Spatial scan statistic methods are commonly used for geographical disease surveillance and cluster detection. The standard spatial scan statistic does not model any variability in the underlying risks of subregions belonging to a detected cluster. For a multilevel risk cluster, the isotonic spatial scan statistic could model a centralized high-risk kernel in the cluster. Because variations in d...

We study a bijective map from integer partitions to the prime factorizations of integers that we call “supernorm” partition, in which multiplicities parts are mapped factors natural numbers. The supernorm is connected family maps define, suggests potential apply techniques partition theory identify and prove multiplicative properties integers. As an application “supernormal” mappings (i.e., per...

Although the methodology for handling ordinal and dichotomous observed variables in structural equation models (SEMs) is developing rapidly, several important issues are unresolved. One of these is the optimal test statistic to apply as a test of overall model fit. We propose a new ‘‘vanishing tetrad’’ test statistic for such models. We build on Bollen’s (1990) simultaneous test statistic for t...

Cluster analysis has become a very popular tool for the exploration of high dimensional data. Dozens of algorithms have been proposed, each with its own merits and shortcomings. It is not known to what extent various methods give the same results, nor is it even clear how to measure how similar is the output of two distinct algorithms. Here we propose a statistic that is designed to measure the...

A common approach to split selection in classification trees is to search through all possible splits generated by predictor variables. A splitting criterion is then used to evaluate those splits and the one with the largest criterion value is usually chosen to actually channel samples into corresponding subnodes. However, this greedy method is biased in variable selection when the numbers of t...

When processing observational data, statistical testing is an essential instrument to hopefully render harmless incidental anomalies and disturbances in the measurements. A commonly used test statistic based on the general linear model is the generalized likelihood ratio test statistic. The standard formula given in the literature for this test statistic is not defined if the noise covariance m...

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a...

Given two sequences of length n over a finite alphabet A of size |A| = d, the D2 statistic is the number of k-letter word matches between the two sequences. This statistic is used in bioinformatics for EST sequence database searches. Under the assumption of independent and identically distributed letters in the sequences, Lippert, Huang and Waterman (2002) raised questions about the asymptotic ...