A STUDY OF SPATIAL BOOTSTRAP TECHNIQUES FOR VARIANCE ESTIMATION IN FINITE POPULATION
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Date
2014
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INDIAN AGRICULTURAL STATISTICS RESEARCH INSTITUTE INDIAN AGRICULTURAL RESEARCH INSTITUTE PUSA, NEW DELHI
Abstract
In agricultural surveys, the important parameters of crop production are often spatial
in nature, in which observations from neighbouring units tend to share similar
statistical properties. In literature, spatial sampling designs were suggested to provide
reliable spatial statistics using the spatial dependency among the sampling units. In
this dissertation, a new efficient approach, viz. Spatial Estimation procedure, for
estimation of the mean of spatially correlated finite population units was developed
by incorporating the spatial dependency at the estimation stages of traditional
without replacement sampling designs like Simple Random Sampling (SRS) and
Ranked Set Sampling (RSS). In this approach, Spatial Estimators (SE) of population
mean were developed following prediction approach in which unobserved population
units were predicted based on their distances with observed sampling units following
Inverse Distance Weighting (IDW) method. Since the proposed SE’s were non-linear
in nature, Rescaled Spatial Bootstrap (RSB) techniques were developed for unbiased
estimation of variance of the SE under both the designs. Also, a spatial simulation
study was carried out in order to study the performance of proposed SE with respect
to the corresponding classical estimators of population mean under both the designs
along with its variance estimation following proposed RSB methods. Proposed SE
under both designs were found to be almost unbiased, consistent, stable and more
efficient for estimation of population mean. Further, in the context of without
replacement sampling both by SRS as well as RSS designs for spatially correlated
finite population, naive bootstrap approach results in considerably high amount of
bias in the estimator of variance of the SE of population mean, whereas, the proposed
RSB methods were found to be approximately unbiased. Further, the statistical
properties of these RSB methods were not desirable in presence of missing
observations. Thus, Proportional Spatial Bootstrap (PSB) methods were proposed
using spatial imputation techniques for unbiased variance estimation of Spatial
Estimator (SE) under SRS without replacement design. This dissertation also
includes efficient rescaling Jackknife and Bootstrap methods for unbiased estimation
of variance of the RSS mean estimator in case of finite population.
Description
t-9085
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