In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the trad...

History of Science and Statistical Education: Examples from Fisherian and Pearsonian schools Paper presented at the 2004 Joint Statistical Meeting, Toronto, Canada Chong Ho Yu, Ph.D. [email protected] website: http://www.creative-wisdom/pub/pub.html Abstract Many students share a popular misconception that statistics is a subject-free methodology derived from invariant and timeless mathematic...

We revisit the outlier hypothesis testing framework of Li et al. (TIT 2014) and derive fundamental limits for optimal test under generalized Neyman-Pearson criterion. In testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The...

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an N -point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probabil...

In the article an application of the fuzzy testing of hypothesis to the stochastic-signal detection problem is considered when the signal-to-noise ratio approaches zero. We first obtain the general reManuscript received March 13, 1992; revised February 1 1 , 1993. This work was supported by the Science and Engineering Foundation of Korea (KOSEF) under Grant 92 1-0800-002-2. The authors are with...

By defining the likelihood ratio as L(y) def = f1(y) f0(y) , we observe that (2) can be completely characterized by three factors: L(y), C(i, j), and πi. However, how should we characterize the performance of such a detection rule? In order to characterize the performance of the detection rule, we first partition the observation Γ into to two subsets Γ0 and Γ1 over which we select H0 and H1. Mo...

The Pearson-Fisher chi-squared test can be used to evaluate the goodnessof-fit of categorized continuous data with known bin endpoints compared to a continuous distribution, in the presence of unknown (nuisance) distribution parameters. Rayner and McAlevey [11] and Rayner and Best [9],[10] demonstrate that in this case, component tests of the Pearson-Fisher chi-squared test statistic can be obt...