Abstract
Quite often sampling distributions for spatial statistics are unknown, are exceedingly complex in form, or do not have closed form solutions for their probability density functions or parameter values. Further, although asymptotic variances can be obtained (see Chapter 4), spatial statistics may behave quite differently when small, finite lattices are studied (possibly due to boundary effects; see Chapter 7), or when irregular lattices are studied. In these various cases, where analytical solutions are elusive for test statistic problems, the identification of estimation properties, or the like, researchers have resorted to simulation experiments in order to gain insights into spatial statistical analysis.
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References
Anderson, T., 1958, An Introduction to Multivariate Statistical Analysis. New York: Wiley.
Besag, J., 1974, Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society, Vol. 36B: 192–236.
Donnelly, J., and R. Shannon, 1981, Minimum mean-squared-error estimators for simulation experiments, Communications of the ACM, Vol. 24: 253–259.
Fishman, G., 1971, Estimating sample size in computing simulation experiments, Management Science, Vol. 18: 21–38.
Fishman, G., 1972, Variance reduction in simulation studies, Journal of Statistical Computation and Simulation, Vol. 1: 173–182.
Fishman, G., 1973, Variance reduction for normal variates in Monte Carlo studies, Journal of Statistical Computation and Simulation, Vol. 2: 365–374.
Gafarian, A., C. Ancker, and T. Morisaku, 1978, Evaluation of commonly used rules for detecting ‘steady state’ in computer simulation, Naval Research Logistics Quarterly, Vol. 25: 511–529.
Goldsmith, H., 1977, The exact distribution of the serial correlation coefficients and an evaluation of some approximate distributions, Journal of Statistical Computation and Simulation, Vol. 5: 115–134.
Goodchild, M., 1980, Algorithm 9: simulation of autocorrelation for aggregate data, Environment and Planning A, Vol. 12: 1073–1081.
Griffith, D., 1981, Interdependence in space and time: numerical and interpretative considerations, in Dynamic Spatial Models, edited by D. Griffith and R. MacKinnon. Alphen aan den Rijn: Sijhoff and Noordhoff, pp. 258–287.
Griffith, D., 1983, The boundary value problem in spatial statistical analysis, Journal of Regional Science, Vol. 23: 377–387.
Griffith, D., and C. Amrhein, 1983, An evaluation of correction techniques for boundary effects in spatial statistical analysis: traditional methods, Geographical Analysis, Vol. 15: 352–360.
Haining, R., 1978, A spatial model for high plains agriculture, Annals, Association of American Geographers, Vol. 68: 493–504.
Haining, R., D. Griffith, and R. Bennett, 1983, Simulating two-dimensional autocorrelated surfaces, Geographical Analysis, Vol. 15: 247–255.
Heidelberger, P., and P. Welch, 1981, A spectral method for confidence interval generation and run length control in simulations, Communications of the ACM, Vol. 24: 233–245.
Hope, A., 1968, A simplified Monte Carlo significance test procedure, Journal of the Royal Statistical Society, Series B, Vol. 30: 582–598.
Kronmal, R., and A. Peterson, 1981, A variant of the acceptance-rejection method for computer generation of random variables, Journal of the American Statistical Association, Vol. 76: 446–451.
Lakhan, V., 1981, Generating autocorrelated pseudo-random numbers with specific distributions, Journal of Statistical Computation and Simulation, Vol. 12: 303–309.
Lavenberg, S., and C. Sauer, 1977, Sequential stopping rules for the regenerative method of simulation, IBM Journal of Research and Development, Vol. 21: 545–558.
Law, A., 1980, Statistical analysis of the output data from terminating simulation, Naval Research Logistics Quarterly, Vol. 27: 131–143.
Law, A., and J. Carson, 1979, A sequential procedure for determining the length of a steady-state simulation, Operations Research, Vol. 27: 1011–1025.
Law, A., and W. Kelton, 1982, Simulation Modeling and Analysis. New York: McGraw-Hill.
Lehman, R., 1977, Computer Simulation and Modeling: An Introduction. New York: Wiley.
Malkovich, J., and A. Affifi, 1973, On tests for multivariate normality, Journal of the American Statistical Association, Vol. 68: 176–179.
Marriott, F., 1979, Barnard’s Monte Carlo tests: how many simulations? Applied Statistics, Vol. 28: 75–77.
Quandt, R., 1983, Computational problems and methods, in Handbook of Econometrics, Vol. 1, edited by Z. Griliches and M. Intriligator. Amsterdam: North-Holland, pp. 699–764.
Roach, W., and R. Wright, 1977, Optimal antithetic sampling plans. Journal of Statistical Computation and Simulation, Vol. 5: 99–114.
Sargent, R., 1976, Statistical analysis of simulation output data, Simuletter (proceedings of the symposium on the simulation of computer systems IV), Vol. 7(4): 39–50.
Schafer, R., 1974, On assessing the precision of simulations, Journal of Statistical Computation and Simulation, Vol. 3: 67–69.
Thomas, M., 1974, A simple sequential procedure for sampling termination in simulation investigations. Journal of Statistical Computation and Simulation, Vol. 3: 161–164.
Vasilopoulos, A., 1983, Generating correlated random variables for quality control applications, in Simulation Symposium, 16th annual record of proceedings, edited by L. Holdbrook. Silver Spring, Maryland: IEEE Computer Society Press, pp. 105–119.
Ziegler, B., 1976, Theory of Modelling and Simulation. New York: Wiley.
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© 1988 Kluwer Academic Publishers, Dordrecht
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Griffith, D.A. (1988). Simulation Experimentation in Spatial Analysis. In: Advanced Spatial Statistics. Advanced Studies in Theoretical and Applied Econometrics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2758-2_9
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DOI: https://doi.org/10.1007/978-94-009-2758-2_9
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