Martellosio, Federico (2006): Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression.
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Abstract
This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005, Journal of Statistical Planning and Inference 128, 489496). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.
Item Type:  MPRA Paper 

Original Title:  Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression 
Language:  English 
Keywords:  CliffOrd test; invariant tests; linear regression model; point optimal tests; power; similar tests; spatial autocorrelation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C31  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  10358 
Depositing User:  Federico Martellosio 
Date Deposited:  11. Sep 2008 04:47 
Last Modified:  11. Feb 2013 19:28 
References:  Anderson, T.W. (1948) On the theory of testing serial correlation. Skandinavisk Aktuarietidskrift 31, 88116. Anselin, L. (1988) Spatial Econometrics: Methods and Models. Kluwer Academic Publishers. Baltagi, B.H. (2006) Random effects and spatial autocorrelation with equal weights. Econometric Theory 22, 973984. Bartels, R. (1992) On the power function of the DurbinWatson test. Journal of Econometrics 51, 101112. Bell, K.P. & N.E. Bockstael (2000) Applying the generalizedmoments estimation approach to spatial problems involving microlevel data. The Review of Economics and Statistics 82, 7282. Berenblut, I.I. & G.I.Webb (1973) A new test for autocorrelated errors in the linear regression model. Journal of the Royal Statistical Society B 35, 3350. Besag, J.E. (1974) Spatial interaction and the statistical analysis of lattice data. Journal of the Royal Statistical Society B 36, 192236. Besag, J.E. & C. Kooperberg (1995) On conditional and intrinsic autoregression. Biometrika 82, 733746. Bhattacharyya, B.B., G.D. Richardson & L.A. Franklin (1997) Asymptotic inference for near unit roots in spatial autoregression. The Annals of Statistics 25, 17091724. Biggs, N.L. (1993) Algebraic Graph Theory, second edition. Cambridge University Press. Case, A. (1991) Spatial patterns in household demand. Econometrica 59, 953—966. Cliff, A.D. & J.K. Ord (1981) Spatial Processes: Models and Applications. Pion. Cox, D.R. & D.V. Hinkley (1974) Theoretical Statistics. Chapman & Hall. Cordy, C.B. & D.A. Griffith (1993) Efficiency of least squares estimators in the presence of spatial autocorrelation. Communications in Statistics: Simulation and Computation 22, 11611179. Cressie, N. (1993) Statistics for Spatial Data, revised edition. Wiley. Cvetkovic, D.M., M. Doob & H. Sachs (1980) Spectra of Graphs. Academic Press. Dielman, D.E. & R.C. Pfaffenberger (1989) Efficiency of ordinary least squares for linear models with autocorrelation. Journal of the American Statistical Association 84, 248. Durbin, J. (1970) An alternative to the bounds test for testing for serial correlation in leastsquares regression. Econometrica 38, 42229. Fingleton, B. (1999) Spurious spatial regression: Some Monte Carlo results with a spatial unit root and spatial cointegration. Journal of Regional Science 39, 119. Florax, R.J.G.M. & T. de Graaff (2004) The performance of diagnostic tests for spatial dependence in linear regression models: a metaanalysis of simulation studies. In L. Anselin, R.J.G.M. Florax & S.J. Rey (eds.), Advances in Spatial Econometrics: Methodology, Tools and Applications, pp. 2965. Springer. Gall, J., G. Pap & M. van Zuijlen (2004) Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet. Journal of Applied Mathematics 4, 293309. Gantmacher, F.R. (1974) The Theory of Matrices, vol. II. Chelsea. Goldstein, R. (2000) The Term Structure of Interest Rates as a Random Field. Review of Financial Studies 13, 365384. Golub, G.H. & C.F. Van Loan (1996) Matrix Computations, vol. II, third edition. The Johns Hopkins University Press. Hardy, G., J.E. Littlewood & G. Pólya (1952) Inequalities, second edition. Cambridge University Press. Hillier, G.H. (1987) Classes of similar regions and their power properties for some econometric testing problems. Econometric Theory 3, 1— 44. Horn, R. & C.R. Johnson (1985) Matrix Analysis. Cambridge University Press. Huse, C., (2006) Term structure modelling with spatial dependence and observable state variables, paper presented at the International Workshop on Spatial