Differentiated logdensity approximants
- Authors
- Provost, Serge B.; Ha, Hyung-Tae
- Issue Date
- Sep-2015
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Density approximation; Moments; Rational functions; Logdensity
- Citation
- STATISTICAL METHODOLOGY, v.26, pp.61 - 71
- Journal Title
- STATISTICAL METHODOLOGY
- Volume
- 26
- Start Page
- 61
- End Page
- 71
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/10163
- DOI
- 10.1016/j.stamet.2015.02.005
- ISSN
- 1572-3127
- Abstract
- A moment-based density approximation technique whereby the derivative of the logarithm of a density approximant is expressed as a rational function is introduced in this paper. Guidelines for the selection of the polynomial orders of the numerator and denominator are proposed. The coefficients are then determined by solving a system of linear equations. The resulting density approximation, referred to as a differentiated logdensity approximant or DLA, satisfies a differential equation whose explicit solution is provided. It is shown that a unique solution exists when a polynomial is utilized in lieu of a rational function. The proposed methodology is successfully applied to two test statistics and several distributions. It is also explained that the same moment-matching technique can yield density estimates on the basis of sample moments. An example involving a widely analyzed data set illustrates this approach. (C) 2015 Elsevier B.V. All rights reserved.
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