Download or read book Non Parametric Estimation Under Strong Dependence written by Zhibiao Zhao and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study non-parametric regression function estimation for models with strong dependence. Compared with short-range dependent models, long-range dependent models often result in slower convergence rates. We propose a simple differencing-sequence based non-parametric estimator that achieves the same convergence rate as if the data were independent. Simulation studies show that the proposed method has good finite sample performance.

Download or read book Non parametric Methods Under Cross sectional Dependence written by Jungyoon Lee and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The possible presence of cross-sectional dependence in economic panel or cross-sectional data needs to be taken into consideration when developing econometric theory for data analysis. This thesis consists of three works that either allow for or estimate cross-sectional dependence in the disturbance terms of a regression model, each addressing different problems, models and methods in the areas of non- and semi-parametric estimation. Chapter 1 provides an overview of the motivations for, and contributions of, the three topics of this thesis. A review of relevant literature is given, followed by a sum- mary of main results obtained in order to help place the present thesis in perspective. Chapter 2 develops asymptotic theory for series estimation under a general setting of spatial dependence in regressors and error term, including cases analogous to those known as long-range dependence in the time series literature. A data-driven studentization, new to non-parametric and cross-sectional contexts, is theoretically justified, then used to develop asymptotically correct inference. Chapter 3 discusses identification and kernel estimation of a non-parametric common regression with additive individual fixed effects in panel data, with weak temporal dependence and arbitrarily strong cross-sectional dependence. An efficiency improvement is obtained by using estimated cross-sectional covariance matrix in a manner similar to generalised least squares, achieving a Gauss-Markov type efficiency bound. Feasible optimal bandwidths and feasible optimal non-parametric regression estimation are established and asymptotically justified. Chapter 4 deals with efficiency improvement in the estimation of pure Spatial Autoregressive model. We construct a two-stage estimator, which adapts to the unknown error distribution of non-parametric form and achieves the Cramer-Rao bound of the correctly specified maximum likelihood estimator. In establishing feasibility of such adaptive estimation, we find that the gain in efficiency from adaptive estimation is typically smaller than in the relevant time series context, but could be also greater under certain asymptotic behaviour of the weight matrix of the model.

Download or read book Nonparametric and Semiparametric Methods in Econometrics and Statistics written by William A. Barnett and published by Cambridge University Press. This book was released on 1991-06-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a 1988 symposium on the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data.

Download or read book Nonparametric Density Estimation written by Luc Devroye and published by New York ; Toronto : Wiley. This book was released on 1985-01-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous, systematic treatment of density estimates, their construction, use and analysis with full proofs. It develops L1 theory, rather than the classical L2, showing how L1 exposes fundamental properties of density estimates masked by L2.

Download or read book Recent Developments in Applied Probability and Statistics written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2010-05-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Professor Jürgen Lehn, who passed away on September 29, 2008, at the age of 67. It contains invited papers that were presented at the Wo- shop on Recent Developments in Applied Probability and Statistics Dedicated to the Memory of Professor Jürgen Lehn, Middle East Technical University (METU), Ankara, April 23–24, 2009, which was jointly organized by the Technische Univ- sität Darmstadt (TUD) and METU. The papers present surveys on recent devel- ments in the area of applied probability and statistics. In addition, papers from the Panel Discussion: Impact of Mathematics in Science, Technology and Economics are included. Jürgen Lehn was born on the 28th of April, 1941 in Karlsruhe. From 1961 to 1968 he studied mathematics in Freiburg and Karlsruhe, and obtained a Diploma in Mathematics from the University of Karlsruhe in 1968. He obtained his Ph.D. at the University of Regensburg in 1972, and his Habilitation at the University of Karlsruhe in 1978. Later in 1978, he became a C3 level professor of Mathematical Statistics at the University of Marburg. In 1980 he was promoted to a C4 level professorship in mathematics at the TUD where he was a researcher until his death.

Download or read book Non Parametric Spectral Density Estimation Under Long Range Dependence written by Young Min Kim and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: One major aim of time series analysis, particularly in the physical and geo-sciences, is the estimation of the spectral density function. With weakly dependent time processes, non-parametric, kernel-based methods are available for spectral density estimation, which involves smoothing the periodogram by a kernel function. However, a similar non-parametric approach is presently unavailable for strongly, or long-range, dependent processes. In particular, as the spectral density function under long-range dependence commonly has a pole at the origin, kernel-based methods developed for weakly dependent processes (i.e., with bounded spectral densities) do not apply readily for long-range dependence without suitable modification. To address this, we propose a non-parametric kernel-based method for spectral density estimation, which is valid under both weak and strong dependence. Based on the initial or pilot estimator of the long-memory parameter, the method involves a frequency domain transformation to dampen the dependence in periodogram ordinates and mimic kernel-based estimation under weak dependence. Under mild assumptions, the proposed non-parametric spectral density estimator is shown to be uniformly consistent, and general expressions are provided for rates of estimation error and optimal kernel bandwidths. The method is investigated through simulation and illustrated through data examples, which also consider bandwidth selection.

Download or read book Dependence in Probability and Statistics written by Patrice Bertail and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.

Download or read book Nonparametric Estimation under Shape Constraints written by Piet Groeneboom and published by Cambridge University Press. This book was released on 2014-12-11 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. Among the topics treated are current status and interval censoring models, competing risk models, and deconvolution. Methods of order restricted inference are used in computing maximum likelihood estimators and developing distribution theory for inverse problems of this type. The authors have been active in developing these tools and present the state of the art and the open problems in the field. The earlier chapters provide an introduction to the subject, while the later chapters are written with graduate students and researchers in mathematical statistics in mind. Each chapter ends with a set of exercises of varying difficulty. The theory is illustrated with the analysis of real-life data, which are mostly medical in nature.

