A Central Limit Theorem for Spatial Samples

Abstract

Geographical AnalysisVolume 12, Issue 4 p. 299-324 Free Access A Central Limit Theorem for Spatial Samples Tony E. Smith, Tony E. Smith This research was supported by the National Science Foundation under Grant SES 79–19457. The author is indebted to Jörgen W. Weibull and to the members of the Regional Theory Workshop for helpful comments on an earlier draft of this paper. Tony E. Smith is professor of regional science, University of Pennsylvania.Search for more papers by this author Tony E. Smith, Tony E. Smith This research was supported by the National Science Foundation under Grant SES 79–19457. The author is indebted to Jörgen W. Weibull and to the members of the Regional Theory Workshop for helpful comments on an earlier draft of this paper. Tony E. Smith is professor of regional science, University of Pennsylvania.Search for more papers by this author First published: October 1980 https://doi.org/10.1111/j.1538-4632.1980.tb00039.xCitations: 10 This research was supported by the National Science Foundation under Grant SES 79–19457. The author is indebted to Jörgen W. Weibull and to the members of the Regional Theory Workshop for helpful comments on an earlier draft of this paper. Tony E. Smith is professor of regional science, University of Pennsylvania. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Bhattacharaya, R. N., and R. R. Rao (1976). Normal Approximation and Asymptotic Expansions, New York: Wiley. Billingsley, P. (1979). Probability and Measure, New York: Wiley. Bulinskii, A. V. and I. G. Zhurbenko (1976). “A Central Limit Theorem for Additive Random Functions,” Theory of Probability and its Applications, 21, 687– 97. Cliff, A. D., and J. K. Ord (1973). Spatial Autocorrelation, London: Pion. Cochran, W. G. (1953). Sampling Techniques, New York: Wiley. Diananda, P. H. (1955). “The Central Limit Problem for m-Dependent Variables,” Proceedings of the Cambridge Philosophical Society, 51, 92– 95. Dugundji, J. (1966). Topology, Boston: Allyn and Bacon. Dvoretsky, A. (1972). “Asymptotic Normality of Sums of Dependent Random Variables,” Proceedings of the Sixth Berkeley Symposium, 2, 513– 34. Dvoretsky, A. (1977). “Asymptotic Normality of Sums of Dependent Random Vectors,” in Multivariate Analysis-IV, edited by P. R. Krishnaiah, 23– 34. Haining, R. P. (1978). “The Moving Average Model for Spatial Interaction,” Transactions of the Institute of British Geographers, 3, 202– 5. Haining, R. P. (1979). “Statistical Tests and Process Generators for Random Fields,” Geographical Analysis, 11, 45– 64. Halmos, P. (1950). Measure Theory, New York: Van Nostrand Reinhold. Hardy, G. H., J. E. Littlewood, and G. Pólya (1934). Inequalities, Cambridge, England: Cambridge University Press. Hoeffding, W., and H. Robbins (1948). “The Central Limit Theorem for Dependent Variables,” Duke Mathematical Journal, 15, 773– 80. Petrov, V. V. (1957). Sums of Independent Random Variables, Berlin: Springer-Verlag. Rao, C. R. (1973). Linear Statistical Inference and its Applications, New York: Wiley. Rozanov, Yu. A. (1960). “A Central Limit Theorem for Additive Random Functions,” Theory of Probability and its Applications, 5, 221– 23. Rosenblatt, M. (1956). “A Central Limit Theorem and Mixing Condition,” Proceedings of the National Academy of Sciences, 42, 43– 47. Rosenblatt, M. (1971). Markov Processes: Structure and Asymptotic Behavior, Berlin: Springer-Verlag. Sen, A. K. (1976). “Large Sample-Size Distribution of Statistics used for Testing Spatial Autocorrelation,” Geographical Analysis, 9, 175– 84. Sen, A. K., and S. Sööt (1977). “Rank Tests for Spatial Correlation,” Environment and Planning A, 9, 897– 903. Simmons, G. F. (1963). Topology and Modern Analysis, New York: McGraw-Hill. Tobler, W. (1975). “Linear Operators Applied to Areal Data,” in Display and Analysis of Spatial Data, edited by J. C. Davis and M. J. McCullagh, pp. 14– 37. New York: Wiley. Tobler, W. (1979). “Lattice Tuning,” Geographical Analysis, 11, 36– 44. Volkonskii, V. A. and Yu. A. Rozanov (1959). “Some Limit Theorems for Random Functions,” Theory of Probability and its Applications, 4, 178– 97. Whittle, P. (1954). “On Stationary Processes in the Plane,” Biometrika, 41, 434– 39. Wilks, S. S. (1962). Mathematical Statistics, New York: Wiley. Citing Literature Volume12, Issue4October 1980Pages 299-324 ReferencesRelatedInformation