ASYMPTOTIC PROPERTY OF WRAPPED CAUCHY KERNEL DENSITY ESTIMATION ON THE CIRCLE | Zendy

Yasuhito Tsuruta | Zendy; Masahiko Sagae | Zendy

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ASYMPTOTIC PROPERTY OF WRAPPED CAUCHY KERNEL DENSITY ESTIMATION ON THE CIRCLE

Author(s) -

Yasuhito Tsuruta,

Masahiko Sagae

Publication year - 2017

Publication title -

bulletin of informatics and cybernetics

Language(s) - English

Resource type - Journals

eISSN - 2435-743X

pISSN - 0286-522X

DOI - 10.5109/2232318

Subject(s) - mathematics , kernel density estimation , cauchy distribution , property (philosophy) , kernel (algebra) , statistics , mathematical analysis , pure mathematics , philosophy , epistemology , estimator

We discuss theoretical properties of the Wrapped Cauchy (WC) kernel. In this paper, we show that the WC kernel has the convergent rate of O(n−2/3) and holds the asymptotic normality. The rate of the WC kernel is not better than the rate O(n−4/5) of the von Mises (VM) kernel. However, some numerical experiments show the better behavior of the WC kernel rather than the VM kernel under the condition of the multimodality and/or the heavy tail.

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