Fuzzy integrals as image lters provide a standard representational form which generalize linear lters such as the averaging lter, morphological lters such as at dilations and erosions, and order statistic lters such as the median lter. However, fuzzy integral lters are computationally intensive. Computing the output value obtained by fuzzy integral ltering at a point involves sorting all the pi...

A test statistic based on population quantiles using sample order statistics is suggested. The quantiles of the test statistics are evaluated for generalized exponential distribution. Similar test statistic based on moments of sample order statistic is referred and the proposed test formula is compared with it. Between the pairs of the above models it is established that the test formula propos...

This paper proposes a test of the null hypothesis of stationarity that is robust to the presence of fat-tailed errors. The test statistic is a modified version of the so-called KPSS statistic. The modified statistic uses the ”sign” of the data minus the sample median, whereas KPSS used deviations from means. This ”indicator” KPSS statistic has the same limit distribution as the standard KPSS st...

The use of the Kolmogorov-Smirnov (KS) statistic for testing hypotheses regarding activation in blood oxygenation level-dependent functional MRI data is critiqued on both theoretical and empirical grounds. Theoretically, it is argued that the KS test is formally unable to support inferences of interest to most neuro-imaging studies and has reduced sensitivity compared with parametric alternativ...

BACKGROUND A common, important problem in spatial epidemiology is measuring and identifying variation in disease risk across a study region. In application of statistical methods, the problem has two parts. First, spatial variation in risk must be detected across the study region and, second, areas of increased or decreased risk must be correctly identified. The location of such areas may give ...

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic...

Estimation of allelic and genotypic distributions for continuous data using kernel density estimation is discussed and illustrated for some variable number of tandem repeat data. These kernel density estimates provide a useful representation of data when only some of the many variants at a locus are present in a sample. Two Hardy-Weinberg test procedures are introduced for continuous data: a co...

Many classiication problems use image or other high-dimensional data, and must be designed from training data. The design and analysis of such systems param-eterized by unknown functions, based on a method of sieves to regularize the function estimates, is described. The test statistic is assumed to be the ideal test statistic with estimated functions substituted for the truth. The test statist...

This article considers two similar likelihood-based test statistics for comparing two fixed trees, the Kishino-Hasegawa (KH) test statistic and the likelihood ratio (LR) statistic, as well as a number of different methods for determining thresholds to declare a significant result. An explanation is given for why the KH test, which uses the KH test statistic and normal theory thresholds, need no...

Normality is a distributional requirement of classical test statistics. In order for the test statistic to provide valid results leading to sound and reliable conclusions this requirement must be satisfied. In the not too distant past, it was claimed that violations of normality would not likely jeopardize scientific findings Wilcox, 2012a, b). Unfortunately the data obtained in psychological i...