Applications of order statistics based on concomitant variables in survey sampling
Applications of order statistics based on concomitant variables in survey sampling
Using auxiliary variables or concomitants to design a survey, to construct an estimator for unknown population parameters for given sample, to select an efficient sample or to make a complete data file for data analysis purposes is common in survey sampling. This thesis uses the theory of concomitants of order statistics to propose an imputation method which is called sequential taxonomy imputation (STI) and a variance estimator for a sample mean under ordered systematic sampling (OSY).
Let (Xi, Yi) i = 1, 2,..., n be n independent and identically distributed random variables from a bivariate normal distribution. If X(r:n) denotes the rth ordered X-variate then the Y-variate Y(r:n), paired with X(r:n) is called the concomitant of the rth order statistic. In this thesis, we develop and evaluate a new imputation method for missing values. The method uses concomitants of order statistics. In particular, the method orders the data according to an auxiliary vector (X) and then selects k-nearest neighbours in order to impute a missing value in the variable Y. Under missing at random (MAR) and missing completely at random (MCAR) assumptions, this so-called single ordered sequential taxonomy imputation (SSTI) method is evaluated theoretically and empirically under a linear relationship between the auxiliary vector X and the variable Y. In particular we describe a generalised form of SSTI which is called doubly ordered sequential taxonomy imputation (DSTI). It is shown that, the bias of estimators for population parameters based on these imputed values is smaller than under other imputation methods. In addition, SSTI and DSTI preserve marginal distributions and individual values better than some commonly used imputation methods such as Hot deck imputation.
Applications of order statistics have introduced new sampling methods such as ranked-set and double sampling in recent years. In this research the statistical properties of ranked-set sampling are examined, the usual systematic sampling (SY) scheme is modified and a variance estimator for ordered systematic sampling (OSY) is suggested. Systematic sampling is a practical and efficient method for selecting samples from administrative registers or other logically arranged files.
University of Southampton
Khodaie-Biramy, Ebrahim
165329b4-e4af-4370-ba31-619ead8ecd45
2005
Khodaie-Biramy, Ebrahim
165329b4-e4af-4370-ba31-619ead8ecd45
Khodaie-Biramy, Ebrahim
(2005)
Applications of order statistics based on concomitant variables in survey sampling.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Using auxiliary variables or concomitants to design a survey, to construct an estimator for unknown population parameters for given sample, to select an efficient sample or to make a complete data file for data analysis purposes is common in survey sampling. This thesis uses the theory of concomitants of order statistics to propose an imputation method which is called sequential taxonomy imputation (STI) and a variance estimator for a sample mean under ordered systematic sampling (OSY).
Let (Xi, Yi) i = 1, 2,..., n be n independent and identically distributed random variables from a bivariate normal distribution. If X(r:n) denotes the rth ordered X-variate then the Y-variate Y(r:n), paired with X(r:n) is called the concomitant of the rth order statistic. In this thesis, we develop and evaluate a new imputation method for missing values. The method uses concomitants of order statistics. In particular, the method orders the data according to an auxiliary vector (X) and then selects k-nearest neighbours in order to impute a missing value in the variable Y. Under missing at random (MAR) and missing completely at random (MCAR) assumptions, this so-called single ordered sequential taxonomy imputation (SSTI) method is evaluated theoretically and empirically under a linear relationship between the auxiliary vector X and the variable Y. In particular we describe a generalised form of SSTI which is called doubly ordered sequential taxonomy imputation (DSTI). It is shown that, the bias of estimators for population parameters based on these imputed values is smaller than under other imputation methods. In addition, SSTI and DSTI preserve marginal distributions and individual values better than some commonly used imputation methods such as Hot deck imputation.
Applications of order statistics have introduced new sampling methods such as ranked-set and double sampling in recent years. In this research the statistical properties of ranked-set sampling are examined, the usual systematic sampling (SY) scheme is modified and a variance estimator for ordered systematic sampling (OSY) is suggested. Systematic sampling is a practical and efficient method for selecting samples from administrative registers or other logically arranged files.
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Published date: 2005
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Local EPrints ID: 465814
URI: http://eprints.soton.ac.uk/id/eprint/465814
PURE UUID: 0264aecd-71ca-47af-a6d2-9e27b4bc918d
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Date deposited: 05 Jul 2022 03:11
Last modified: 16 Mar 2024 20:23
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Author:
Ebrahim Khodaie-Biramy
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