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重探伪逆：高维 Moore–Penrose 逆与岭型逆的渐近性质及应用AI 解读

In this paper, we derive high-dimensional asymptotic properties of the Moore–Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic behavior of the weighted sample trace moments of generalized inverse matrices are deduced in terms of the partial exponential Bell polynomials, which can be easily computed in practice. The existent results for pseudo-inverses are extended…

高维情形下基于最优收缩的投资组合选择AI 解读

In this article, we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense of maximizing with probability 1 the asymptotic out-of-sample expected utility, that is, mean-variance objective function for different values of risk aversion coefficient which in particular leads to the maximization of the…

高维向量独立性的检验AI 解读

In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we…