Variance prediction for pseudosystematic sampling on the sphere
Geometric sampling, and local stereology in particular, often require observations at isotropic random directions on the sphere, and some sort of systematic design on the sphere becomes necessary on grounds of efficiency and practical applicability. Typically, the relevant probes are of nucleator ty...
Gespeichert in:
Veröffentlicht in: | Advances in applied probability 2002-09, Vol.34 (3), p.469-483 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 483 |
---|---|
container_issue | 3 |
container_start_page | 469 |
container_title | Advances in applied probability |
container_volume | 34 |
creator | Gual-Arnau, Ximo Cruz-Orive, Luis M. |
description | Geometric sampling, and local stereology in particular, often require observations at isotropic random directions on the sphere, and some sort of systematic design on the sphere becomes necessary on grounds of efficiency and practical applicability. Typically, the relevant probes are of nucleator type, in which several rays may be contained in a sectioning plane through a fixed point (e.g. through a nucleolus within a biological cell). The latter requirement considerably reduces the choice of design in practice; in this paper, we concentrate on a nucleator design based on splitting the sphere into regions of equal area, but not of identical shape; this design is pseudosystematic rather than systematic in a strict sense. Firstly, we obtain useful exact representations of the variance of an estimator under pseudosystematic sampling on the sphere. Then we adopt a suitable covariogram model to obtain a variance predictor from a single sample of arbitrary size, and finally we examine the prediction accuracy by way of simulation on a synthetic particle model. |
doi_str_mv | 10.1239/aap/1033662160 |
format | Article |
fullrecord | <record><control><sourceid>jstor_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_aap_1033662160</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1239_aap_1033662160</cupid><jstor_id>1428241</jstor_id><sourcerecordid>1428241</sourcerecordid><originalsourceid>FETCH-LOGICAL-c271t-ccfe27056f8b2987fb60d09cefc2caffcb38e379566b7bf327fc7a05d2588743</originalsourceid><addsrcrecordid>eNp1kD1PwzAQhi0EEqWwMjHkD6T1R2I7E6CKL6kSS2GNHOfcOmpiy3aH_nuCGsGAmE53977P8CB0S_CCUFYtlfJLghnjnBKOz9CMFKLMOebFOZphjEkuuZCX6CrGblyZkHiG7j9VsGrQkPkArdXJuiEzLmQ-wqF18RgT9CpZnUXV-70dttkYSDvIot9BgGt0YdQ-ws0052jz_LRZvebr95e31eM611SQlGttgApcciMbWklhGo5bXGkwmmpljG6YBCaqkvNGNIZRYbRQuGxpKaUo2Bw9nLA-uA50goPe27b2wfYqHGunbL36WE_XaYw-6l8fI2JxQujgYgxgftoE198C_xbuToUuJhd-0wWVtCDjG0881TfBtluoO3cIw2jhP-IXYZ1-bw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Variance prediction for pseudosystematic sampling on the sphere</title><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><creator>Gual-Arnau, Ximo ; Cruz-Orive, Luis M.</creator><creatorcontrib>Gual-Arnau, Ximo ; Cruz-Orive, Luis M.</creatorcontrib><description>Geometric sampling, and local stereology in particular, often require observations at isotropic random directions on the sphere, and some sort of systematic design on the sphere becomes necessary on grounds of efficiency and practical applicability. Typically, the relevant probes are of nucleator type, in which several rays may be contained in a sectioning plane through a fixed point (e.g. through a nucleolus within a biological cell). The latter requirement considerably reduces the choice of design in practice; in this paper, we concentrate on a nucleator design based on splitting the sphere into regions of equal area, but not of identical shape; this design is pseudosystematic rather than systematic in a strict sense. Firstly, we obtain useful exact representations of the variance of an estimator under pseudosystematic sampling on the sphere. Then we adopt a suitable covariogram model to obtain a variance predictor from a single sample of arbitrary size, and finally we examine the prediction accuracy by way of simulation on a synthetic particle model.