Mardia, K. V.; Watkins, A. J. On multimodality of the likelihood in the spatial linear model. (English) Zbl 0666.62084 Biometrika 76, No. 2, 289-295 (1989). A popular covariance scheme used for the spatial linear model in geostatistics has spherical form. However, the likelihood is not twice differentiable with respect to the range parameter, and this raises some questions regarding the unimodality of the likelihood. We compare the likelihoods of the spatial linear model for small samples under this scheme and the doubly geometric scheme. Also, a power covariance with range parameter is proposed. In view of potential multimodal likelihoods for small samples for this model, a convenient profile likelihood is introduced and studied. Cited in 21 Documents MSC: 62M09 Non-Markovian processes: estimation 62M99 Inference from stochastic processes 62N99 Survival analysis and censored data 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P99 Applications of statistics Keywords:covariance scheme; Kriging; maximum likelihood estimation; spherical correlation scheme; stationary Gaussian process; geostatistics; spatial linear model; small samples; doubly geometric scheme; multimodal likelihoods; profile likelihood PDFBibTeX XMLCite \textit{K. V. Mardia} and \textit{A. J. Watkins}, Biometrika 76, No. 2, 289--295 (1989; Zbl 0666.62084) Full Text: DOI