Kolmogorov-Smirnov Goodness-of-Fit Test for Spatial Data

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jose Guardiola*+ and Nancy Glenn
• Companies: Texas A&M and Texas Southern University
• Keywords: Kolmogorov-Smirnov ; Spatial Statistics ; Goodness of fit ; Bootstrap

Abstract

A key observation in the Kolmogorov-Smirnov Goodness-of-Fit test is that the largest difference between the cumulative distribution function F(x) and the empirical distribution function Fn(x) converges to 0 in probability. This observation allows one to test the null hypothesis of whether a given distribution does not differ from a hypothesized distribution, assuming the data are unbiased and independent. However, these assumptions render the test inadequate for spatial data. We extend the Kolmogorov-Smirnoff goodness-of-fit test to spatial data, and assume the data are from a regularly spaced lattice. The parametric bootstrap method for spatial statistics is used here to obtain the samples. The p-value and D statistic for the Kolmogorov-Smirnov Goodness-of-Fit test are computed here for the spatially correlated case and for an analogous uncorrelated data set. These results indicate that the p-values for the spatially correlated case are always greater than those for uncorrelated samples of the same size. This implies that if the null hypothesis was not rejected in the uncorrelated case then it will not be rejected in the correlated case either.