In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.
In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for investigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spatial systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population with one dimension, and we derive in general these estimators for n-dimensional population. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions are derived.
","abstract_html":"<p>In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.</p> <p>In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for investigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spatial systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population with one dimension, and we derive in general these estimators for n-dimensional population. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions are derived.</p>","abstract_has_math":false,"creators":["Lakkis, Hassan"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Ram C. Dahiya","N. Rao Chaganty","Dayanand N. Naik","Douglas Robson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1994,"date_issued":"1994-07-01T07:00:00Z","date_published":"1994-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:15Z","subjects":["Finite geometries","Probabilistic number theory","Estimation problems","Sampling designs","Mathematics","Statistics and Probability"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/98","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ram C. Dahiya","N. Rao Chaganty","Dayanand N. Naik","Douglas Robson"]},{"key":"dc:creator","label":"Author","values":["Lakkis, Hassan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-02T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Finite geometries","Probabilistic number theory","Estimation problems","Sampling designs","Mathematics","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for investigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spatial systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population with one dimension, and we derive in general these estimators for n-dimensional population. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions are derived.
"]},{"key":"dc:title","label":"Title","values":["Some Sampling Designs and Estimation Problems"]}]}],"canonical_facts":{"dc:contributor":["Ram C. Dahiya","N. Rao Chaganty","Dayanand N. Naik","Douglas Robson"],"dc:creator":["Lakkis, Hassan"],"dc:date.available":["2019-10-02T07:00:00Z"],"dc:description.abstract":["In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.
In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for investigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spatial systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population with one dimension, and we derive in general these estimators for n-dimensional population. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions are derived.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/98"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Finite geometries","Probabilistic number theory","Estimation problems","Sampling designs","Mathematics","Statistics and Probability"],"dc:title":["Some Sampling Designs and Estimation Problems"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:15Z"}