On Sparse Nonparametric Conditional Covariance Selection

We develop a penalized kernel smoothing method for the problem of selecting nonzero elements of the conditional precision matrix, known as conditional covariance selection. This problem has a key role in many modern applications such as finance and computational biology. However, it has not been properly addressed. Our estimator is derived under minimal assumptions on the underlying probability distribution and works well in the high-dimensional setting. The effi- ciency of the algorithm is demonstrated on both simulation studies and the analysis of the stock market.