Inference for Spatial Processes Using Subsampling: a Simulation Study
Many environmental studies involve the measurement of ecological indices that yield spatially dependent data. One quantity that captures the empirical distribution of ecological measurements is the spatial cumulative distribution function (SCDF). Methods for making inferential statements about SCDFs...
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| Veröffentlicht in: | Environmetrics (London, Ont.) Jg. 8; H. 5; S. 485 - 502 |
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Chichester, UK
John Wiley & Sons, Ltd
01.09.1997
Wiley |
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| ISSN: | 1180-4009, 1099-095X |
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| Abstract | Many environmental studies involve the measurement of ecological indices that yield spatially dependent data. One quantity that captures the empirical distribution of ecological measurements is the spatial cumulative distribution function (SCDF). Methods for making inferential statements about SCDFs have only recently been developed, one being that of spatial subsampling. While spatial subsampling produces inferential quantities with known asymptotic properties, the performance of this methodology in a finite‐sample setting has not previously been investigated. In this article, we review the subsampling method and its theoretical justification, and investigate the performance of this method for finite samples with a simulation study involving several subsampling designs and types of spatial dependence. The subsampling methodology appears to give quite good results over a range of realistic spatial processes. For application to a set of spatially dependent data, an appropriate subsampling procedure may be designed on the basis of quantities contained in the (estimated) variogram. © 1997 John Wiley & Sons, Ltd. |
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| AbstractList | Many environmental studies involve the measurement of ecological indices that yield spatially dependent data. One quantity that captures the empirical distribution of ecological measurements is the spatial cumulative distribution function (SCDF). Methods for making inferential statements about SCDFs have only recently been developed, one being that of spatial subsampling. While spatial subsampling produces inferential quantities with known asymptotic properties, the performance of this methodology in a finite‐sample setting has not previously been investigated. In this article, we review the subsampling method and its theoretical justification, and investigate the performance of this method for finite samples with a simulation study involving several subsampling designs and types of spatial dependence. The subsampling methodology appears to give quite good results over a range of realistic spatial processes. For application to a set of spatially dependent data, an appropriate subsampling procedure may be designed on the basis of quantities contained in the (estimated) variogram. © 1997 John Wiley & Sons, Ltd. |
| Author | Hsu, Nan-Jung Cressie, Noel Lahiri, Soumendra N. Kaiser, Mark S. |
| Author_xml | – sequence: 1 givenname: Mark S. surname: Kaiser fullname: Kaiser, Mark S. organization: Department of Statistics, Iowa State University, Ames, IA 50011, U.S.A – sequence: 2 givenname: Nan-Jung surname: Hsu fullname: Hsu, Nan-Jung organization: Department of Statistics, Iowa State University, Ames, IA 50011, U.S.A – sequence: 3 givenname: Noel surname: Cressie fullname: Cressie, Noel organization: Department of Statistics, Iowa State University, Ames, IA 50011, U.S.A – sequence: 4 givenname: Soumendra N. surname: Lahiri fullname: Lahiri, Soumendra N. organization: Department of Statistics, Iowa State University, Ames, IA 50011, U.S.A |
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| Cites_doi | 10.1080/01621459.1994.10476773 10.1007/BF01199899 10.1002/9781119115151 10.1093/biomet/71.1.135 10.1214/lnms/1215460508 10.1007/978-1-4613-8762-6_10 10.1080/00031305.1984.10483181 10.1214/aos/1176347742 10.1007/BF00893213 10.1080/01621459.1987.10478394 10.1214/aos/1176325770 |
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| Keywords | prediction environment protection digital simulation spatial variations statistical analysis spatial distribution |
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| References | Sherman, M. and Carlstein, E. (1994) 'Nonparametric estimation of the moments of a general statistic computed from spatial data', Journal of the American Statistical Association, 89, 496-500. Cressie, N. A. C. (1993) Statistics for Spatial Data (rev. edn). Wiley, New York. Majure, J. J., Cook, D., Cressie, N., Kaiser, M. S., Lahiri, S. N. and Symanzik, J. (1996) 'Spatial CDF estimation and visualization with applications to forest health monitoring', Computing Science and Statistics, 27, 93-101. Pickard, D. K. (1987) 'Inference for discrete Markov fields: The simplest nontrivial case', Journal of the American Statistical Association, 82, 90-96. Stein, M. L. (1990b) 'Bounds on the effciency of linear predictors using an incorrect covariance function', Annals of Statistics, 18, 1116-1138. Mardia, K. V. and Marshall, R. J. (1984) 'Maximum likelihood estimation of models for residual covariance in spatial regression', Biometrika, 71, 135-146. Stein, M. L. (1990a) 'Uniform asymptotic optimality of linear predictions of a random field using an incorrect second-order structure', Annals of Statistics, 18, 839-861. Stein, M. L. and Handcock, M. S. (1989) 'Some asymptotic properties of kriging when the covariance function is misspecified', Mathematical Geology, 21, 171-190. Poltis, D. and Romano, J. P. (1994) 'Large sample confidence regions based on sub-samples under minimal assumptions', Annals of Statistics, 22, 2031-2050. Morris, M. D. and Edey, S. F. (1984) 'An interesting property of the sample mean under a first order autoregressive model', American Statistician, 38, 127-129. Hall, P. and Patil, P. (1994) 'Properties of nonparametric estimators of autocovariance function for stationary random fields', Probability Theory and Related Fields, 99, 399-424. Lahiri, S. N. (1996) 'On inconsistency of estimators under infill asymptotics for spatial data', Sankhya, Ser. A, 58, 403-417. 