For many classical tests like t-test, chi-square test, the co-called null distribution is well-known. That is, the distribution of the test statistic, given the null hypothesis of no effect, has been derived analytically and can be looked up in published tables. In some situations, however, it is desirable to define a test statistic, for which the null distribution cannot be obtained, for examp...

We derive the analytical mean and variance of the score test statistic in gene-dropping simulations and approximate the null distribution of the test statistic by a normal distribution. We provide insights into the gene-dropping test by decomposing the test statistic into two components: the first component provides information about linkage, and the second component provides information about ...

Xie and Priebe [2002. “Generalizing the Mann–Whitney–Wilcoxon Statistic”. J. Nonparametric Statist. 12, 661–682] introduced the class of weighted generalized Mann–Whitney–Wilcoxon (WGMWW) statistics which contained as special cases the classical Mann–Whitney test statistic and many other nonparametric distribution-free test statistics commonly used for the two-sample testing problem. The two-sa...

We illustrate the need to use higher-order (specifically sixth-order) expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity. The test statistic is a quasi-likelihood ratio (QLR) statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activat...

Increases in populations and in particular in developing countries are placing increased pressure on both natural and agricultural resources. In many cases, especially in semi-arid regions, the pressures are compounded by restricted agricultural lands. Reliable and relevant land evaluation is a requirement for land use policy and decision making to support sustainable rural development. Land ev...

Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. This paper introduces a new strategy to classify surfaces against their intersection status, where exact geometric entities are replaced by fuzzy geometric ones. Intersecting surfaces are thus replaced by fuzzy intersecting faces and a fuzzy intersection algorith...

Performance evaluation of a bridge is critical for determining the optimal maintenance strategy. An unsupervised bridge superstructure state assessment method is proposed in this paper based on fuzzy clustering and bridge field measured data. Firstly, the evaluation index system of bridge is constructed. Secondly, a certain number of bridge health monitoring data are selected as clustering samp...

In this study, a fuzzy probability-based Markov chain model is developed for forecasting regional long-term electric power demand. The model can deal with the uncertainties in electric power system and reflect the vague and ambiguous during the process of power load forecasting through allowing uncertainties expressed as fuzzy parameters and discrete intervals. The developed model is applied to...

For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio statistic is proposed to test the null hypothesis of no change. Under the null hypothesis of no change, the proposed test statistic is empirically shown asymptotically Gumbel distributed with robust location and scale parameters against various parameter settings and ...