In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies in an area of sparse data so that users may be able to identify problematic situations. Additional simulations results are shown to assess the tests overall performance.
","abstract_html":"<p>In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies in an area of sparse data so that users may be able to identify problematic situations. Additional simulations results are shown to assess the tests overall performance.</p>","abstract_has_math":false,"creators":["Faires, Jackson"],"institution":null,"degree_name":"Master of Science - Statistics","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Jacob A. Turner"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-08-01T07:00:00Z","date_published":"2021-08-01T07:00:00Z","updated_at":"2026-07-24T04:30:30Z","subjects":["sparsity","random forest","k-nearest nighbors","Other Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/406","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jacob A. Turner"]},{"key":"dc:creator","label":"Author","values":["Faires, Jackson"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-07-30T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Statistics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["sparsity","random forest","k-nearest nighbors","Other Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/406"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies in an area of sparse data so that users may be able to identify problematic situations. Additional simulations results are shown to assess the tests overall performance.
"]},{"key":"dc:title","label":"Title","values":["Prediction Intervals: The Effects and Identification of Sparse Regions for Nonparametric Regression Methods"]}]}],"canonical_facts":{"dc:contributor":["Jacob A. Turner"],"dc:creator":["Faires, Jackson"],"dc:date.available":["2021-07-30T07:00:00Z"],"dc:description.abstract":["In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies in an area of sparse data so that users may be able to identify problematic situations. Additional simulations results are shown to assess the tests overall performance.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/406"],"dc:subject":["sparsity","random forest","k-nearest nighbors","Other Statistics and Probability"],"dc:title":["Prediction Intervals: The Effects and Identification of Sparse Regions for Nonparametric Regression Methods"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Statistics"]},"updated_at":"2026-07-24T04:30:30Z"}