</description><identifier>ISSN: 0001-8678</identifier><identifier>EISSN: 1475-6064</identifier><identifier>DOI: 10.1239/aap/1033662160</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>52A22 ; 53C65 ; 60D05 ; Approximation ; Bernoulli polynomial ; Coefficients ; covariogram ; Estimators ; Fourier analysis ; Geometric planes ; geometric sampling ; Mathematical functions ; Modeling ; nucleator ; periodic function ; Sample size ; Spheres ; Statistical variance ; stereology ; Stochastic Geometry and Statistical Applications ; Unbiased estimators</subject><ispartof>Advances in applied probability, 2002-09, Vol.34 (3), p.469-483</ispartof><rights>Copyright © Applied Probability Trust 2002</rights><rights>Copyright 2002 Applied Probability Trust</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c271t-ccfe27056f8b2987fb60d09cefc2caffcb38e379566b7bf327fc7a05d2588743</citedby><cites>FETCH-LOGICAL-c271t-ccfe27056f8b2987fb60d09cefc2caffcb38e379566b7bf327fc7a05d2588743</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/1428241$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/1428241$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,885,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>Gual-Arnau, Ximo</creatorcontrib><creatorcontrib>Cruz-Orive, Luis M.</creatorcontrib><title>Variance prediction for pseudosystematic sampling on the sphere</title><title>Advances in applied probability</title><addtitle>Advances in Applied Probability</addtitle><description>Geometric sampling, and local stereology in particular, often require observations at isotropic random directions on the sphere, and some sort of systematic design on the sphere becomes necessary on grounds of efficiency and practical applicability. Typically, the relevant probes are of nucleator type, in which several rays may be contained in a sectioning plane through a fixed point (e.g. through a nucleolus within a biological cell). The latter requirement considerably reduces the choice of design in practice; in this paper, we concentrate on a nucleator design based on splitting the sphere into regions of equal area, but not of identical shape; this design is pseudosystematic rather than systematic in a strict sense. Firstly, we obtain useful exact representations of the variance of an estimator under pseudosystematic sampling on the sphere. Then we adopt a suitable covariogram model to obtain a variance predictor from a single sample of arbitrary size, and finally we examine the prediction accuracy by way of simulation on a synthetic particle model.</description><subject>52A22</subject><subject>53C65</subject><subject>60D05</subject><subject>Approximation</subject><subject>Bernoulli polynomial</subject><subject>Coefficients</subject><subject>covariogram</subject><subject>Estimators</subject><subject>Fourier analysis</subject><subject>Geometric planes</subject><subject>geometric sampling</subject><subject>Mathematical functions</subject><subject>Modeling</subject><subject>nucleator</subject><subject>periodic function</subject><subject>Sample size</subject><subject>Spheres</subject><subject>Statistical variance</subject><subject>stereology</subject><subject>Stochastic Geometry and Statistical Applications</subject><subject>Unbiased estimators</subject><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAQhi0EEqWwMjHkD6T1R2I7E6CKL6kSS2GNHOfcOmpiy3aH_nuCGsGAmE53977P8CB0S_CCUFYtlfJLghnjnBKOz9CMFKLMOebFOZphjEkuuZCX6CrGblyZkHiG7j9VsGrQkPkArdXJuiEzLmQ-wqF18RgT9CpZnUXV-70dttkYSDvIot9BgGt0YdQ-ws0052jz_LRZvebr95e31eM611SQlGttgApcciMbWklhGo5bXGkwmmpljG6YBCaqkvNGNIZRYbRQuGxpKaUo2Bw9nLA-uA50goPe27b2wfYqHGunbL36WE_XaYw-6l8fI2JxQujgYgxgftoE198C_xbuToUuJhd-0wWVtCDjG0881TfBtluoO3cIw2jhP-IXYZ1-bw</recordid><startdate>200209</startdate><enddate>200209</enddate><creator>Gual-Arnau, Ximo</creator><creator>Cruz-Orive, Luis M.