Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
","abstract_html":"<p>Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.</p>","abstract_has_math":false,"creators":["Peiris, Thelge Buddika"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bhattacharya, Bhaskar","Olive, David","Ban, Dubravka"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-08-01T07:00:00Z","date_published":"2014-08-01T07:00:00Z","updated_at":"2026-07-24T04:34:30Z","subjects":["chi-bar square distribution","dual cone","hyperplane","in-equalities","least favorable disribution","nonnegative least squre"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/934","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bhattacharya, Bhaskar","Olive, David","Ban, Dubravka"]},{"key":"dc:creator","label":"Author","values":["Peiris, Thelge Buddika"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-04-23T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["chi-bar square distribution","dual cone","hyperplane","in-equalities","least favorable disribution","nonnegative least squre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/934"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
"]},{"key":"dc:title","label":"Title","values":["Constrained Statistical Inference in Regression"]}]}],"canonical_facts":{"dc:contributor":["Bhattacharya, Bhaskar","Olive, David","Ban, Dubravka"],"dc:creator":["Peiris, Thelge Buddika"],"dc:date.available":["2015-04-23T07:00:00Z"],"dc:description.abstract":["Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
"],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/934"],"dc:subject":["chi-bar square distribution","dual cone","hyperplane","in-equalities","least favorable disribution","nonnegative least squre"],"dc:title":["Constrained Statistical Inference in Regression"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:34:30Z"}