Spatial statistics is a relatively new area of development and remains an area of active statistical research. Spatial data is distinguished by observations that are obtained at spatial locations in the plane or space. Time series processes attempt to model the correlations between responses at different time points. Similarly, with spatial data, the spatial correlation structure needs to be incorporated and modeled.
We are mainly interest in two problems. The first one deals with the correlation between two spatial sequences. Several coefficients have been defined to quantify the spatial association. One of them is the codispersion coefficient. Theoretical properties have been proved and applications in forest sciences and environmental sciences have been carried out. The second problem is related to the determination of effective sample size when the an available data set has spatial correlation. The main idea is quantify the sample size reduction due to spatial correlation. A new definition of effective sample size has been proposed. Currently, we are working to obtain asymptotic results for the estimated effective sample size and trying to characterize our notion of effective sample size when the coordinates of the data are uniformly distributed on a d-dimensional unit circle.
- Vallejos R. Testing for the absence of correlation between two spatial or temporal sequences. Pattern Recognition Letters 2012;33:1741-1748. [Bibtex]
- Ojeda S, Vallejos R, Lamberti P. Measure of similarity between images based on the codispersion coefficient. Journal of Electronic Imaging 2012;21(2):023019. [Bibtex]
- Meza C, Osorio F, La Cruz R. D. Estimation in nonlinear mixed-effects models using heavy-tailed distributions. Statistics and Computing 2012;22(1):121-139. [Digital version] [Bibtex]
- Ojeda S, Vallejos R, Bustos O. A New Image Segmentation Algorithm with Applications to Image Inpainting. Computational Statistics & Data Analysis 2010;54:2082-2093. [Digital version] [Bibtex]
- Osorio F, Paula G. A, Galea M. On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions. Computational Statistics & Data Analysis 2009;53(4):1249-1263. [Digital version] [Bibtex]
- Fondecyt 1120048. Association Characteristics Between Two Spatial Processes and Reduction of Sample sizes in Spatial Statistics.
- Proyecto de Inserción CONICYT. Fortalecimiento del Área Estadística en el Departamento de Matemática de la USM
- Proyecto CCTVal FB/01RV/11. Estimación no Paramétrica del Coeficiente de Codispersión: Aspectos Teóricos y Prácticos
- PROSUL 490429/2008-4, CNPq-Brazil: Desenvolvimento de métodos de diagnóstico e teoria assintótica em modelos de regressão
- SECyT 05/B412: Procesos Autoregresivos Bidimensionales, Segmentación de Texturas y Similaridad Espacial: Problemas y Aplicaciones.