## 学术活动

1. 中心公开课 短期课程 讨论班 学术报告 会议论坛

## 课程描述 Description

1)Cluster Detection and Unmasking in L2-regression
Two cluster detection methods are presented. The first is based on an Unusual Variance Decomposition, used to define an affine invariant PP-cluster Index from one-dimensional data projections. The second method is based on Residual’s Influence Index (RINFIN) that is obtained via the derivatives of the Influence functions in linear regression, which allow for unmasking of bad leverage cases. Both methods are successful with real and simulated data.
2) Assessing the quality of the Bootstrap
The Bootstrap method is briefly presented. It is examined theoretically and is compared in simulations with Jackknife estimates when the dimension of the data and of the model parameters, as well as the parameter values increase.
3)(If time permits) Option Pricing with Statistical Experiments
A Risk Neutral Probability, P*, is constructed via stock prices using  Statistical Experiments, without model assumptions. The results contribute in understanding the relation between P*, statistical contiguity and the market’s informational efficiency. The price of a European option is obtained, confirming the universal quote of the Black-Scholes-Merton price for the class of calm stock prices that includes the log-normal price. Other consequences are presented.

## 预备知识 Prerequisites

By topic: Yatracos, Y. (2013) Detecting clusters in the data from variance decompositions of its projections. Jour. of Classification 30, 30-55.
(2018) Residual's Influence Index (RINFIN), Bad Leverage and Unmasking in High Dimensional L2-regression.https://www.researchgate.net/publication/328837840
(2002) Assessing the quality of bootstrap samples and of the bootstrap estimates obtained with finite resampling. Stat. & Prob. Let. 59, 281-292.
(2018) Distributional Divergence, Statistical Experiments and Consequences in Option Pricing. Statistics 52, 18-33.

## 参考资料 References

Topics 1) and 2): First Year B.Sc. course in Statistics (with Calculus).
Topic 3): A course in Probability. Knowledge of Finance notions is not necessary.