In many statistical experiments one wishes to obtain a desirable “level of response” corresponding to some “level of treatment.” The response to a given treatment, however, is usually random, and the best one hopes for is to locate the level of treatment that produces the desired response on the average. The mathematical formulation of the problem is as follows.
For every level of treatment x, which we assume to be numerical and refer to as an “observation point,” the response (“observation”) y at x is a random variable on some probability space with distribution function Fx and mean m(x) < ∞. Thus m defines a regression function. One wishes to locate a point θ such that m(θ) = α1, where α1 is the desired level of response. A stochastic approximation is a sequential estimation procedure where future observation points are determined on the basis of past information. The two most-discussed procedures for the problem described are the Robbins-Monro (R-M) procedure and the up-and-down method of Dixon and Mood.
","abstract_html":"<p>In many statistical experiments one wishes to obtain a desirable “level of response” corresponding to some “level of treatment.” The response to a given treatment, however, is usually random, and the best one hopes for is to locate the level of treatment that produces the desired response on the average. The mathematical formulation of the problem is as follows.</p><p>For every level of treatment x, which we assume to be numerical and refer to as an “observation point,” the response (“observation”) y at x is a random variable on some probability space with distribution function F<sub>x</sub> and mean m(x) < ∞. Thus m defines a regression function. One wishes to locate a point θ such that m(θ) = α<sub>1</sub>, where α<sub>1</sub> is the desired level of response. A stochastic approximation is a sequential estimation procedure where future observation points are determined on the basis of past information. The two most-discussed procedures for the problem described are the Robbins-Monro (R-M) procedure and the up-and-down method of Dixon and Mood.</p>","abstract_has_math":false,"creators":["Mukerjee, Hari G."],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["David A. Edwards","David L. Hanson","Eugene M. Klimko"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1976,"date_issued":"1976-01-01T08:00:00Z","date_published":"1976-01-01T08:00:00Z","updated_at":"2026-07-24T01:10:35Z","subjects":["Stochastic analysis","Approximation theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://orb.binghamton.edu/dissertation_and_theses/421","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["David A. Edwards","David L. Hanson","Eugene M. Klimko"]},{"key":"dc:creator","label":"Author","values":["Mukerjee, Hari G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"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":["Stochastic analysis","Approximation theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://orb.binghamton.edu/dissertation_and_theses/421"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In many statistical experiments one wishes to obtain a desirable “level of response” corresponding to some “level of treatment.” The response to a given treatment, however, is usually random, and the best one hopes for is to locate the level of treatment that produces the desired response on the average. The mathematical formulation of the problem is as follows.
For every level of treatment x, which we assume to be numerical and refer to as an “observation point,” the response (“observation”) y at x is a random variable on some probability space with distribution function Fx and mean m(x) < ∞. Thus m defines a regression function. One wishes to locate a point θ such that m(θ) = α1, where α1 is the desired level of response. A stochastic approximation is a sequential estimation procedure where future observation points are determined on the basis of past information. The two most-discussed procedures for the problem described are the Robbins-Monro (R-M) procedure and the up-and-down method of Dixon and Mood.
"]},{"key":"dc:title","label":"Title","values":["On stochastic approximation"]}]}],"canonical_facts":{"dc:contributor":["David A. Edwards","David L. Hanson","Eugene M. Klimko"],"dc:creator":["Mukerjee, Hari G."],"dc:description.abstract":["In many statistical experiments one wishes to obtain a desirable “level of response” corresponding to some “level of treatment.” The response to a given treatment, however, is usually random, and the best one hopes for is to locate the level of treatment that produces the desired response on the average. The mathematical formulation of the problem is as follows.
For every level of treatment x, which we assume to be numerical and refer to as an “observation point,” the response (“observation”) y at x is a random variable on some probability space with distribution function Fx and mean m(x) < ∞. Thus m defines a regression function. One wishes to locate a point θ such that m(θ) = α1, where α1 is the desired level of response. A stochastic approximation is a sequential estimation procedure where future observation points are determined on the basis of past information. The two most-discussed procedures for the problem described are the Robbins-Monro (R-M) procedure and the up-and-down method of Dixon and Mood.
"],"dc:identifier":["https://orb.binghamton.edu/dissertation_and_theses/421"],"dc:subject":["Stochastic analysis","Approximation theory"],"dc:title":["On stochastic approximation"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:10:35Z"}