4,099 research outputs found
Development of Estimation Procedure of Population Mean in Two-Phase Stratified Sampling
This article describes the problem of estimation of finite population mean in two-phase stratified random sampling. Using information on two auxiliary variables, a class of product to regression chain type estimators has been proposed and its characteristic is discussed. The unbiased version of the proposed class of estimators has been constructed and the optimality condition for the proposed class of estimators is derived. The efficacy of the proposed methodology has been justified through empirical investigations carried over the data set of natural population as well as the data set of artificially generated population. The survey statistician may be suggested to use it
On Improvement in Estimating Population Parameter(s) Using Auxiliary Information
The purpose of writing this book is to suggest some improved estimators using
auxiliary information in sampling schemes like simple random sampling and
systematic sampling.
This volume is a collection of five papers. The following problems have been
discussed in the book:
In chapter one an estimator in systematic sampling using auxiliary
information is studied in the presence of non-response. In second chapter some
improved estimators are suggested using auxiliary information. In third chapter
some improved ratio-type estimators are suggested and their properties are
studied under second order of approximation.
In chapter four and five some estimators are proposed for estimating unknown
population parameter(s) and their properties are studied.
This book will be helpful for the researchers and students who are working in
the field of finite population estimation.Comment: 63 pages, 8 tables. Educational Publishing & Journal of Matter
Regularity (Beijing
Conditional inference with a complex sampling: exact computations and Monte Carlo estimations
In survey statistics, the usual technique for estimating a population total
consists in summing appropriately weighted variable values for the units in the
sample. Different weighting systems exit: sampling weights, GREG weights or
calibration weights for example. In this article, we propose to use the inverse
of conditional inclusion probabilities as weighting system. We study examples
where an auxiliary information enables to perform an a posteriori
stratification of the population. We show that, in these cases, exact
computations of the conditional weights are possible. When the auxiliary
information consists in the knowledge of a quantitative variable for all the
units of the population, then we show that the conditional weights can be
estimated via Monte-Carlo simulations. This method is applied to outlier and
strata-Jumper adjustments
Properties of Design-Based Functional Principal Components Analysis
This work aims at performing Functional Principal Components Analysis (FPCA)
with Horvitz-Thompson estimators when the observations are curves collected
with survey sampling techniques. One important motivation for this study is
that FPCA is a dimension reduction tool which is the first step to develop
model assisted approaches that can take auxiliary information into account.
FPCA relies on the estimation of the eigenelements of the covariance operator
which can be seen as nonlinear functionals. Adapting to our functional context
the linearization technique based on the influence function developed by
Deville (1999), we prove that these estimators are asymptotically design
unbiased and consistent. Under mild assumptions, asymptotic variances are
derived for the FPCA' estimators and consistent estimators of them are
proposed. Our approach is illustrated with a simulation study and we check the
good properties of the proposed estimators of the eigenelements as well as
their variance estimators obtained with the linearization approach.Comment: Revised version for J. of Statistical Planning and Inference (January
2009
On the two-phase framework for joint model and design-based inference
We establish a mathematical framework that formally validates the two-phase
``super-population viewpoint'' proposed by Hartley and Sielken [Biometrics 31
(1975) 411--422] by defining a product probability space which includes both
the design space and the model space. The methodology we develop combines
finite population sampling theory and the classical theory of infinite
population sampling to account for the underlying processes that produce the
data under a unified approach. Our key results are the following: first, if the
sample estimators converge in the design law and the model statistics converge
in the model, then, under certain conditions, they are asymptotically
independent, and they converge jointly in the product space; second, the sample
estimating equation estimator is asymptotically normal around a
super-population parameter.Comment: Published at http://dx.doi.org/10.1214/009053605000000651 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …