The goal of noisy high-dimensional phase retrieval is to estimate an s-sparse parameter β∗ ∈ R from n realizations of the model Y = (X>β∗)2 + ε. Based on this model, we propose a significant semi-parametric generalization called misspecified phase retrieval (MPR), in which Y = f(X>β∗, ε) with unknown f and Cov(Y, (X>β∗)2) > 0. For example, MPR encompasses Y = h(|X>β∗|) + ε with increasing h as ...

In this paper, we present an R package that combines feature-based (X) data and graph-based (G) data for prediction of the response Y . In this particular case, Y is observed for a subset of the observations (labeled) and missing for the remainder (unlabeled). We examine an approach for fitting Ŷ = Xβ̂ + f̂(G) where β̂ is a coefficient vector and f̂ is a function over the vertices of the graph. The...

In a classical parametric setup, a key factor in the implementation of the Empirical Bayes methodology is the incorporation of a suitable prior that is compatible with the parametric setup and yet lends to the estimation of the Bayes (shrinkage) factor in an empirical manner. The situation is more complex in semi-parametric and (ev,:,n more in) nonparametric models. Although the Dirichlet prior...

An accurate estimate of the uncertainty associated with a parameter estimate is important if we want to avoid misleading inference. The bootstrap technique (Efron, 1979; Efron and Tisbshirani, 1993) is a very general way of measuring the accuracy of estimators, and was originally developed for parameter estimation given independent identically distributed (i.i.d.) data. However, random effects ...

This work implements alternative algorithms to that of Taleb and Jutten for blind source separation in post nonlinear mixtures. We use the same mutual information criterion as them, but we exploit its invariance with respect to translation to express its relative gradient in terms of the derivatives of the nonlinear transformations. Then we develop algorithms based on these derivatives. In a se...

In this paper, we propose a misspeci…cation test for the drift coe¢ cient in a semi-parametric di¤usion model. Our test is based on the score marked empirical process whose asymptotic behavior will be distorted by the estimation of the drift parameters. We use martingale transformtion to take away the estimation e¤ects which makes our test asymptotic distribution-free. The limit theory relies o...

This paper details a new clustering methodology that is based on the use of a semi-parametric density estimation procedure, called adaptive mixtures density estimation, as a “smart start” to a standard model-based clustering approach. This technique allows one to process large datasets without the necessity of precomputation of the interpoint distance matrix which is inherently an O(n) operatio...

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A method is given to estimate the geometry and motion of a moving body surface from image sequences. To this aim a parametric model of the surface is used, in order to reformulate the problem to one of parameter estimation. After linearization of the model standard linear estimation methods can be used to estimate the parameters. The main contribution of this paper is that a method is provided ...