Econometrics and Statistics, Rome. Imhof, J.P. (1961) Computing the distribution of quadratic forms in normal variables. Biometrika 48, 41926. James, A.T. (1954) Normal multivariate analysis and the orthogonal group. Annals of Mathematical Statistics 25, 4075. Kadiyala, K.R. (1970) Testing for the independence of regression disturbances. Econometrica 38, 97117. Kalbfleisch, J.D. & D.A. Sprott (1970) Application of likelihood methods to models involving large numbers of parameters. Journal of the Royal Statistical Society B 32, 175—208. Kariya, T. (1980) Locally robust tests for serial correlation in least squares regression. Annals of Statistics 8, 10651070. Kariya, T. (1988) The Class of Models for Which the DurbinWatson Test is Locally Optimal. International Economic Review 29, 167175. Kelejian, H.H. & I.R. Prucha (2001) On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219—257. Kelejian, H.H. & I.R. Prucha (2007) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, forthcoming. Kennedy, D. (1994) The term structure of interest rates as a Gaussian random field. Mathematical. Finance 4, 247258. King, M.L. (1980) Robust tests for spherical symmetry and their application to least squares regression. Annals of Statistics 8, 12651271. King, M.L. (1981) A small sample property of the CliffOrd test for spatial autocorrelation. Journal of the Royal Statistical Society B 43, 2634. King, M.L. (1988) Towards a theory of point optimal testing. Econometric Reviews 6, 169—255. King, M.L. & G.H. Hillier (1985) Locally best invariant tests of the error covariance matrix of the linear regression model. Journal of the Royal Statistical Society B 47, 98102. Kleiber, C. & W. Krämer (2005) Finitesample power of the DurbinWatson test against fractionally integrated disturbances. Econometrics Journal 8, 406417. Krämer, W. (1985) The power of the DurbinWatson test for regressions without an intercept. Journal of Econometrics 28, 363370. Krämer, W. (2005) Finite sample power of Cliff—Ordtype tests for spatial disturbance correlation in linear regression. Journal of Statistical Planning and Inference 128, 489496. Krämer, W. & and C. Donninger (1987) Spatial autocorrelation among errors and relative efficiency of OLS in the linear regression model. Journal of the A merican Statistical Association 82, 577579. Lee, L.F. (2002) Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models. Econometric Theory 18, 252277. Lehmann, E.L. & J. Romano (2005) Testing Statistical Hypotheses, third edition. Springer. Militino, A.F., Ugarte, M.D. & L. GarcíaReinaldos (2004) Alternative models for describing spatial dependence among dwelling selling prices. Journal of Real Estate Finance and Economics 29, 193209. Moran, P.A.P. (1950) Notes on continuos stochastic phenomena. Biometrika 37, 1723. Ord, J.K. (1975) Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70, 1206. Pace, R.K. & J.P. LeSage (2002) Semiparametric maximum likelihood estimates of spatial dependence. Geographical Analysis 34, 7690. Paulauskas, V. (2007) On unit roots for spatial autoregressive models. Journal of Multivariate Analysis 98, 209226. Pinske, J. & M.E. Slade (1998). Contracting in space: an application of spatial statistics to discrete choice models. Journal of Econometrics 85, 125154. Rahman, S. & M.L. King (1997) Marginallikelihood scorebased tests of regression disturbances in the presence of nuisance parameters. Journal of Econometrics 82, 81106. Small, J.P. (1993) The limiting power of point optimal autocorrelation tests. Communications in Statistics: Theory and Methods 22, 24632470. Tillman, J.A. (1975) The power of the DurbinWatson test. Econometrica 43, 95974. Tunnicliffe Wilson, G. (1989) On the use of marginal likelihood in time series model estimation. Journal of the Royal Statistical Society B 51, 1527. Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434449. Zeisel, H. (1989) On the power of the DurbinWatson test under high autocorrelation. Communications in Statistics: Theory and Methods 18, 39073916. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/10358 
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Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression. (deposited 19. Feb 2008 00:38)
 Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression. (deposited 11. Sep 2008 04:47) [Currently Displayed]