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Markowitz 投资组合的稳健化AI 解读

Markowitz mean–variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high sensitivity to change in input parameters. The heavy-tail characteristics of financial time series are in fact the cause for these erratic fluctuations of weights that consequently create substantial transaction costs. In robustifying the…

具有两个有界矩的分布下的稳健 k-means 聚类AI 解读

We consider the robust algorithms for the k-means clustering problem where a quantizer is constructed based on N independent observations. Our main results are median of means based nonasymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of (Ann. Statist. 9 (1981) 135–140) who showed that the existence of two moments is sufficient for…

L4–L2 范数等价条件下的稳健协方差估计AI 解读

Let $X$ be a centered random vector taking values in $\mathbb{R}^{d}$ and let $\Sigma=\mathbb{E}(X\otimes X)$ be its covariance matrix. We show that if $X$ satisfies an $L_{4}-L_{2}$ norm equivalence (sometimes referred to as the bounded kurtosis assumption), there is a covariance estimator $\hat{\Sigma}$ that exhibits almost the same performance one would expect had $X$ been a Gaussian vector. The procedure also improves the current state-of-the-art regarding high…