Download or read book The Statistical Analysis of Doubly Truncated Data written by Jacobo de Uña-Álvarez and published by John Wiley & Sons. This book was released on 2021-11-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough treatment of the statistical methods used to analyze doubly truncated data In The Statistical Analysis of Doubly Truncated Data, an expert team of statisticians delivers an up-to-date review of existing methods used to deal with randomly truncated data, with a focus on the challenging problem of random double truncation. The authors comprehensively introduce doubly truncated data before moving on to discussions of the latest developments in the field. The book offers readers examples with R code along with real data from astronomy, engineering, and the biomedical sciences to illustrate and highlight the methods described within. Linear regression models for doubly truncated responses are provided and the influence of the bandwidth in the performance of kernel-type estimators, as well as guidelines for the selection of the smoothing parameter, are explored. Fully nonparametric and semiparametric estimators are explored and illustrated with real data. R code for reproducing the data examples is also provided. The book also offers: A thorough introduction to the existing methods that deal with randomly truncated data Comprehensive explorations of linear regression models for doubly truncated responses Practical discussions of the influence of bandwidth in the performance of kernel-type estimators and guidelines for the selection of the smoothing parameter In-depth examinations of nonparametric and semiparametric estimators Perfect for statistical professionals with some background in mathematical statistics, biostatisticians, and mathematicians with an interest in survival analysis and epidemiology, The Statistical Analysis of Doubly Truncated Data is also an invaluable addition to the libraries of biomedical scientists and practitioners, as well as postgraduate students studying survival analysis.

Download or read book Introduction to Nonparametric Estimation written by Alexandre B. Tsybakov and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.

Download or read book Statistical Inference on Linear and Partly Linear Regression with Spatial Dependence written by Supachoke Thawornkaiwong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The typical assumption made in regression analysis with cross-sectional data is that of independent observations. However, this assumption can be questionable in some economic applications where spatial dependence of observations may arise, for example, from local shocks in an economy, interaction among economic agents and spillovers. The main focus of this thesis is on regression models under three di§erent models of spatial dependence. First, a multivariate linear regression model with the disturbances following the Spatial Autoregressive process is considered. It is shown that the Gaussian pseudo-maximum likelihood estimate of the regression and the spatial autoregressive parameters can be root-n-consistent under strong spatial dependence or explosive variances, given that they are not too strong, without making restrictive assumptions on the parameter space. To achieve e¢ ciency improvement, adaptive estimation, in the sense of Stein (1956), is also discussed where the unknown score function is nonparametrically estimated by power series estimation. A large section is devoted to an extension of power series estimation for random variables with unbounded supports. Second, linear and semiparametric partly linear regression models with the disturbances following a generalized linear process for triangular arrays proposed by Robinson (2011) are considered. It is shown that instrumental variables estimates of the unknown slope parameters can be root-n-consistent even under some strong spatial dependence. A simple nonparametric estimate of the asymptotic variance matrix of the slope parameters is proposed. An empirical illustration of the estimation technique is also conducted. Finally, linear regression where the random variables follow a marked point process is considered. The focus is on a family of random signed measures, constructed from the marked point process, that are second-order stationary and their spectral properties are discussed. Asymptotic normality of the least squares estimate of the regression parameters are derived from the associated random signed measures under mixing assumptions. Nonparametric estimation of the asymptotic variance matrix of the slope parameters is discussed where an algorithm to obtain a positive deÖnite estimate, with faster rates of convergence than the traditional ones, is proposed.

Download or read book Nonparametric Functional Estimation and Related Topics written by G.G Roussas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.

Download or read book Nonparametric Econometrics written by Qi Li and published by Princeton University Press. This book was released on 2007 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate textbook for econometricians and statisticians containing developments in the field. It emphasises nonparametric methods for real world problems containing the mix of discrete and continuous data found in many applications.

Download or read book Central Limit Theorems for Nonparametric Estimators with Real Time Random Variables written by Tae Yoon Kim and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, asymptotic theories for nonparametric methods are studied when they are applied to real-time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real-time random variables indexed by a parameter related to fine gridding of time domain (or fine discretization). Our results show that the impact of fine gridding is greater in the density estimation case in the sense that strong dependence due to fine gridding severely affects the major strength of nonparametric density estimator (or its data-adaptive property). In addition, we discuss some issues about nonparametric regression model with fine gridding of time domain.

Download or read book Nonparametric Functional Data Analysis written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Download or read book Semiparametric Methods in Econometrics written by Joel L. Horowitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many econometric models contain unknown functions as well as finite- dimensional parameters. Examples of such unknown functions are the distribution function of an unobserved random variable or a transformation of an observed variable. Econometric methods for estimating population parameters in the presence of unknown functions are called "semiparametric." During the past 15 years, much research has been carried out on semiparametric econometric models that are relevant to empirical economics. This book synthesizes the results that have been achieved for five important classes of models. The book is aimed at graduate students in econometrics and statistics as well as professionals who are not experts in semiparametic methods. The usefulness of the methods will be illustrated with applications that use real data.

Download or read book Nonparametric Statistics written by Ricardo Cao and published by Springer. This book was released on 2016-09-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cádiz (Spain) between June 11–16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.