Integration by parts and representation of information functionals

in Abstract book of 2014 IEEE International Symposium on Information Theory (ISIT) (2014)

Parametric Stein operators and variance bounds

E-print/Working paper (2013)

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary ... [more ▼]

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric distributions with continuous dependence on the parameter. We provide explicit general expressions for location, scale and skewness families. We also provide a general expression for discrete distributions. For specific choices of target distributions (including the Gaussian, Gamma and Poisson) we compare the operators hereby obtained with those provided by the classical approaches from the literature on Stein's method. We use properties of our operators to provide upper and lower variance bounds (only lower bounds in the discrete case) on functionals h(X) of random variables X following parametric distributions. These bounds are expressed in terms of the first two moments of the derivatives (or differences) of h. We provide general variance bounds for location, scale and skewness families and apply our bounds to specific examples (namely the Gaussian, exponential, Gamma and Poisson distributions). The results obtained via our techniques are systematically competitive with, and sometimes improve on, the best bounds available in the literature. [less ▲]

A note on the normal approximation error for randomly weighted self-normalized sums

in Periodica Mathematica Hungarica (2013)

One-step R-estimation in linear models with stable errors

in Journal of Econometrics (2013), 172(2), 195--204

Optimal rank-based inference for spherical location

in Statistica Sinica (2013), 23

Efficient ANOVA for directional data

E-print/Working paper (2012)

In this paper we tackle the ANOVA problem for directional data (with particular emphasis on geological data) by having recourse to the Le Cam methodology usually reserved for linear multivariate analysis ... [more ▼]

In this paper we tackle the ANOVA problem for directional data (with particular emphasis on geological data) by having recourse to the Le Cam methodology usually reserved for linear multivariate analysis. We construct locally and asymptotically most stringent parametric tests for ANOVA for directional data within the class of rotationally symmetric distributions. We turn these parametric tests into semi-parametric ones by (i) using a studentization argument (which leads to what we call pseudo-FvML tests) and by (ii) resorting to the invariance principle (which leads to efficient rank-based tests). Within each construction the semi-parametric tests inherit optimality under a given distribution (the FvML distribution in the first case, any rotationally symmetric distribution in the second) from their parametric antecedents and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behaviour of the proposed tests is investigated by means of a Monte Carlo simulation. We conclude by applying our findings on a real-data example involving geological data. [less ▲]

On a connection between Stein characterizations and Fisher information

Report (2011)