Exact inequalities for sums of asymmetric random variables, with applications
Let BS1,...BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p E (0,1). Let ... if 0
Gespeichert in:
| Veröffentlicht in: | Probability theory and related fields 2007-11, Vol.139 (3-4), p.605-635 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 635 |
|---|---|
| container_issue | 3-4 |
| container_start_page | 605 |
| container_title | Probability theory and related fields |
| container_volume | 139 |
| creator | PINELIS, Iosif |
| description | Let BS1,...BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p E (0,1). Let ... if 0 |
| doi_str_mv | 10.1007/s00440-007-0055-4 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2661274990</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1308527251</sourcerecordid><originalsourceid>FETCH-LOGICAL-c373t-16da8fbec4471c1480485ce792730c291e958d9985103d0336ca7adae1493e7f3</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wFtQvLk6-dhNcpRSP6DiRc9hms1iyn60ya7af--WFjx5GGYOz_sOPIRcMrhjAOo-AUgJ2XiOk-eZPCITJgXPOBTymEyAKZ1pyNkpOUtpBQBcSD4hr_MfdD0Nrd8MWIc--ESrLtI0NIl2FcW0bRrfx-BoxLbsGvqFMeCy9umWfof-k-J6XQeHfejadE5OKqyTvzjsKfl4nL_PnrPF29PL7GGROaFEn7GiRF0tvZNSMcekBqlz55XhSoDjhnmT69IYnTMQJQhROFRYomfSCK8qMSXX-9517DaDT71ddUNsx5eWFwXjShoDI3X1LyUEz5VmZoTYHnKxSyn6yq5jaDBuLQO7U2v3au3u3Km1cszcHIoxOayr0YwL6S-ojRRMg_gFYGd3mg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>233257819</pqid></control><display><type>article</type><title>Exact inequalities for sums of asymmetric random variables, with applications</title><source>SpringerNature Journals</source><source>EBSCOhost Business Source Complete</source><creator>PINELIS, Iosif</creator><creatorcontrib>PINELIS, Iosif</creatorcontrib><description>Let BS1,...BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p E (0,1). Let ... if 0<p</=1/2 and ... . Let m>/=m,(p). Let f be such a function that f and f'' are nondecreasing and convex. Then it is proved that for all nonnegative numbers c1,...cn one has the inequality ... where ... . The lower bound m*(p) on m is exact for each p E(0,1). Moreover, ... is Schur-concave in (c 2m/1,...c2m/n). A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t -statistics are given. (ProQuest: ... denotes formula omitted)</description><identifier>ISSN: 0178-8051</identifier><identifier>EISSN: 1432-2064</identifier><identifier>DOI: 10.1007/s00440-007-0055-4</identifier><identifier>CODEN: PTRFEU</identifier><language>eng</language><publisher>Heidelberg: Springer</publisher><subject>Asymmetry ; Distribution theory ; Exact sciences and technology ; General topics ; Independent variables ; Inequality ; Lower bounds ; Martingales ; Mathematical models ; Mathematics ; Probability ; Probability and statistics ; Probability theory and stochastic processes ; Random variables ; Sciences and techniques of general use ; Statistics ; Stochastic processes ; Studies ; Sums ; Upper bounds</subject><ispartof>Probability theory and related fields, 2007-11, Vol.139 (3-4), p.605-635</ispartof><rights>2008 INIST-CNRS</rights><rights>Springer-Verlag 2007</rights><rights>Springer-Verlag 2007.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c373t-16da8fbec4471c1480485ce792730c291e958d9985103d0336ca7adae1493e7f3</citedby><cites>FETCH-LOGICAL-c373t-16da8fbec4471c1480485ce792730c291e958d9985103d0336ca7adae1493e7f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18943180$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>PINELIS, Iosif</creatorcontrib><title>Exact inequalities for sums of asymmetric random variables, with applications</title><title>Probability theory and related fields</title><description>Let BS1,...BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p E (0,1). Let ... if 0<p</=1/2 and ... . Let m>/=m,(p). Let f be such a function that f and f'' are nondecreasing and convex. Then it is proved that for all nonnegative numbers c1,...cn one has the inequality ... where ... . The lower bound m*(p) on m is exact for each p E(0,1). Moreover, ... is Schur-concave in (c 2m/1,...c2m/n). A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t -statistics are given. (ProQuest: ... denotes formula omitted)</description><subject>Asymmetry</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Independent variables</subject><subject>Inequality</subject><subject>Lower