Halkos, George and Kevork, Ilias (2006): Estimating population means in covariance stationary process.
Download (244kB) | Preview
In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags.
|Item Type:||MPRA Paper|
|Original Title:||Estimating population means in covariance stationary process|
|Keywords:||Jackknife estimation; ARMA; Longitudinal data; Actual confidence level|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General
|Depositing User:||Nickolaos Tzeremes|
|Date Deposited:||26 Jun 2011 10:18|
|Last Modified:||25 Aug 2016 23:22|
Adam, N.R., 1983. Achieving a confidence interval for parameters estimated by simulation. Management Science, Vol.29, pp. 856-866.
Conway, R.W., 1963. Some tactical problems in digital simulation. Management Science, Vol. 10, pp. 47-61.
Crane, M.A., and D.L. Iglehart, 1974a. Simulating stable stochastic systems, I: General multi-server queues. Journal of the Association for Computing Machinery, Vol. 21, pp.103-113.
Crane, M.A., and D.L. Iglehart, 1974b. Simulating stable stochastic systems, II: Markov chains. Journal of the Association for Computing Machinery, Vol. 21, pp.114-123.
Crane, M.A., and D.L. Iglehart, 1974c Simulating stable stochastic systems, III: Regenerative processes and discrete event simulations. Operations Research, Vol. 23, pp.33-45.
Crane, M.A., and D.L. Iglehart, 1975. Simulating stable stochastic systems, IV: Approximation techniques. Management Science, Vol. 21, pp.1215-1224.
Ducket, S.D., and A.A.B. Pritsker, 1978. Examination of simulation output using spectral methods. Mathematical Computing Simulation, Vol. 20, pp. 53-60.
Efron, B., 1979. Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7, 1-26
Efron, B. and Tibshirani, R., 1993. An Introduction to the Bootstrap. Chapman & Hall, New York.
Fishman, G.S., 1971. Estimating the sample size in computing simulation experiments. Management Science, Vol. 18, pp. 21-38.
Fishman, G.S., 1973a. Statistical analysis for queuing simulations. Management Science, Vol. 20, pp. 363-369.
Fishman, G.S., 1973b. Concepts and methods in discrete event digital simulation. John Wiley and Sons, New York.
Fishman, G.S., 1977. Achieving specific accuracy in simulation output analysis. Communication of the Association for computing Machinery, Vol. 20, pp. 310-315.
Fishman, G., 1978. Principles of Discrete Event Simulation. Wiley, New York.
Fishman, G., 1999. Monte Carlo: Concepts, Algorithms, and Applications. Springer, New York.
Gafarian, A.V., Ancker, C.J., JR, and T. Morisaku, 1978. Evaluation of commonly used rules for detecting steady state in computer simulation. Naval Research Logistics Quarterly, Vol. 25, pp. 511-529.
Gordon, G., 1969. System simulation. Prentice-Hall, Englewood Cliffs N.j.
Hall, P., Horowitz, J. and Jing, B.-Y., 1995. On blocking rules for the bootstrap with dependent data. Biometrika 82, 561-574.
Heidelberger, P., and P.D. Welch, 1981a. A spectral method for confidence interval generation and run length control in simulations. Communications of the Association for Computing Machinery, Vol. 24, pp. 233-245.
Heidelberger, P., and P.D. Welch, 1981b. Adaptive spectral methods for simulation output analysis. IBM Journal of Research and Development, Vol. 25, pp. 860-876.
Heidelberger, P., and P.D. Welch, 1983. Simulation run length control in the presence of an initial transient. Operations Research, Vol. 31, pp. 1109-1144.
Kevork, I.S, 1990. Confidence Interval Methods for Discrete Event Computer Simulation: Theoretical Properties and Practical Recommendations. Unpublished Ph.D. Thesis, University of London, London
Kim, Y., Haddock, J. and Willemain, T., 1993a. The binary bootstrap: Inference with autocorrelated binary data. Communications in Statistics: Simulation and Computation 22, 205-216.
Kim, Y., Willemain, T., Haddock, J. and Runger, G., 1993b. The threshold bootstrap: A new approach to simulation output analysis. In: Evans, G.W., Mollaghasemi, M., Russell, E.C., Biles, W.E. (Eds.), Proceedings: 1993 Winter Simulation Conference, pp. 498-502.
Kelton, D.W. and A.M. Law, 1983. A new approach for dealing with the startup problem in discrete event simulation. Naval Research Logistics Quarterly, Vol. 30, pp. 6410658.
Künsch, H., 1989. The jackknife and the bootstrap for general stationary observations. The Annals of Statistics 17, 1217-1241.
Lavenberg, S., S., and C. H. Sauer, 1977. Sequential stopping rules for the regenerative method of simulation. IBM Journal of Research and Development, Vol. 21, pp. 545-558.
Law, A.M., 1983. Statistical analysis of simulation output data. Operations Research, Vol. 31, pp. 983-1029.
Law, A.M., and J.S. Carson, 1978. A sequential procedure for determining the length of a steady state simulation. Operation Research, Vol. 27, pp. 1011-1025.
Law, A.M., and W.D. Kelton, 1982a. Confidence interval for steady state simulations: II. A survey of sequential procedures. Management Science, Vol. 28, pp. 560-562.
Law, A.M., and W.D. Kelton, 1982b. Simulation modelling and analysis. McGraw Hill, New York.
Law, A.M., and W.D. Kelton, 1984. Confidence intervals for steady state simulations: I. A survey of fixed sample size procedures. Operation Research, Vol. 32, pp. 1221-1239.
Law, A. and Kelton, W., 1991. Simulation Modeling and Analysis, second ed. McGraw-Hill, New York.
Liu, R. and Singh, K., 1992. Moving blocks jackknife and bootstrap capture weak dependence. In: Le Page, R., Billard, L., (Eds.), Exploring the Limits of Bootstrap. Wiley, New York, pp.225-248.
Mechanic, H., and W. McKay, 1966. Confidence intervals for averages of dependent data in simulation II. Technical report 17-202 IBM, Advanced Systems Development Division.
Park, D. and Willemain, T., 1999. The threshold bootstrap and threshold jackknife. Computational Statistics and Data Analysis 31, 187-202.
Park, D.S., Kim, Y.B., Shin, K.I. and Willemain, T.R., 2001. Simulation output Analysis using the threshold bootstrap, European Journal of Operational Research 134, 17-28.
Quenouille, M., 1949. Approximation tests of correlation in time series. Journal of Royal Statistical Society Series B 11, 68-84.
Schriber, T.J., 1974. Simulation using GPSS. John Wiley and Sons, New York.
Sargent, R.G., Kang, K. and Goldsman, D., 1992. An investigation of finite-sample behavior of confidence interval estimators. Operation Research 40, 898-913.
Schruben, L., 1983. Confidence interval estimation using standardized time series. Operations Research 31, 1090-1108.
Song, W.T., 1996. On the estimation of optimal batch sizes in the analysis of simulation output. European Journal of Operational Research 88, 304-319.
Song, W.T. and Schmeiser, B.W., 1995. Optimal mean-squared-error batch sizes. Management Science 41, 111-123.
Tukey, J., 1958. Bias and confidence interval in not quite large samples (Abstract). The Annals of Mathematical Statistics 29, 614.
Voss, P., Haddock, J. and Willemain, T., 1996. Estimating steady state mean from short transient simulations. In: Charnes, J.M., Morrice, D.M., Brunner, D.T.
Welch, P.D., 1987. On the relationship between batch means, overlapping batch means and spectral estimation. Proceedings of the 1987 Winter Simulation Conference, pp. 320-323.