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We propose a novel 3-way alternating regression (3-AR) method as an effective strategy for the estimation of parameter values in S-distributions from frequency data. The 3-AR algorithm is very fast and performs well for error-free distributions and artificial noisy data obtained as random samples generated from S-distributions, as well as for traditional statistical distributions and for actual observation data. In rare cases where the algorithm does not immediately converge, its enormous speed...
This paper deals with the problem of estimating a regression function f, in a random design framework. We build and study two adaptive estimators based on model selection, applied with warped bases. We start with a collection of finite dimensional linear spaces, spanned by orthonormal bases. Instead of expanding directly the target function f on these bases, we rather consider the expansion of h = f ∘ G-1, where G is the cumulative distribution function of the design, following Kerkyacharian and...
This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by...
A method for estimation of probability distribution of transformed random variables is presented. The proposed approach admits an approximation of the transformation of the random variables. The approximate probability density function (pdf) is corrected to obtain a resulting pdf which incorporates a prior knowledge of approximation errors. The corrected pdf is not contaminated by any uncontrollable approximation. The method is applied to pattern recognition. It is shown that class conditional pdf...
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