Author: Stella DavidPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Central Limit Theorem for the Integrated Squared Error of the Empirical Second-Order Product Density and Goodness-of-fit Tests for Stationary Point Processes
Author: Stella DavidCentral Limit Theorems for Empirical Product Densities of Stationary Point Processes
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
In the present work we investigate kernel-type estimators for product densities and for the pair correlation function for stationary spatial point processes. In the setting of Brillinger-mixing point processes we present central limit theorems for these estimators and for the integrated squared error of the estimators for the second-order product density and the pair correlation function. Based on these central limit theorems we can construct asymptotic goodness-of-fit tests for the distribution of a stationary point process.
Stochastic Geometry, Spatial Statistics and Random Fields
Author: Evgeny SpodarevPublisher: Springer
ISBN: 3642333052
Category : Mathematics
Languages : en
Pages : 470
Book Description
This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Central Limit Theorems for Empirical Product Densities of Stationary Point Processes
Author: Stella Veronica DavidCentral Limit Theorems for Empirical Product Densities of Stationary Point Processes
Author: Lothar HeinrichUniform Central Limit Theorems
Author: R. M. DudleyPublisher: Cambridge University Press
ISBN: 1107728886
Category : Mathematics
Languages : en
Pages : 485
Book Description
In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.
Theory of Spatial Statistics
Author: M.N.M. van LieshoutPublisher: CRC Press
ISBN: 0429627033
Category : Mathematics
Languages : en
Pages : 162
Book Description
Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.
Partially Linear Models
Author: Wolfgang HärdlePublisher: Springer Science & Business Media
ISBN: 3642577008
Category : Mathematics
Languages : en
Pages : 210
Book Description
In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Uniform Central Limit Theorems
Author: R. M. DudleyPublisher: Cambridge University Press
ISBN: 0521498848
Category : Mathematics
Languages : en
Pages : 485
Book Description
This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.
Introduction to Empirical Processes and Semiparametric Inference
Author: Michael R. KosorokPublisher: Springer Science & Business Media
ISBN: 0387749780
Category : Mathematics
Languages : en
Pages : 482
Book Description
Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.