bounds</subject><subject>Martingales</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Probability</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Random variables</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>Stochastic processes</subject><subject>Studies</subject><subject>Sums</subject><subject>Upper bounds</subject><issn>0178-8051</issn><issn>1432-2064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kE1LAzEQhoMoWKs_wFtQvLk6-dhNcpRSP6DiRc9hms1iyn60ya7af--WFjx5GGYOz_sOPIRcMrhjAOo-AUgJ2XiOk-eZPCITJgXPOBTymEyAKZ1pyNkpOUtpBQBcSD4hr_MfdD0Nrd8MWIc--ESrLtI0NIl2FcW0bRrfx-BoxLbsGvqFMeCy9umWfof-k-J6XQeHfejadE5OKqyTvzjsKfl4nL_PnrPF29PL7GGROaFEn7GiRF0tvZNSMcekBqlz55XhSoDjhnmT69IYnTMQJQhROFRYomfSCK8qMSXX-9517DaDT71ddUNsx5eWFwXjShoDI3X1LyUEz5VmZoTYHnKxSyn6yq5jaDBuLQO7U2v3au3u3Km1cszcHIoxOayr0YwL6S-ojRRMg_gFYGd3mg</recordid><startdate>20071101</startdate><enddate>20071101</enddate><creator>PINELIS, Iosif</creator><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>0U~</scope><scope>1-H</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20071101</creationdate><title>Exact inequalities for sums of asymmetric random variables, with applications</title><author>PINELIS, Iosif</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-16da8fbec4471c1480485ce792730c291e958d9985103d0336ca7adae1493e7f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Asymmetry</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Independent variables</topic><topic>Inequality</topic><topic>Lower bounds</topic><topic>Martingales</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Probability</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Random variables</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Stochastic processes</topic><topic>Studies</topic><topic>Sums</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>PINELIS, Iosif</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Probability theory and related fields</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>PINELIS, Iosif</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact inequalities for sums of asymmetric random variables, with applications</atitle><jtitle>Probability theory and related fields</jtitle><date>2007-11-01</date><risdate>2007</risdate><volume>139</volume><issue>3-4</issue><spage>605</spage><epage>635</epage><pages>605-635</pages><issn>0178-8051</issn><eissn>1432-2064</eissn><coden>PTRFEU</coden><abstract>Let BS1,...BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p E (0,1). Let ... if 0<p</=1/2 and ... . Let m>/=m,(p). Let f be such a function that f and f'' are nondecreasing and convex. Then it is proved that for all nonnegative numbers c1,...cn one has the inequality ... where ... . The lower bound m*(p) on m is exact for each p E(0,1). Moreover, ... is Schur-concave in (c 2m/1,...c2m/n). A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t -statistics are given. (ProQuest: ... denotes formula omitted)</abstract><cop>Heidelberg</cop><cop>Berlin</cop><cop>New York, NY</cop><pub>Springer</pub><doi>10.1007/s00440-007-0055-4</doi><tpages>31</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0178-8051 |
| ispartof | Probability theory and related fields, 2007-11, Vol.139 (3-4), p.605-635 |
| issn | 0178-8051 1432-2064 |
| language | eng |
| recordid | cdi_proquest_journals_2661274990 |
| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Asymmetry Distribution theory Exact sciences and technology General topics Independent variables Inequality Lower bounds Martingales Mathematical models Mathematics Probability Probability and statistics Probability theory and stochastic processes Random variables Sciences and techniques of general use Statistics Stochastic processes Studies Sums Upper bounds |
| title | Exact inequalities for sums of asymmetric random variables, with applications |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T19%3A20%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exact%20inequalities%20for%20sums%20of%20asymmetric%20random%20variables,%20with%20applications&rft.jtitle=Probability%20theory%20and%20related%20fields&rft.au=PINELIS,%20Iosif&rft.date=2007-11-01&rft.volume=139&rft.issue=3-4&rft.spage=605&rft.epage=635&rft.pages=605-635&rft.issn=0178-8051&rft.eissn=1432-2064&rft.coden=PTRFEU&rft_id=info:doi/10.1007/s00440-007-0055-4&rft_dat=%3Cproquest_cross%3E1308527251%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=233257819&rft_id=info:pmid/&rfr_iscdi=true |