Skip to main content
SpringerLink
Log in

An empirical likelihood method for spatial regression

  • Published:
Metrika Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bradley RC (1989). A caution on mixing conditions for random fields. Stat Probab Lett 8: 489–491

    Article  MATH  MathSciNet  Google Scholar 

  • Bravo F (2002). Testing linear restrictions in linear models with empirical likelihood. Econom J Online 5: 104–130

    MATH  MathSciNet  Google Scholar 

  • Bravo F (2004). Empirical likelihood based inference with applications to some econometric models. Econom Theory 20: 231–264

    Article  MATH  MathSciNet  Google Scholar 

  • Bravo F (2005). Blockwise empirical entropy tests for time series regressions. J Time Ser Anal 26: 185–210

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Chan G and Wood ATA (1997). An algorithm for simulating stationary Gaussian random fields. Appl Stat 46: 171–181

    MATH  Google Scholar 

  • Chen SX (1993). On the coverage accuracy of empirical likelihood regions for linear regression models. Ann Inst Stat Math 45: 621–637

    Article  MATH  Google Scholar 

  • Chuang C and Chan NH (2002). Empirical likelihood for autoregressive models, with applications to unstable time series. Stat Sin 12: 387–407

    MATH  MathSciNet  Google Scholar 

  • Cressie N (1993). Statistics for Spatial Data, 2nd edn. Wiley, New York

    Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Hall P and La Scala B (1990). Methodology and algorithms of empirical likelihood. Int Stat Rev 58: 109–127

    Article  MATH  Google Scholar 

  • Imbens GW, Spady RH and Johnson P (1998). Information theoretic approaches to inference in moment condition models. Econometrika 66: 333–357

    Article  MATH  MathSciNet  Google Scholar 

  • Kitamura Y (1997). Empirical likelihood methods with weakly dependent processes. Ann Stat 25: 2084–2102

    Article  MATH  MathSciNet  Google Scholar 

  • Künsch HR (1989). The jackknife and the bootstrap for general stationary observations. Ann Stat 17: 1217–1241

    Article  MATH  Google Scholar 

  • Lahiri SN (2003a). Resampling methods for dependent data. Springer, New York

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • Lee YD and Lahiri SN (2002). Least squares variogram fitting by spatial subsampling. J R Stat Soc Ser B 64: 837–854

    Article  MATH  MathSciNet  Google Scholar 

  • Lin L and Zhang R (2001). Blockwise empirical Euclidean likelihood for weakly dependent processes. Stat Probab Lett 53: 143–152

    Article  MATH  MathSciNet  Google Scholar 

  • Monti AC (1997). Empirical likelihood confidence regions in time series models. Biometrika 84: 395–405

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Nordman DJ and Lahiri SN (2006). A frequency domain empirical likelihood for short- and long-range dependence. Ann Stat 34: 3019–3050

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Owen AB (1991). Empirical likelihood for linear models. Ann Stat 19: 1725–1747

    Article  MATH  MathSciNet  Google Scholar 

  • Owen AB (2001). Empirical likelihood. Chapman & Hall, London

    MATH  Google Scholar 

  • Politis DN and Romano JP (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann Stat 22: 2031–2050

    Article  MATH  MathSciNet  Google Scholar 

  • Politis DN, Romano JP and Wolf M (1999). Subsampling. Springer, New York

    MATH  Google Scholar 

  • Qin J and Lawless J (1994). Empirical likelihood and general estimating equations. Ann Stat 22: 300–325

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang J (2006). Empirical likelihood for NA series. Stat Probab Lett 76: 153–160

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Iowa State University, Ames, IA, 50011, USA

    Daniel J. Nordman

Authors
  1. Daniel J. Nordman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel J. Nordman.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0167-y

Keywords

Search

Navigation