</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200209</creationdate><title>Variance prediction for pseudosystematic sampling on the sphere</title><author>Gual-Arnau, Ximo ; Cruz-Orive, Luis M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c271t-ccfe27056f8b2987fb60d09cefc2caffcb38e379566b7bf327fc7a05d2588743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>52A22</topic><topic>53C65</topic><topic>60D05</topic><topic>Approximation</topic><topic>Bernoulli polynomial</topic><topic>Coefficients</topic><topic>covariogram</topic><topic>Estimators</topic><topic>Fourier analysis</topic><topic>Geometric planes</topic><topic>geometric sampling</topic><topic>Mathematical functions</topic><topic>Modeling</topic><topic>nucleator</topic><topic>periodic function</topic><topic>Sample size</topic><topic>Spheres</topic><topic>Statistical variance</topic><topic>stereology</topic><topic>Stochastic Geometry and Statistical Applications</topic><topic>Unbiased estimators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gual-Arnau, Ximo</creatorcontrib><creatorcontrib>Cruz-Orive, Luis M.</creatorcontrib><collection>CrossRef</collection><jtitle>Advances in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gual-Arnau, Ximo</au><au>Cruz-Orive, Luis M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Variance prediction for pseudosystematic sampling on the sphere</atitle><jtitle>Advances in applied probability</jtitle><addtitle>Advances in Applied Probability</addtitle><date>2002-09</date><risdate>2002</risdate><volume>34</volume><issue>3</issue><spage>469</spage><epage>483</epage><pages>469-483</pages><issn>0001-8678</issn><eissn>1475-6064</eissn><abstract>Geometric sampling, and local stereology in particular, often require observations at isotropic random directions on the sphere, and some sort of systematic design on the sphere becomes necessary on grounds of efficiency and practical applicability. Typically, the relevant probes are of nucleator type, in which several rays may be contained in a sectioning plane through a fixed point (e.g. through a nucleolus within a biological cell). The latter requirement considerably reduces the choice of design in practice; in this paper, we concentrate on a nucleator design based on splitting the sphere into regions of equal area, but not of identical shape; this design is pseudosystematic rather than systematic in a strict sense. Firstly, we obtain useful exact representations of the variance of an estimator under pseudosystematic sampling on the sphere. Then we adopt a suitable covariogram model to obtain a variance predictor from a single sample of arbitrary size, and finally we examine the prediction accuracy by way of simulation on a synthetic particle model.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1239/aap/1033662160</doi><tpages>15</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0001-8678 |
ispartof | Advances in applied probability, 2002-09, Vol.34 (3), p.469-483 |
issn | 0001-8678 1475-6064 |
language | eng |
recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aap_1033662160 |
source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
subjects | 52A22 53C65 60D05 Approximation Bernoulli polynomial Coefficients covariogram Estimators Fourier analysis Geometric planes geometric sampling Mathematical functions Modeling nucleator periodic function Sample size Spheres Statistical variance stereology Stochastic Geometry and Statistical Applications Unbiased estimators |
title | Variance prediction for pseudosystematic sampling on the sphere |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T20%3A37%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Variance%20prediction%20for%20pseudosystematic%20sampling%20on%20the%20sphere&rft.jtitle=Advances%20in%20applied%20probability&rft.au=Gual-Arnau,%20Ximo&rft.date=2002-09&rft.volume=34&rft.issue=3&rft.spage=469&rft.epage=483&rft.pages=469-483&rft.issn=0001-8678&rft.eissn=1475-6064&rft_id=info:doi/10.1239/aap/1033662160&rft_dat=%3Cjstor_proje%3E1428241%3C/jstor_proje%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_cupid=10_1239_aap_1033662160&rft_jstor_id=1428241&rfr_iscdi=true |