1984; 71 1990b; 18 1989; 21 1987; 82 1984; 38 1988; 10 1994; 89 1994; 99 1994; 22 1996 1995 1994 1990a; 18 1993 1991 1996; 58 1996; 27 Lahiri (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB7) 1996 Pickard (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB11) 1987; 82 Mardia (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB9) 1984; 71 Hall (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB4) 1994; 99 Lahiri (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB5) 1995 Stein (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB15) 1990a; 18 Stein (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB16) 1990b; 18 Lahiri (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB6) 1996; 58 Majure (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB8) 1996; 27 Stein (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB17) 1989; 21 Cressie (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB1) 1993 Possolo (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB13) 1991 Gidas (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB2) 1988; 10 Poltis (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB12) 1994; 22 Hall (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB3) 1994 Morris (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB10) 1984; 38 Sherman (10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB14) 1994; 89 |
| References_xml | – reference: Poltis, D. and Romano, J. P. (1994) 'Large sample confidence regions based on sub-samples under minimal assumptions', Annals of Statistics, 22, 2031-2050. – reference: Sherman, M. and Carlstein, E. (1994) 'Nonparametric estimation of the moments of a general statistic computed from spatial data', Journal of the American Statistical Association, 89, 496-500. – reference: Lahiri, S. N. (1996) 'On inconsistency of estimators under infill asymptotics for spatial data', Sankhya, Ser. A, 58, 403-417. – reference: Morris, M. D. and Edey, S. F. (1984) 'An interesting property of the sample mean under a first order autoregressive model', American Statistician, 38, 127-129. – reference: Stein, M. L. (1990a) 'Uniform asymptotic optimality of linear predictions of a random field using an incorrect second-order structure', Annals of Statistics, 18, 839-861. – reference: Stein, M. L. (1990b) 'Bounds on the effciency of linear predictors using an incorrect covariance function', Annals of Statistics, 18, 1116-1138. – reference: Cressie, N. A. C. (1993) Statistics for Spatial Data (rev. edn). Wiley, New York. – reference: Majure, J. J., Cook, D., Cressie, N., Kaiser, M. S., Lahiri, S. N. and Symanzik, J. (1996) 'Spatial CDF estimation and visualization with applications to forest health monitoring', Computing Science and Statistics, 27, 93-101. – reference: Stein, M. L. and Handcock, M. S. (1989) 'Some asymptotic properties of kriging when the covariance function is misspecified', Mathematical Geology, 21, 171-190. – reference: Hall, P. and Patil, P. (1994) 'Properties of nonparametric estimators of autocovariance function for stationary random fields', Probability Theory and Related Fields, 99, 399-424. – reference: Mardia, K. V. and Marshall, R. J. (1984) 'Maximum likelihood estimation of models for residual covariance in spatial regression', Biometrika, 71, 135-146. – reference: Pickard, D. K. (1987) 'Inference for discrete Markov fields: The simplest nontrivial case', Journal of the American Statistical Association, 82, 90-96. – volume: 99 start-page: 399 year: 1994 end-page: 424 article-title: Properties of nonparametric estimators of autocovariance function for stationary random fields publication-title: Probability Theory and Related Fields – volume: 71 start-page: 135 year: 1984 end-page: 146 article-title: Maximum likelihood estimation of models for residual covariance in spatial regression publication-title: Biometrika – volume: 18 start-page: 839 year: 1990a end-page: 861 article-title: Uniform asymptotic optimality of linear predictions of a random field using an incorrect second‐order structure publication-title: Annals of Statistics – volume: 18 start-page: 1116 year: 1990b end-page: 1138 article-title: Bounds on the effciency of linear predictors using an incorrect covariance function publication-title: Annals of Statistics – volume: 58 start-page: 403 year: 1996 end-page: 417 article-title: On inconsistency of estimators under infill asymptotics for spatial data publication-title: Sankhya, Ser. A – volume: 10 start-page: 129 year: 1988 end-page: 145 – year: 1996 – year: 1995 – volume: 38 start-page: 127 year: 1984 end-page: 129 article-title: An interesting property of the sample mean under a first order autoregressive model publication-title: American Statistician – volume: 22 start-page: 2031 year: 1994 end-page: 2050 article-title: Large sample confidence regions based on sub‐samples under minimal assumptions publication-title: Annals of Statistics – volume: 82 start-page: 90 year: 1987 end-page: 96 article-title: Inference for discrete Markov fields: The simplest nontrivial case publication-title: Journal of the American Statistical Association – volume: 89 start-page: 496 year: 1994 end-page: 500 article-title: Nonparametric estimation of the moments of a general statistic computed from spatial data publication-title: Journal of the American Statistical Association – year: 1993 – year: 1994 – volume: 27 start-page: 93 year: 1996 end-page: 101 article-title: Spatial CDF estimation and visualization with applications to forest health monitoring publication-title: Computing Science and Statistics – start-page: 286 year: 1991 end-page: 294 – volume: 21 start-page: 171 year: 1989 end-page: 190 article-title: Some asymptotic properties of kriging when the covariance function is misspecified publication-title: Mathematical Geology – volume: 58 start-page: 403 year: 1996 ident: 10.1002/(SICI)1099-095X(199709/10)8:5<485::AID-ENV271>3.0.CO;2-3-BIB6 publication-title: Sankhya, Ser. 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| SubjectTerms | Earth sciences Earth, ocean, space Engineering and environment geology. Geothermics Exact sciences and technology Pollution, environment geology prediction region spatial cumulative distribution function spatial dependence |
| Title | Inference for Spatial Processes Using Subsampling: a Simulation Study |
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