On robust regression with high-dimensional predictors.

We study regression M-estimates in the setting where p, the number of covariates, and n, the number of observations, are both large, but p ≤ n. We find an exact stochastic representation for the distribution of β = argmin(β∈ℝ(p)) Σ(i=1)(n) ρ(Y(i) - X(i')β) at fixed p and n under various assumptions on the objective function ρ and our statistical model. A scalar random variable whose deterministic limit rρ(κ) can be studied when p/n → κ > 0 plays a central role in this representation.

Optimal M-estimation in high-dimensional regression.

We consider, in the modern setting of high-dimensional statistics, the classic problem of optimizing the objective function in regression using M-estimates when the error distribution is assumed to be known. We propose an algorithm to compute this optimal objective function that takes into account the dimensionality of the problem. Although optimality is achieved under assumptions on the design matrix that will not always be satisfied, our analysis reveals generally interesting families of dimension-dependent objective functions.

Ranking TEM cameras by their response to electron shot noise.

We demonstrate two ways in which the Fourier transforms of images that consist solely of randomly distributed electrons (shot noise) can be used to compare the relative performance of different electronic cameras. The principle is to determine how closely the Fourier transform of a given image does, or does not, approach that of an image produced by an ideal camera, i.e.

The Missing Censoring Indicator Model and the Smoothed Bootstrap.

For right censored data with missing censoring indicators, sub-density function kernel estimators play a significant role for estimating a survival function. Data-driven bandwidths for computing these kernel estimators are proposed. The bandwidths are obtained as minimizers of certain estimates of the mean integrated squared error (MISE).