Abstract
Properties of a “blockwise”empirical likelihood for spatial regression with non-stochastic regressors are investigated for spatial data on a lattice. The method enables nonparametric confidence regions for spatial trend parameters to be calibrated, even though non-random regressors introduce non-stationary forms of spatial dependence into the “blockwise” construction. Additionally, the regression results are valid in a general framework allowing for a variety of behavior in regressor variables as well as the underlying spatial error process. The same regression method also applies when the regressors are stochastic.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bradley RC (1989). A caution on mixing conditions for random fields. Stat Probab Lett 8: 489–491
Bravo F (2002). Testing linear restrictions in linear models with empirical likelihood. Econom J Online 5: 104–130
Bravo F (2004). Empirical likelihood based inference with applications to some econometric models. Econom Theory 20: 231–264
Bravo F (2005). Blockwise empirical entropy tests for time series regressions. J Time Ser Anal 26: 185–210
Carlstein E (1986). The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Ann Stat 14: 1171–1179
Chan G and Wood ATA (1997). An algorithm for simulating stationary Gaussian random fields. Appl Stat 46: 171–181
Chen SX (1993). On the coverage accuracy of empirical likelihood regions for linear regression models. Ann Inst Stat Math 45: 621–637
Chuang C and Chan NH (2002). Empirical likelihood for autoregressive models, with applications to unstable time series. Stat Sin 12: 387–407
Cressie N (1993). Statistics for Spatial Data, 2nd edn. Wiley, New York
Doukhan P (1994) Mixing: properties and examples. Lecture notes in Statistics. vol 85, Springer, New York
Hall P and Horowitz JL (1996). Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica 64: 891–916
Hall P and La Scala B (1990). Methodology and algorithms of empirical likelihood. Int Stat Rev 58: 109–127
Imbens GW, Spady RH and Johnson P (1998). Information theoretic approaches to inference in moment condition models. Econometrika 66: 333–357
Kitamura Y (1997). Empirical likelihood methods with weakly dependent processes. Ann Stat 25: 2084–2102
Künsch HR (1989). The jackknife and the bootstrap for general stationary observations. Ann Stat 17: 1217–1241
Lahiri SN (2003a). Resampling methods for dependent data. Springer, New York
Lahiri SN (2003b). Central limit theorems for weighted sums of a spatial process under a class of stochastic and fixed designs. Sankhya Ser A 65: 356–388
Lee YD and Lahiri SN (2002). Least squares variogram fitting by spatial subsampling. J R Stat Soc Ser B 64: 837–854
Lin L and Zhang R (2001). Blockwise empirical Euclidean likelihood for weakly dependent processes. Stat Probab Lett 53: 143–152
Monti AC (1997). Empirical likelihood confidence regions in time series models. Biometrika 84: 395–405
Nordman DJ, Caragea PC (2007) Joint and interval estimation of variogram models using spatial empirical likelihood. J Am Stat Assoc (in press)
Nordman DJ and Lahiri SN (2004). On optimal spatial subsample size for variance estimation. Ann Stat 32: 1981–2027
Nordman DJ and Lahiri SN (2006). A frequency domain empirical likelihood for short- and long-range dependence. Ann Stat 34: 3019–3050
Nordman DJ, Sibbertsen P, Lahiri SN (2006) Empirical likelihood for the mean under long-range dependence. J Time Ser Anal (in press)
Owen AB (1990). Empirical likelihood confidence regions. Ann Stat 18: 90–120
Owen AB (1991). Empirical likelihood for linear models. Ann Stat 19: 1725–1747
Owen AB (2001). Empirical likelihood. Chapman & Hall, London
Politis DN and Romano JP (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann Stat 22: 2031–2050
Politis DN, Romano JP and Wolf M (1999). Subsampling. Springer, New York
Qin J and Lawless J (1994). Empirical likelihood and general estimating equations. Ann Stat 22: 300–325
Zhang J (2006). Empirical likelihood for NA series. Stat Probab Lett 76: 153–160
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nordman, D.J. An empirical likelihood method for spatial regression. Metrika 68, 351–363 (2008). https://doi.org/10.1007/s00184-007-0167-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-007-0167-y