written by Robert L. Launer and published by . This book was released on 1979 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to robust estimation; The robustness of residual displays; Robust smoothing; Robust pitman-like estimators; Robust estimation in the presence of outliers; Study of robustness by simulation: particularly improvement by adjustment and combination; Robust techniques for the user; Application of robust regression to trajectory data reduction; Tests for censoring of extreme values (especially) when population distributions are incompletely defined; Robust estimation for time series autoregressions; Robust techniques in communication; Robustness in the strategy of scientific model building; A density-quantile function perspective on robust.

Download or read book Empirical Likelihood and Quantile Methods for Time Series written by Yan Liu and published by Springer. This book was released on 2018-12-05 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.

Download or read book Theory and Applications of Recent Robust Methods written by Mia Hubert and published by Birkhäuser. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statistics Treats computational aspects and algorithms and shows interesting and new applications.

Download or read book Quantile Regression written by Lingxin Hao and published by SAGE Publications. This book was released on 2007-04-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile Regression, the first book of Hao and Naiman′s two-book series, establishes the seldom recognized link between inequality studies and quantile regression models. Though separate methodological literature exists for each subject, the authors seek to explore the natural connections between this increasingly sought-after tool and research topics in the social sciences. Quantile regression as a method does not rely on assumptions as restrictive as those for the classical linear regression; though more traditional models such as least squares linear regression are more widely utilized, Hao and Naiman show, in their application of quantile regression to empirical research, how this model yields a more complete understanding of inequality. Inequality is a perennial concern in the social sciences, and recently there has been much research in health inequality as well. Major software packages have also gradually implemented quantile regression. Quantile Regression will be of interest not only to the traditional social science market but other markets such as the health and public health related disciplines. Key Features: Establishes a natural link between quantile regression and inequality studies in the social sciences Contains clearly defined terms, simplified empirical equations, illustrative graphs, empirical tables and graphs from examples Includes computational codes using statistical software popular among social scientists Oriented to empirical research

Download or read book Introduction to Robust and Quasi Robust Statistical Methods written by W.J.J. Rey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Academic Press. This book was released on 2016-09-02 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a 'how-to' on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition - 35% revised content - Covers many new and improved R functions - New techniques that deal with a wide range of situations - Extensive revisions to cover the latest developments in robust regression - Covers latest improvements in ANOVA - Includes newest rank-based methods - Describes and illustrated easy to use software

Download or read book Robust Inference with Quantile Regression in Stochastic Volatility Models with Application to Value at Risk Calculation written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Volatility (SV) models play an integral role in modeling time varying volatility, with widespread application in finance. Due to the absence of a closed form likelihood function, estimation is a challenging problem. In the presence of outliers, and the high kurtosis prevalent in financial data, robust estimation techniques are desirable. Also, in the context of risk assessment when the underlying model is SV, computing the one step ahead predictive return densities for Value at Risk (VaR) calculation entails a numerically indirect procedure. The Quantile Regression (QR) estimation is an increasingly important tool for analysis, which helps in fitting parsimonious models in lieu of full conditional distributions. We propose two methods (i) Regression Quantile Method of Moments (RQMM) and (ii) Regression Quantile - Kalman Filtering method (RQ-KF) based on the QR approach that can be used to obtain robust SV model parameter estimates as well as VaR estimates. The RQMM is a simulation based indirect inference procedure where auxiliary recursive quantile models are used, with gradients of the RQ objective function providing the moment conditions. This was motivated by the Efficient Method of Moments (EMM) approach used in SV model estimation and the Conditional Autoregressive Value at Risk (CAViaR) method. An optimal linear quantile model based on the underlying SV assumption is derived. This is used along with other CAViaR specifications for the auxiliary models. The RQ-KF is a computationally simplified procedure combining the QML and QR methodologies. Based on a recursive model under the SV framework, quantile estimates are produced by the Kalman filtering scheme and are further refined using the RQ objective function, yielding robust estimates. For illustration purposes, comparison of the RQMM method with EMM under different data scenarios show that RQMM is stable under model misspecification, presence of outliers and heavy-tailedness. Comparison of the RQ.

Download or read book Quantile Regression written by Marilena Furno and published by John Wiley & Sons. This book was released on 2018-07-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Download or read book Statistical Postprocessing of Ensemble Forecasts written by Stéphane Vannitsem and published by Elsevier. This book was released on 2018-05-17 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Postprocessing of Ensemble Forecasts brings together chapters contributed by international subject-matter experts describing the current state of the art in the statistical postprocessing of ensemble forecasts. The book illustrates the use of these methods in several important applications including weather, hydrological and climate forecasts, and renewable energy forecasting. After an introductory section on ensemble forecasts and prediction systems, the second section of the book is devoted to exposition of the methods available for statistical postprocessing of ensemble forecasts: univariate and multivariate ensemble postprocessing are first reviewed by Wilks (Chapters 3), then Schefzik and Möller (Chapter 4), and the more specialized perspective necessary for postprocessing forecasts for extremes is presented by Friederichs, Wahl, and Buschow (Chapter 5). The second section concludes with a discussion of forecast verification methods devised specifically for evaluation of ensemble forecasts (Chapter 6 by Thorarinsdottir and Schuhen). The third section of this book is devoted to applications of ensemble postprocessing. Practical aspects of ensemble postprocessing are first detailed in Chapter 7 (Hamill), including an extended and illustrative case study. Chapters 8 (Hemri), 9 (Pinson and Messner), and 10 (Van Schaeybroeck and Vannitsem) discuss ensemble postprocessing specifically for hydrological applications, postprocessing in support of renewable energy applications, and postprocessing of long-range forecasts from months to decades. Finally, Chapter 11 (Messner) provides a guide to the ensemble-postprocessing software available in the R programming language, which should greatly help readers implement many of the ideas presented in this book. Edited by three experts with strong and complementary expertise in statistical postprocessing of ensemble forecasts, this book assesses the new and rapidly developing field of ensemble forecast postprocessing as an extension of the use of statistical corrections to traditional deterministic forecasts. Statistical Postprocessing of Ensemble Forecasts is an essential resource for researchers, operational practitioners, and students in weather, seasonal, and climate forecasting, as well as users of such forecasts in fields involving renewable energy, conventional energy, hydrology, environmental engineering, and agriculture. - Consolidates, for the first time, the methodologies and applications of ensemble forecasts in one succinct place - Provides real-world examples of methods used to formulate forecasts - Presents the tools needed to make the best use of multiple model forecasts in a timely and efficient manner

Download or read book Quantile Processes with Statistical Applications written by Miklos Csorgo and published by SIAM. This book was released on 1983-01-01 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.

Download or read book Developments in Robust Statistics written by Rudolf Dutter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aspects of Robust Statistics are important in many areas. Based on the International Conference on Robust Statistics 2001 (ICORS 2001) in Vorau, Austria, this volume discusses future directions of the discipline, bringing together leading scientists, experienced researchers and practitioners, as well as younger researchers. The papers cover a multitude of different aspects of Robust Statistics. For instance, the fundamental problem of data summary (weights of evidence) is considered and its robustness properties are studied. Further theoretical subjects include e.g.: robust methods for skewness, time series, longitudinal data, multivariate methods, and tests. Some papers deal with computational aspects and algorithms. Finally, the aspects of application and programming tools complete the volume.

Download or read book Robust Statistics written by Ricardo A. Maronna and published by John Wiley & Sons. This book was released on 2018-10-19 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.