Sampling Algorithms [Tillé 2006-05-18].pdf

(1457 KB) Pobierz
Springer Series in Statistics
Advisors:
P. Bickel, P. Diggle, S. Fienberg, U. Gather,
I. Olkin, S. Zeger
Springer Series in Statistics
Alho/Spencer:
Statistical Demography and Forecasting.
Andersen/Borgan/Gill/Keiding:
Statistical Models Based on Counting Processes.
Atkinson/Riani:
Robust Diagnostic Regression Analysis.
Atkinson/Riani/Cerioli:
Exploring Multivariate Data with the Forward Search.
Berger:
Statistical Decision Theory and Bayesian Analysis, 2nd edition.
Borg/Groenen:
Modern Multidimensional Scaling: Theory and Applications,
2nd edition.
Brockwell/Davis:
Time Series: Theory and Methods, 2nd edition.
Bucklew:
Introduction to Rare Event Simulation.
Cappé/Moulines/Rydén:
Inference in Hidden Markov Models.
Chan/Tong:
Chaos: A Statistical Perspective.
Chen/Shao/Ibrahim:
Monte Carlo Methods in Bayesian Computation.
Coles:
An Introduction to Statistical Modeling of Extreme Values.
David/Edwards:
Annotated Readings in the History of Statistics.
Devroye/Lugosi:
Combinatorial Methods in Density Estimation.
Efromovich:
Nonparametric Curve Estimation: Methods, Theory, and Applications.
Eggermont/LaRiccia:
Maximum Penalized Likelihood Estimation, Volume I: Density
Estimation.
Fahrmeir/Tutz:
Multivariate Statistical Modelling Based on Generalized Linear
Models, 2nd edition.
Fan/Yao:
Nonlinear Time Series: Nonparametric and Parametric Methods.
Farebrother:
Fitting Linear Relationships: A History of the Calculus of Observations
1750-1900.
Federer:
Statistical Design and Analysis for Intercropping Experiments, Volume I:
Two Crops.
Federer:
Statistical Design and Analysis for Intercropping Experiments, Volume II:
Three or More Crops.
Ferraty/Vieu:
Nonparametric Functional Data Analysis: Models, Theory, Applications,
and Implementation
Ghosh/Ramamoorthi:
Bayesian Nonparametrics.
Glaz/Naus/Wallenstein:
Scan Statistics.
Good:
Permutation Tests: Parametric and Bootstrap Tests of Hypotheses, 3rd edition.
Gouriéroux:
ARCH Models and Financial Applications.
Gu:
Smoothing Spline ANOVA Models.
•
Györfi/Kohler/Krzyzak/Walk:
A Distribution-Free Theory of Nonparametric
Regression.
Haberman:
Advanced Statistics, Volume I: Description of Populations.
Hall:
The Bootstrap and Edgeworth Expansion.
Härdle:
Smoothing Techniques: With Implementation in S.
Harrell:
Regression Modeling Strategies: With Applications to Linear Models, Logistic
Regression, and Survival Analysis.
Hart:
Nonparametric Smoothing and Lack-of-Fit Tests.
Hastie/Tibshirani/Friedman:
The Elements of Statistical Learning: Data Mining,
Inference, and Prediction.
Hedayat/Sloane/Stufken:
Orthogonal Arrays: Theory and Applications.
Heyde:
Quasi-Likelihood and its Application: A General Approach to Optimal
Parameter Estimation.
(continued after index)
Yves Tille
´
Sampling Algorithms
Yves Tillé
Institut de Statistique,
Université de Neuchâtel
Espace de l’Europe 4,
Case postale 805
2002 Neuchâtel,
Switzerland
yves.tille@unine.ch
Library of Congress Control Number: 2005937126
ISBN-10: 0-387-30814-8
ISBN-13: 978-0387-30814-2
© 2006 Springer Science+Business Media, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science+Business Media, Inc., 233 Springer
Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or
scholarly analysis. Use in connection with any form of information storage and retrieval, elec-
tronic adaptation, computer software, or by similar or dissimilar methodology now known or
hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even
if they are not identified as such, is not to be taken as an expression of opinion as to whether
or not they are subject to proprietary rights.
Printed in the United States of America.
9 8 7 6 5 4 3 2 1
springer.com
(MVY)
Preface
This book is based upon courses on sampling algorithms. After having used
scattered notes for several years, I have decided to completely rewrite the
material in a consistent way. The books of Brewer and Hanif (1983) and
H´jek (1981) have been my works of reference. Brewer and Hanif (1983) have
a
drawn up an exhaustive list of sampling methods with unequal probabilities,
which was probably a very tedious work. The posthumous book of H´jek
a
(1981) contains an attempt at writing a general theory for conditional Poisson
sampling. Since the publication of these books, things have been improving.
New techniques of sampling have been proposed, to such an extent that it
is difficult to have a general idea of the interest of each of them. I do not
claim to give an exhaustive list of these new methods. Above all, I would
like to propose a general framework in which it will be easier to compare
existing methods. Furthermore, forty-six algorithms are precisely described,
which allows the reader to easily implement the described methods.
This book is an opportunity to present a synthesis of my research and
to develop my convictions on the question of sampling. At present, with the
splitting method, it is possible to construct an infinite amount of new sampling
methods with unequal probabilities. I am, however, convinced that conditional
Poisson sampling is probably the best solution to the problem of sampling with
unequal probabilities, although one can object that other procedures provide
very similar results.
Another conviction is that the joint inclusion probabilities are not used for
anything. I also advocate for the use of the cube method that allows selecting
balanced samples. I would also like to apologize for all the techniques that
are not cited in this book. For example, I do not mention all the methods
called “order sampling” because the methods for coordinating samples are
not examined in this book. They could be the topic of another publication.
This material is aimed at experienced statisticians who are familiar with
the theory of survey sampling, to Ph.D. students who want to improve their
knowledge in the theory of sampling and to practitioners who want to use or
implement modern sampling procedures. The R package “sampling” available

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin