We consider extensions of the famous GARCH(1, 1) model where the recursive equation for the volatilities is not specified by a parametric link but by a smooth autoregression function. Our goal is to estimate this function under nonparametric constraints when the volatilities are observed with multiplicative innovation errors. We construct an estimation procedure whose risk attains the usual con...

This paper reviews the main estimation and prediction results derived in the context of functional time series, when Hilbert and Banach spaces are considered, specially, in the context of autoregressive processes of order one (ARH(1) and ARB(1) processes, for H and B being a Hilbert and Banach space, respectively). Particularly, we pay attention to the estimation and prediction results, and sta...

Mutual information (MI) is a common criterion in independent component analysis (ICA) optimization. MI is derived from probability density functions (PDF). There are scenarios in which assuming a parametric form for the PDF leads to poor performance. Therefore, the need arises for non-parametric PDF and MI estimation. Existing nonparametric algorithms suffer from high complexity, particularly i...

Motivated from the bandwidth selection problem in local likelihood density estimation and from the problem of assessing a final model chosen by a certain model selection procedure, we consider estimation of the Kullback–Leibler divergence. It is known that the best bandwidth choice for the local likelihood density estimator depends on the distance between the true density and the ‘vehicle’ para...

The accuracy and the fast convergence of a leakage model are both essential components for the efficiency of side-channel analysis. Thus for efficient leakage estimation an evaluator is requested to pick a Probability Density Function (PDF) that constitutes the optimal tradeoff between both aspects. In the case of parametric estimation, Gaussian templates are a common choice due to their fast c...

This paper investigates the performance of three types of random coefficients logistic regression models; that is, models using parametric, semi-parametric, and nonparametric specifications of the distribution of the random effects. Whereas earlier studies focussed on models with a single random effect, here we look at models with multidimensional random effects (intercepts and slopes). Moreove...

We review gene mapping, or inference for quantitative trait loci, in the context of recent research in semi-parametric and non-parametric inference for mixture models. Gene mapping studies the relationship between a phenotypic trait and inherited genotype. Semi-parametric gene mapping using the exponential tilt covers most standard exponential families and improves estimation of genetic effects...

The power divergence family of Cressie and Read (1984) is a highly popular family of density-based divergences which is widely used in robust parametric estimation and multinomial goodness-of-fit testing. This family forms a subclass of the family of φ-divergences (Csiszár, 1963; Pardo, 2006) or disparities (Lindsay, 1994). The more recently described family of density power divergences (Basu e...

We consider one of the two the most classical non-parametric problems in this example: estimating a regression function on a subset of the real line (the most classical problem being estimation of a density). In non-parametric regression, we assume there is an unknown function f : R → R, where f belongs to a pre-determined class of functions F ; usually this class is parameterized by some type ...

During financial crises equity portfolios have suffered large losses. Methodologies for portfolio selection taking into account the possibility of large losses have existed for decades but their economic value is not well established. This article investigates the economic value in reducing the probability of large losses in portfolio selection. We combine mean-variance analysis with semi-param...