The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation of Spatial Dependence by Quasi-likelihood Method

의사우도법을 이용한 공간 종속 모형의 추정

  • 이윤동 (건국대학교 상경대학 응용통계학과) ;
  • 최혜미 (건국대학교 상경대학 응용통계학과)
  • Published : 2004.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we suggest quasi-likelihood estimation (QLE) method and its robust version in estimating spatial dependence modelled through variogram used for spatial data modelling. We compare the statistical characteristics of the estimators with other popular least squares estimators of parameters for variogram model by simulation study. The QLE method for estimating spatial dependence has the advantages that it does not need the concept of lags commonly required for least squares estimation methods as well as its statistical superiority. The QLE method also shows the statistical superiority to the other methods for the tested Gaussian and non-Gaussian spatial processes.

본 연구에서는 베리오그램 추정을 통한 공간 종속성 추정방법에 있어서 의사우도 사용 방법을 설명하고, 모의실험을 통하여 전통적으로 사용되는 다른 방법들과 그 특성을 비교하고자 한다. 의사우도를 이용한 공간 종속 추정방법들은 그 통계적 성질이 우수할 뿐만 아니라, 전통적인 방법들에서 요구되어지는 관측치가 갖는 래그(lag)들을 미리 지정된 래그로 그룹화하는 과정이 필요 없어서 활용상의 우수성도 함께 가지고 있다. 또한, 이 방법에 대한 로버스트 방법을 개발하고 그 특성을 알아보고자 한다.

Keywords

References

  1. Adimari, G and Ventura, L. (2001). Robust inference for generalized linear models with application to logistic regression, Statistics and Probabitity Letters, 515, 413-419
  2. Albert, P. and McShane, M. (1995). A generalized estimating equations approach for spatially correlated binary data: applications to the analysis of neuroimaging data, Biometrics, 51, 627-638 https://doi.org/10.2307/2532950
  3. Cantoni, E. and Ronchetti, E. (2001). Robust inference for generalized linear models, Journal of the American Statistical Associciation, 96, 1022-1030 https://doi.org/10.1198/016214501753209004
  4. Cha, K., Kim, S. and Lee, S. (2003). Robust estimation using quasi-score estimating functions for nonlinear time series models, Journal of the Korean Statistical Society, 32, 385-400
  5. Cressie, N. (1985). Fitting variogram models by weighted least squares, Journal of the International Association for Mathematical Geology, 17, 563-586 https://doi.org/10.1007/BF01032109
  6. Cressie, N. (1993). Statistics for Spalial Data, revised edition. Wiley
  7. Cressie, N and Hawkins, D. M. (1980). Robust estimation of the variogram, I, Journal of the International Association for Mathematical Geology, 12, 115-125 https://doi.org/10.1007/BF01035243
  8. Davis, J. C. (1973). Statistics and Data Analysis in Geology, Wiley
  9. Ecker, M. and Gelfand, A. (1997). Bayesian variogram modeling for an isopropic spatial process, Journal of Agricultural, Biological and Environmental Statistics, 2, 347-369 https://doi.org/10.2307/1400508
  10. Lahiri, S., Lee, Y. D. and Cressie, N. (2002). On asymptotic disthbution and asymptotic efficiency of least squares estimators of spatial variogram parameters, Journal of Statistical Planning and Inference, 103, 65-85 https://doi.org/10.1016/S0378-3758(01)00198-7
  11. Mallows, C. L. (1975). On some topics in robustness, Technical Memorandum, Bell Telephone Laboratorie, Murray Hill
  12. McCullagh, P. (1983). Quasi-likelihood functions, The Annals of Statistics, 11, 59-67 https://doi.org/10.1214/aos/1176346056
  13. McCullagh, P. and Nelder, J. (1989). Generalized Linear Model, 2nd edition, Chapman and Hall
  14. Peixoto, J. L. (1990). A property of well-formulated polynomial regression models, The American Statistician, 44, 26-30 https://doi.org/10.2307/2684952
  15. Ribeiro, P. and Diggle, P. (2003). GeoR package manual at R contributed package site, http://www.cran.r-project.org
  16. So, B. S. and Shin, D. W. (2001). An invariant sign test for random walks based on recursive median adjustment, Journal of Econometrics, 102, 197-229 https://doi.org/10.1016/S0304-4076(01)00053-7
  17. Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S., Fourth edition Springer
  18. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and Gauss Newton method, Biometrika, 61, 439-447
  19. Wand, M. P. (2002). Vector differential calculus in statistics, The American Statisticians, 56, 55-62 https://doi.org/10.1198/000313002753631376
  20. Young, D. M. (1971). Iterative Solution of Large Linear System, Academic Press