Using high-frequency data, we estimate the risk of a large portfolio with weights being the solution of an optimization problem subject to some linear inequality constraints. We propose a fully nonparametric approach as a benchmark, as well as a factor-based semiparametric approach with observable factors to attack the curse of dimensionality. We provide in-fill asymptotic distributions of the realized volatility estimators of the optimal portfolio, while taking into account the estimation error in the optimal portfolio weights as a result of the covariance matrix estimation. Our theoretical findings suggest that ignoring such an error leads to a first-order asymptotic bias which undermines the statistical inference. Such a bias is related to in-sample optimism in portfolio allocation. Our simulation results suggest satisfactory finite sample performance after bias correction, and that the factor-based approach becomes increasingly superior with a growing cross-sectional dimension. Empirically, using a large cross-section of high-frequency stock returns, we find our estimator successfully addresses the issue of in-sample optimism.

The multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the -values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon(LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR, to accommodate the spatial information of neighboring -values, via a local aggregation of -values. Theoretical properties of the FDR procedure are investigated under weak dependence of -values. It is shown that the FDR procedure alleviates the LIP of the FDR procedure, thus substantially facilitating the selection of more stringent control levels. Simulation evaluations indicate that the FDR procedure improves the detection sensitivity of the FDR procedure with little loss in detection specificity. The computational simplicity and detection effectiveness of the FDR procedure are illustrated through a real brain fMRI dataset.

The problem of estimating the density function and the regression function involving errors-in-variables in time series is considered. Under appropriate conditions, it is shown that the rates obtained in Fan (1991), Fan and Truong (1990) are also achievable in the context of dependent observations. Consequently, the results presented here extend our previous results for cross-sectional data to the longitudinal ones. oAbbreviated title. Measurement Errors in Time Series AMS 1980 subject classification. Primary 62G20. Secondary 62G05, 62J99.

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic significance level and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. Numerical results and real data analysis show the superiority of the new method.

In this note we include a correction for Equation (19) on page 840 which is a step in the proof of Theorem 4 of Fan et al.(2014). There is no change in the statement of Theorem 4, and the rest of the proof stays unchanged. Equation (19) on page 840 should be corrected to as follows: We apply the coordinatewise mean-value theorem with respect to each coordinate of (ie, j) to obtain that