2009/10/31 by Ethan Anderes, Michael L. Stein, Anderes, Ethan +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Soil Geostatistics and Mapping #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.0911.0047
openalex publication_date 2009/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence of far away observations, works for irregular sampling locations, and when designed appropriately, can trade bias and variance for reducing estimation error. This paper starts with an exposition of our technique on the problem of estimating an unknown positive function when multiplied by a stationary random field. This example gives concrete evidence of the benefits of our local likelihood as compared to naïve local likelihoods where the stationary model is assumed throughout a neighborhood. We then discuss the difficult problem of estimating a bandwidth parameter that controls the amount of influence from distant observations. Finally we present a simulation experiment for estimating the local smoothness of a local Matérn random field when observing the field at random sampling locations in [0,1]2.