A Modified Robbins-Monro Procedure Approximating the Zero of a Regression Function from Below
A Robbins-Monro type procedure for estimating the zero of a regression function is discussed. The procedure is a modification of the Robbins-Monro procedure which is designed to approximate the zero from below. An almost sure convergence is proved and it is shown that one can guarantee that the proc...
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| Veröffentlicht in: | The Annals of statistics 1977-01, Vol.5 (1), p.229-234 |
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| container_end_page | 234 |
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| container_title | The Annals of statistics |
| container_volume | 5 |
| creator | Anbar, Dan |
| description | A Robbins-Monro type procedure for estimating the zero of a regression function is discussed. The procedure is a modification of the Robbins-Monro procedure which is designed to approximate the zero from below. An almost sure convergence is proved and it is shown that one can guarantee that the procedure overestimate the zero only finitely many times with probability one. |
| doi_str_mv | 10.1214/aos/1176343758 |
| format | Article |
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The procedure is a modification of the Robbins-Monro procedure which is designed to approximate the zero from below. An almost sure convergence is proved and it is shown that one can guarantee that the procedure overestimate the zero only finitely many times with probability one.</description><subject>62L05</subject><subject>62L20</subject><subject>Applied statistics</subject><subject>Approximation</subject><subject>Dosage</subject><subject>Martingales</subject><subject>Mathematical procedures</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Perceptron convergence procedure</subject><subject>Random variables</subject><subject>Robbins-Monro procedure</subject><subject>search procedure</subject><subject>sequential design</subject><subject>Short Communications</subject><subject>Stochastic approximation</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1977</creationdate><recordtype>article</recordtype><recordid>eNplkE9LAzEUxIMoWKtXTx7yBdYmm797sxarQotS7EWQJZt9qSntpiRb1G_vlpZ68DSPx8ww_BC6puSW5pQPTEgDSpVknCmhT1Avp1JnupDyFPUIKUgmmOTn6CKlJSFEFJz10McQT0PtnYcaz0JV-SZl09DEgF9jsFBvI-DhZhPDt1-b1jcL3H4CfofOEBw2eAaLCCn50ODxtrHt7nAxrPE9rMLXJTpzZpXg6qB9NB8_vI2essnL4_NoOMlsrlXb7aq0rAmwyuZGGKct48Ac4aBorqgmrK6cpZpVYCxwMEoYCUQ6nUsLgrE-utv3dkOXYFvY2pWvy03sRsefMhhfjuaTw_cgHa7yD1dXcbuvsDGkFMEd05SUO77_Azf7wDK1IR7deSG0UgX7BYayeco</recordid><startdate>19770101</startdate><enddate>19770101</enddate><creator>Anbar, Dan</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19770101</creationdate><title>A Modified Robbins-Monro Procedure Approximating the Zero of a Regression Function from Below</title><author>Anbar, Dan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c287t-53b86d0e3bc2a5af8c34e3f04e71271803dbfc183beace4ea75a6e06f826ce533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1977</creationdate><topic>62L05</topic><topic>62L20</topic><topic>Applied statistics</topic><topic>Approximation</topic><topic>Dosage</topic><topic>Martingales</topic><topic>Mathematical procedures</topic><topic>Mathematical theorems</topic><topic>Mathematics</topic><topic>Perceptron convergence procedure</topic><topic>Random variables</topic><topic>Robbins-Monro procedure</topic><topic>search procedure</topic><topic>sequential design</topic><topic>Short Communications</topic><topic>Stochastic approximation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Anbar, Dan</creatorcontrib><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Anbar, Dan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Modified Robbins-Monro Procedure Approximating the Zero of a Regression Function from Below</atitle><jtitle>The Annals of statistics</jtitle><date>1977-01-01</date><risdate>1977</risdate><volume>5</volume><issue>1</issue><spage>229</spage><epage>234</epage><pages>229-234</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><abstract>A Robbins-Monro type procedure for estimating the zero of a regression function is discussed. The procedure is a modification of the Robbins-Monro procedure which is designed to approximate the zero from below. An almost sure convergence is proved and it is shown that one can guarantee that the procedure overestimate the zero only finitely many times with probability one.</abstract><pub>Institute of Mathematical Statistics</pub><doi>10.1214/aos/1176343758</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | The Annals of statistics, 1977-01, Vol.5 (1), p.229-234 |
| issn | 0090-5364 2168-8966 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1176343758 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Project Euclid Complete |
| subjects | 62L05 62L20 Applied statistics Approximation Dosage Martingales Mathematical procedures Mathematical theorems Mathematics Perceptron convergence procedure Random variables Robbins-Monro procedure search procedure sequential design Short Communications Stochastic approximation |
| title | A Modified Robbins-Monro Procedure Approximating the Zero of a Regression Function from Below |
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