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高维投资组合优化中的样本外夏普比率估计AI 解读

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on…

使用非线性筛方法推断时间序列非参数条件矩限制AI 解读

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series…

基于多项比较首选结果的排序推断AI 解读

This paper considers ranking inference of $n$ items based on the observed data on the top choice among $M$ randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for $M$-way ranking with only the top choice observed and is an extension of the celebrated Bradley-Terry-Luce model that corresponds to $M=2$. Under a uniform sampling scheme in which any $M$ distinguished items are selected for comparisons with probability $p$ and the…

利用稳健波动率代理比较波动率预测：经验偏差视角AI 解读

Volatility forecasting is crucial to risk management and portfolio construction. One particular challenge of assessing volatility forecasts is how to construct a robust proxy for the unknown true volatility. In this work, we show that the empirical loss comparison between two volatility predictors hinges on the deviation of the volatility proxy from the true volatility. We then establish non-asymptotic deviation bounds for three robust volatility proxies, two of which are…

重尾数据的收缩原则：高维稳健低秩矩阵恢复AI 解读

This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from subexponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ∗ from the trace regression model Y=Tr(Θ∗⊤X)+ε. It encompasses four popular problems: sparse…

近似因子模型的稳健协方差估计AI 解读

In this paper, we study robust covariance estimation under the approximate factor model with observed factors. We propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors, and then use it to recover the covariance matrix of the observed data. We prove that once the initial matrix estimator is good enough to maintain the element-wise optimal rate, the whole procedure will generate an estimated covariance with desired…

通过椭圆因子模型估计大型协方差矩阵AI 解读

We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the…

高维尖峰协方差经验特征结构的渐近理论AI 解读

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those…

因子模型中的投影主成分分析AI 解读

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor…

稀疏协方差矩阵泛函的估计AI 解读

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_{r}$ norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of…