1. Basic Assumptions. Assume that (i) {Tt} is a strongly-continuous semigroup of bounded linear operators on the Banach space B = C0(I) = { f continuous on I = [0, 1] : f(0) = f(1) = 0 } (ii) If f(x) ≥ 0 and f ∈ B, then Ttf(x) ≥ 0 and Ttf(x) ≤ maxy∈I f(y). In general, the infinitesimal generator of a strongly-continuuous semigroup of linear operators Tt on any Banach space B is defined by Af = ...

We consider the online one-class collaborative filtering (CF) problem that consists of recommending items to users over time in an online fashion based on positive ratings only. This problem arises when users respond only occasionally to a recommendation with a positive rating, and never with a negative one. We study the impact of the probability of a user responding to a recommendation, pf , o...

Bayesian predictive functions for future observations from a generalized Pareto distribution based on generalized order statistics are obtained. Two cases are considered unknown one parameter and unknown two parameters. We also consider two cases fixed sample size and random sample size. The Bayesian predictive functions are specialized to ordinary order statistics, progressive type II censorin...

In the speech recognition, a mandarin syllable wave is compressed into a matrix of linear predict coding cepstra (LPCC), i.e., a matrix of LPCC represents a mandarin syllable. We use the Bayes decision rule on the matrix to identify a mandarin syllable. Suppose that there are K different mandarin syllables, i.e., K classes. In the pattern classification problem, it is known that the Bayes decis...

Subspace methods have been extensively used to solve a variety of problems in computer vision including object detection, recognition, and tracking. Typically the subspaces are learned from a training set that contains different configurations or states of a particular object (e.g., variations on shape or appearance). However, in some situations it is not possible to have access to data with mu...

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We consider the situation in two sample testing when one variance is assumed to be known while the other variance is considered unknown. This situation arises, for example, when one is interested in comparing a standard treatment with a new treatment. Although this situation occurs relatively infrequently, our example discusses the important tool of moment matching and makes the classic two sam...

We study a hypothesis-testing problem involving the location model suggested by Olkin and Tate (1961). Specifically, we derive a likelihood ratio test of the associated location hypothesis as an alternative to the con\entional method of carrying out sepalate tests for each of the parameters. A small sample Monte Carlo colnparison indicates the general superiority of the former in terms of stati...

In this paper, we study the problem of face identification from only one training sample per person(OSPP). For a face identification system, the most critical obstacles towards real-world applications are often caused by the disguised, corrupted and varying illuminated images in limited sample sets. Meanwhile, storing fewer training samples would essentially reduce the cost for collecting, stor...

This article concerns inference on the correlation coefficients of a multivariate normal distribution. Inferential procedures based on the concepts of generalized variables (GVs) and generalized p-values are proposed for elements of a correlation matrix. For the simple correlation coefficient, the merits of the generalized confidence limits and other approximate methods are evaluated using a nu...