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PKU Ph.D. candidate published paper in the Annals of Statistics
Mar 23, 2012

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Peking University, Mar. 21, 2012: Chang Jinyuan, a Ph.D. candidate of Peking University (PKU) recently published a paper titled “On the approximate maximum likelihood estimation for diffusion processes” on the Annals of Statistics as first author, which is the most prestigious academic journal in statistics. He entered the 5-year Ph.D. program with a bachelor's degree in the Department of Business Statistics and Econometrics, Guanghua School of Management in 2009. The paper was written under the guidance of his tutor Professor Chen Song Xi. 

 

The paper can be accessed online

 

Diffusion process has a wide application in econometric field. The pricing of many financial assets relies on models derived from it, such as Black-Schole model. However, the transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Thus, how to make the proper statistic estimation in this circumstance is of great importance.

 

One solution proposed is to apply asymptotic expansions to the transition densities of diffusion processes, which leads to an approximate maximum likelihood estimation (AMLE) for parameters. Although the idea was already applied in financial data analysis, there are some key issues that remain to be addressed, among which is the consistency of the AMLE. In the paper, Chang Jinyuan establishes the consistency and convergence rate of the AMLE, which reveal the roles played by the number of terms used in the asymptotic density expansions and the sampling interval between successive observations. The paper also discusses the approximation for the Fisher information matrix with simulation results reported.

 

The journal edited by the Institute of Mathematic Statistics aims to publish research papers of the highest quality reflecting the many facets of contemporary statistics. Its primary emphasis is placed on importance and originality.

 

 

Written by: Fang Runiu
Edited by: Chen Long
Source: PKU News (Chinese)

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