Systematic sampling with errors in sample locations
Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid i...
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| Veröffentlicht in: | Biometrika 2010-03, Vol.97 (1), p.1-13 |
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| container_title | Biometrika |
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| creator | ZIEGEL, JOHANNA BADDELEY, ADRIAN DORPH-PETERSEN, KARL-ANTON JENSEN, EVA B. VEDEL |
| description | Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy. |
| doi_str_mv | 10.1093/biomet/asp067 |
| format | Article |
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Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. 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VEDEL</creatorcontrib><title>Systematic sampling with errors in sample locations</title><title>Biometrika</title><description>Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy.</description><subject>Applications</subject><subject>Asymptotic methods</subject><subject>Asymptotic variance</subject><subject>Biology, psychology, social sciences</subject><subject>Cavalieri estimator</subject><subject>Convergence</subject><subject>Cumulative error</subject><subject>Density</subject><subject>Error rates</subject><subject>Errors</subject><subject>Estimating techniques</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Factorials</subject><subject>General topics</subject><subject>Geometric shapes</subject><subject>Integrable functions</subject><subject>Linear inference, regression</subject><subject>Mathematics</subject><subject>Microscopy</subject><subject>Moment measure</subject><subject>Perturbed systematic sampling</subject><subject>Physical training</subject><subject>Point process</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Random sampling</subject><subject>Sampling</subject><subject>Sampling errors</subject><subject>Sampling techniques</subject><subject>Sciences and techniques of general use</subject><subject>Spatial statistics</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Stereology</subject><subject>Stochastic processes</subject><subject>Studies</subject><subject>Unbiased estimators</subject><subject>Variance analysis</subject><issn>0006-3444</issn><issn>1464-3510</issn><issn>1464-3510</issn><issn>0006-3444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFkU1v1DAQhi0EEkvhyBEpQkLiEurJ-CM5woq2oEpIFBDai-V1vNRLEqd2Fth_z5SslooLh_HI9uN3Zl4z9hT4K-ANnq5D7P10avPIlb7HFiCUKFECv88WnHNVohDiIXuU8_Z2q6RaMLza58n3dgquyLYfuzB8K36G6brwKcWUizDM577ooiMsDvkxe7CxXfZPDvmEfT57-2l5UV5-OH-3fH1ZOlnhVKKVEiRgW4HSVE6shag0KnCu4dJjUwuNXKxbQF-3ruUbX7tWqLaVlW65wBP2ctYdU7zZ-TyZPmTnu84OPu6yAdBQq0Y3NaHP_0G3cZcG6s5UHIiRiASVM-RSzDn5jRlT6G3aG-Dm1kEzO2hmB4k_n_nkR--OcNyNB-6HQdtoWvYUVIdTChRAMf7JgOZ66knpxaE9m53tNskOLuSjYlXJpgZ5Z2Kq8d_mns3oNk8x_ZXSZEfd3Bk20P_-Ot7b9N3Qay3NxdeVWV2dfVy-ef_FrPA3Z4qwew</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>ZIEGEL, JOHANNA</creator><creator>BADDELEY, ADRIAN</creator><creator>DORPH-PETERSEN, KARL-ANTON</creator><creator>JENSEN, EVA B. VEDEL</creator><general>Oxford University Press</general><general>Biometrika Trust, University College London</general><general>Oxford University Press for Biometrika Trust</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20100301</creationdate><title>Systematic sampling with errors in sample locations</title><author>ZIEGEL, JOHANNA ; BADDELEY, ADRIAN ; DORPH-PETERSEN, KARL-ANTON ; JENSEN, EVA B. VEDEL</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c523t-3a551513d21670664b4427361cc905e39847304bd13e8dcd0fe8cd46dd527d043</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applications</topic><topic>Asymptotic methods</topic><topic>Asymptotic variance</topic><topic>Biology, psychology, social sciences</topic><topic>Cavalieri estimator</topic><topic>Convergence</topic><topic>Cumulative error</topic><topic>Density</topic><topic>Error rates</topic><topic>Errors</topic><topic>Estimating techniques</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Factorials</topic><topic>General topics</topic><topic>Geometric shapes</topic><topic>Integrable functions</topic><topic>Linear inference, regression</topic><topic>Mathematics</topic><topic>Microscopy</topic><topic>Moment measure</topic><topic>Perturbed systematic sampling</topic><topic>Physical training</topic><topic>Point process</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Random sampling</topic><topic>Sampling</topic><topic>Sampling errors</topic><topic>Sampling techniques</topic><topic>Sciences and techniques of general use</topic><topic>Spatial statistics</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Stereology</topic><topic>Stochastic processes</topic><topic>Studies</topic><topic>Unbiased estimators</topic><topic>Variance analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>ZIEGEL, JOHANNA</creatorcontrib><creatorcontrib>BADDELEY, ADRIAN</creatorcontrib><creatorcontrib>DORPH-PETERSEN, KARL-ANTON</creatorcontrib><creatorcontrib>JENSEN, EVA B. 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VEDEL</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Systematic sampling with errors in sample locations</atitle><jtitle>Biometrika</jtitle><date>2010-03-01</date><risdate>2010</risdate><volume>97</volume><issue>1</issue><spage>1</spage><epage>13</epage><pages>1-13</pages><issn>0006-3444</issn><issn>1464-3510</issn><eissn>1464-3510</eissn><eissn>0006-3444</eissn><coden>BIOKAX</coden><abstract>Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/asp067</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| source | Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); RePEc; Alma/SFX Local Collection; JSTOR Mathematics & Statistics |
| subjects | Applications Asymptotic methods Asymptotic variance Biology, psychology, social sciences Cavalieri estimator Convergence Cumulative error Density Error rates Errors Estimating techniques Estimators Exact sciences and technology Factorials General topics Geometric shapes Integrable functions Linear inference, regression Mathematics Microscopy Moment measure Perturbed systematic sampling Physical training Point process Probability and statistics Probability theory and stochastic processes Random sampling Sampling Sampling errors Sampling techniques Sciences and techniques of general use Spatial statistics Statistical variance Statistics Stereology Stochastic processes Studies Unbiased estimators Variance analysis |
| title | Systematic sampling with errors in sample locations |
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