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题目：Generalized Cornish Fisher Expansions and its Applications
嘉宾：Professor Vladimir V. Ulyanov (Lomonosov Moscow State University)
时间：2014年11月11日（周二）下午16:15
地点：管理科研楼1018会议室
主办：管理学院统计与金融系
摘要：
The talk is a report of the state-of-the-art in Cornish-Fisher expansions and its applications on the base of recent publications.
In statistical inference it is of fundamental importance to obtain the sampling distribution of statistics. However, we often encounter situations where the exact distribution cannot be obtained in closed form, or even if it is obtained, it might be of little use because of its complexity. One practical way of getting around the problem is to provide reasonable approximations of the distribution function and its quantiles, along with extra information on their possible errors. It can be made with help of Chebyshev-Edgeworth and Cornish-Fisher expansions (CEE and CFE resp.). Recently the interest for CFE stirred up because of intensive study of quantiles in models in financial mathematics and financial risk management.
In the talk we discuss new approaches to CFE appeared in last years: in particular, a technique of rearrangement to monotonize CFE. We consider as well the computable error bounds for CFE in the case when there are error bounds for CEE of the distributions of statistics. The results are illustrated for t- and chi-squared statistics. The Bartlett type corrections will be also considered.
嘉宾：Professor Vladimir V. Ulyanov (Lomonosov Moscow State University)
时间：2014年11月11日（周二）下午16:15
地点：管理科研楼1018会议室
主办：管理学院统计与金融系
摘要：
The talk is a report of the state-of-the-art in Cornish-Fisher expansions and its applications on the base of recent publications.
In statistical inference it is of fundamental importance to obtain the sampling distribution of statistics. However, we often encounter situations where the exact distribution cannot be obtained in closed form, or even if it is obtained, it might be of little use because of its complexity. One practical way of getting around the problem is to provide reasonable approximations of the distribution function and its quantiles, along with extra information on their possible errors. It can be made with help of Chebyshev-Edgeworth and Cornish-Fisher expansions (CEE and CFE resp.). Recently the interest for CFE stirred up because of intensive study of quantiles in models in financial mathematics and financial risk management.
In the talk we discuss new approaches to CFE appeared in last years: in particular, a technique of rearrangement to monotonize CFE. We consider as well the computable error bounds for CFE in the case when there are error bounds for CEE of the distributions of statistics. The results are illustrated for t- and chi-squared statistics. The Bartlett type corrections will be also considered.
