On Nonparametric Curve Estimation with Spatial Data

• Activity Number: 345
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Sucharita Ghosh*+
• Companies: Swiss Federal Research Institute WSL
• Keywords: spatial process ; kernel smoothing ; latent processes ; local stationarity

Abstract

We consider kernel smoothing for spatial data that are transformations of unobserved Gaussian processes with location dependent marginal distributions of arbitrary shapes. We address bandwidth selection, extrapolation in the vicinity & change point estimation. In another context, Ghosh (2009) considers a Gaussian subordination on a lattice with long memory & short memory correlations; Hallin et al. (2004) & Robinson (2011) provide further results for curve estimation with spatial data; Beran et al. (2009) consider estimation in a long memory lattice process. We present some asymptotic results and examples from environmental research.

References:

Beran, J., Ghosh, S., Schell, D. (2009) Least square estimation for stationary lattice processes with long-memory. Journal of Multivariate Analysis, 100: 2178-2194.

Ghosh, S. (2009) The unseen species number revisited. Sankhya, 71-B, 2: 137-150.

Hallin, M., Lu, Z., Tran L.T. (2004) Kernel density estimation for spatial processes: the L_1 theory. Journal of Multivariate Analysis, 88, 61-75.

Robinson, Peter (2011) Asymptotic theory for nonparametric regression with spatial data. Journal of econometrics, 165 (1). pp. 5-19.