Distributional assumptions can be examined with multidimensional goodness-of-fit tests. We propose a conceptually simple test with an appealing logic and accessible asymptotic properties, which is generalizable to a variety of problems and appears to work well against diverse alternatives. To test whether a k-dimensional random sample X1, …, Xn follows the distribution G, consider a triangle formed by two randomly selected data points Xi and Xj and a variable Y ∼ G. Our statistic estimates the likelihood that the side formed by the line from Xi to Xj is the smallest, the middle, or the largest side of the triangle.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty