We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in At-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.

Motivated by the sampling problems and heterogeneity issues common in high-dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such discordant additive index models in both low and high-dimensional settings. Our estimators are based on factorizing certain moment tensors and are also applicable in the overcomplete setting, where the number of indices is more than the dimensionality of the datasets. Furthermore, we provide rates of convergence of our estimator in both high and low-dimensional setting. Establishing such results requires deriving tensor operator norm concentration inequalities that might be of independent interest. Finally, we provide simulation results supporting our theory. Our contributions extend the applicability of tensor methods for novel models in addition to making progress on understanding theoretical properties of such tensor methods.

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Coxs proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that non-concave penalties lead to significant reduction of the irrepresentable condition needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing

Regularity properties such as the incoherence condition, the restricted isometry property, compatibility, restricted eigenvalue and iq sensitivity of covariate matrices play a pivotal role in high-dimensional regression and compressed sensing. Yet, like computing the spark of a matrix, we first show that it is NP-hard to check the conditions involving all submatrices of a given size.

Several large volatility matrix estimation procedures have been recently developed for factor-based It processes whose integrated volatility matrix consists of low-rank and sparse matrices. Their performance depends on the accuracy of input volatility matrix estimators. When estimating co-volatilities based on high-frequency data, one of the crucial challenges is non-synchronization for illiquid assets, which makes their co-volatility estimators inaccurate. In this paper, we study how to estimate the large integrated volatility matrix without using co-volatilities of illiquid assets. Specifically, we pretend that the co-volatilities for illiquid assets are missing, and estimate the low-rank matrix using a matrix completion scheme with a structured missing pattern. To further regularize the sparse volatility matrix, we employ the principal orthogonal complement thresholding method (POET). We also investigate the asymptotic