For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...

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...

Steganography is a science of hiding messages into multimedia documents. A message can be hidden in a document only if the content of a document has high redundancy. Although the embedded message changes the characteristics and nature of the document, it is required that these changes are difficult to be identified by an unsuspecting user. On the other hand, steganalysis develops theories, meth...

This thesis explores how to sparsely represent distributions of points for geometric statistical problems. A coreset C is a small summary of a point set P such that if a certain statistic is computed on P and C, then the difference in the results is guaranteed to be bounded by a parameter ε. Two examples of coresets are εsamples and ε-kernels. An ε-sample can estimate the density of a point set...

We consider the problem of testing for homogeneity of variance in a time series that has long memory structure. We demonstrate that a test whose null hypothesis is designed to be white noise can in fact be applied, on a scale by scale basis, to the discrete wavelet transform of long memory processes. In particular, we show that evaluating a normalized cumulative sum of squares test statistic us...

| This paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate { a widely used statistic for non-parametric detection of a common signal on two noisy channels. ...