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Wavelet transforms for discrete-time periodic signals are developed. In this nite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported… (More)

—The sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well-known; however, the evaluation of its performance is a very difficult problem. In this paper it is shown that the distribution of the sufficient statistic can be approximated by the distribution of a Poisson-driven shot-noise random variable,… (More)

The new problem of nonparametric estimation of the interaction function of pairwise interaction point processes is addressed. We rst generalize some limit theorems of Saunders and Funk. Then we propose a very simple nonparametric estimation method based on the generalization. Several examples are shown to illustrate its eecacy.

Nonparametric estimation of interaction functions for two-type pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point… (More)

In speech recognition systems, a common problem is transcription of new additions to the recognition lexicon into their phonetic symbols. Specific to the Japanese language, such a problem can be dealt with in two steps. In this paper, we focus on the first step, in which the new lexical entry is converted into a set of hiragana syllabaries, which is almost… (More)

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