This paper deals with statistical inferences based on the generalized varying-coeÆcient models proposed by Hastie and Tibshirani (1993). Local polynomial regression techniques are used to estimate coeÆcient functions and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coeÆcients are derived and are empirically tested. A goodness-oft...

In the domain of the Side Channel Attacks, various statistical tools have succeeded to retrieve a secret key, as the Pearson coefficient or the Mutual Information. In this paper we propose to study the Maximal Information Coefficient (MIC) which is a non-parametric method introduced by Reshef et al. [13] to compare two random variables. The MIC is based on the mutual information but it is easie...

We give new q-(1+q)-analogue of the Gaussian coefficient, also know as the q-binomial which, like the original q-binomial [ n k ] q , is symmetric in k and n− k. We show this q-(1 + q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birk...

Let f(x1, . . . , xk) be a polynomial over a field K. This paper considers such questions as the enumeration of the number of nonzero coefficients of f or of the number of coefficients equal to α ∈ K∗. For instance, if K = Fq then a matrix formula is obtained for the number of coefficients of fn that are equal to α ∈ Fq , as a function of n. Many additional results are obtained related to such ...

Abstract: Bivariate (or pairwise) information measures such as mutual information or correlation are heavily used in variable selection and network inference algorithms mainly because they are faster and require fewer samples than multivariate (or multidimensional) strategies. This paper proposes a new relevance measure that aims at improving the detection of relevant variables based on pairwis...