Abstract The paper gives characterizations of the supernorm statistic $$\widehat{N} :\mathcal {P}\rightarrow \mathbb {N}^{+}$$ N ^ : P → + for partitions,...

We define Dumont’s statistic on the symmetric group Sn to be the function dmc: Sn → N which maps a permutation σ to the number of distinct nonzero letters in code(σ). Dumont showed that this statistic is Eulerian. Naturally extending Dumont’s statistic to the rearrangement classes of arbitrary words, we create a generalized statistic which is again Eulerian. As a consequence, we show that for e...

Sample covariance matrices are also of essential importance in multivariate statistical analysis because many test statistics involve their eigenvalues and/or eigenvectors. The typical example is T 2 statistic, which was proposed by Hotelling [2]. We refer to [1] and [3] for various uses of the T 2 statistic. The T 2 statistic, which is the origin of multivariate linear hypothesis tests and the...

A novel method of quantifying the level of detail preservation ability of digital filters is proposed. The method assumes only the input distribution of the filter and estimates how much the filter changes the signal. The change is measured by the expectation of the absolute difference between the input and output signal. The method is applicable for many filters and input distributions. As an ...

In this paper, our objective is to test the statistical hypothesis : ( ) ( ) for all against : ( ) ( ) 1 H F x F x x H F x F x o o o = ≠ for some , x where ( ) F x o is a known distribution function. In this study, a goodness of fit test statistics for Gumbel distribution based on Kullback-Leibler information is studied. The performance of the test under simple random sampling is investigated u...

Fisher randomization tests for Neyman’s null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the F statistic to conduct such a test are examined both theoretically and computationally, and it is argued that under treatment effect heterogeneity, use ...

BACKGROUND The spatial and space-time scan statistics are commonly applied for the detection of geographical disease clusters. Monte Carlo hypothesis testing is typically used to test whether the geographical clusters are statistically significant as there is no known way to calculate the null distribution analytically. In Monte Carlo hypothesis testing, simulated random data are generated mult...

MOTIVATION Time-course microarray experiments are designed to study biological processes in a temporal fashion. Longitudinal gene expression data arise when biological samples taken from the same subject at different time points are used to measure the gene expression levels. It has been observed that the gene expression patterns of samples of a given tumor measured at different time points are...