Éric Marchand

Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval

For location families with densitiesf0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f0, ρ), the Bayes estimator δU with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous dominance results due to Katz and Farrell, we make use of KubokawasIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and are characterized in terms of δU. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint of the form θ∈[a, b].

On the comparison between standard and random knockout tournaments

obtained for a two-outlier model, while numerical results are obtained for an alternative model. In both cases, we provide evidence that suggests that the outcomes of the standard knockout tournament and the random knockout tournament may not vary as much as one might expect. A secondary objective is the illustration of probability models that serve in analysing such problems.

A unified minimax result for restricted parameter spaces

We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under a lower (or upper) bound restriction, location parameter vectors restricted to a polyhedral cone, scale parameters subject to restricted ratios or products, linear combinations of restricted location parameters, location parameters bounded to an interval with unknown scale, quantiles for location-scale families with parametric restrictions and restricted covariance matrices.

On the minimax estimator of a bounded normal mean

For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space ([delta]BU) is minimax whenever . Further descriptions of the cutoff points of small enough radiuses (i.e., m[less-than-or-equals, slant]m0(p)) for [delta]BU to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of . Finally, implications for the associated minimax risk are described.

On the behavior of Bayesian credible intervals for some restricted parameter space problems

For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100(

On improved predictive density estimation with parametric constraints

1-\alpha)%

On the frequentist coverage of Bayesian credible intervals for lower bounded means

HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the restricted parameter space. Namely, they establish the attractive lower bound of

Statistical Evaluation of Compositional Differences Between Upper Eocene Impact Ejecta Layers

\frac{1-\alpha}{1+\alpha}

Bayesian improvements of a MRE estimator of a bounded location parameter

for the frequentist coverage probability of these procedures. In this work, we establish that the lower bound of

Computing the moments of a truncated noncentral chi-square distribution

\frac{1-\alpha}{1+\alpha}