We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional factor model implemented by the principal component analysis. Using the extracted factors, we develop a link-free...

Testing multi-factor asset pricing models is instrumental for the asset pricing theory and practice. Due to the accumulation of errors in estimating high-dimensional parameters, traditional quadratic-form tests such as the Wald test perform poorly against the sparse alternative hypothesis in the...

We propose a novel technique to boost the power of testing a high-dimensional vector $H:\theta=0$ against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due...

Compressed sensing is a very powerful and popular tool for sparse recovery of high dimensional signals. Random sensing matrices are often employed in compressed sensing. In this paper we introduce a new method named aggressive betting using sure independence screening for sparse noiseless signal...

Cai et al. (2010) [4] have studied the minimax optimal estimation of a collection of large bandable covariance matrices whose off-diagonal entries decay to zero at a polynomial rate. They have shown that the minimax optimal procedures are fundamentally different under Frobenius and spectral...

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ₁-penalized covariance...