For a general definition of depth in data analysis a differential-like calculus is constructed in which the location case (the framework of Tukeyâ€™s median) plays a fundamental role similar to that ofâ€¦ (More)

Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannonâ€¦ (More)

Hansen, Kooperberg, and Sardy (1998) introduced a family of continuous, piecewise linear functions defined over adaptively selected triangulations of the plane as a general approach to statisticalâ€¦ (More)

Directional quantile envelopesâ€”essentially, depth contoursâ€”are a possible way to condense the directional quantile information, the information carried by the quantiles of projections. In typicalâ€¦ (More)

The breakdown point behavior of M-estimators in linear models with xed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at xed designsâ€¦ (More)

We formulate versions of Hampelâ€™s theorem and its converse, establishing the connection between qualitative robustness and weak continuity in full generality and under minimal assumptions. 1.â€¦ (More)

The lower bounds for the explosion and implosion breakdown points of the simultaneous Cauchy M-estimator (Cauchy MLE) of the regression and scale parameters are derived. For appropriate tuningâ€¦ (More)

We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR)â€¦ (More)

We give some empirical comparisons between two nonparametric regression methods based on regularization: the elastic or thin-plate splines, and plastic splines based on total variation penalties. 1.â€¦ (More)