Data Envelopment Analysis (DEA) is known as a nonparametric mathematical programming approach to productive efficiency analysis. In this paper we show that DEA can be alternatively interpreted as nonparametric least squares regression subject to shape constraints on frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and C...

We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a log-concave distribution with smooth potential. This gives a new Markov chain to sample from a log-concave distribution. Our main result shows in particular that when...

In this paper we consider Newton’s problem of finding a convex body of least resistance. This problem could equivalently be written as a variational problem over concave functions in R. We propose two different methods for solving it numerically. First, we discretize this problem by writing the concave solution function as a infimum over a finite number of affine functions. The discretized prob...

Abstract We show that the sequence of moments order less than 1 averages i.i.d. positive random variables is log-concave. For at least 1, we conjecture log-convex and this holds eventually for integer (after neglecting first $p^2$ terms sequence).

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) Minimax Concave Penalty via Generalized Linear Models (GLMs). The related disturbance controls the influence skewness spread in corrected path solutions coefficients.

This paper investigates a particular type of slice sampler algorithm, the polar slice sampler. This algorithm is shown to have convergence properties which are essentially independent of the dimension of the problem, at least for log-concave densities. For such densities, the algorithm provably converges (from appropriate starting point) to within 0:01 of stationarity in total variation distanc...