Nonparametric regression for functional data: Automatic smoothing parameter selection

We study regression estimation when the explanatory variable is functional. Nonparametric estimates of the regression operator have been recently introduced. They depend on a smoothing factor which controls its behavior, and the aim of our work is to construct some data-driven criterion for choosing this smoothing parameter. The criterion can be formulated in terms of a functional version of cross-validation ideas. Under mild assumptions on the unknown regression operator, it is seen that this rule is asymptotically optimal. As by-products of this result, we state some asymptotic equivalences for several measures of accuracy for nonparametric estimate of the regression operator. We also present general inequalities for bounding moments of random sums involving functional variables. Finally, a short simulation study is carried out to illustrate the behavior of our method for finite samples.     

Mixed-spectra analysis for stationary random fields

We consider a, discrete time, weakly stationary bidimensional process, for which the spectral measure is the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. In this paper we are interested in estimating the spectral density of the absolutely continuous measure and of the density on the lines. For this aim, by using the double kernel method, we construct consistent estimators of these densities and we study their asymptotic behaviors in term of the mean squared error with rate.     

Local Weighted Average Estimation of the Regression Operator for Functional Data

We are concerned with the problem of local weighted average estimation of the regression operator when the responses are real-valued random variables, the explanatory data are of functional fixed-design type, and the errors consist of an independent and identically distributed variables. In this article, our main contributions on the local linear functional estimation concern from one part, the situation when the data are of functional fixed-design kind, and from the other part, in deriving uniform asymptotic results on the behavior of this estimator with respect to the topological properties of the space data (normed or semi-metric).     

Liberalization,crisis and growth in MENA region: Do institutions matter?

The main purpose of this study is to investigate the interaction between financial liberalization, banking crisis and economic growth by taking into consideration the role of institutions. Our sample covers 15 Middle East and North African observed during the period 2000–2013. Using a dynamic panel data framework, our findings reveal that financial liberalization contributed to improve economic growth in MENA countries while banking crisis had harmful effects on MENA economies. The quality of institutions did not have a clear impact except for rule and order and democratic institution. These results have important policy implications. To grow output and avoid the occurrence of banking crisis, MENA countries should reinforce their institutions quality by adopting good practice of governance and regulation.     

New sensitivity analysis subordinated to a contrast

ABSTRACT

In a model of the form Y = h(X₁, …, X_d) where the goal is to estimate a parameter of the probability distribution of Y, we define new sensitivity indices which quantify the importance of each variable X_i with respect to this parameter of interest. The aim of this paper is to define goal oriented sensitivity indices and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution Y. We name the framework we present as Goal Oriented Sensitivity Analysis (GOSA).     

Regression operator estimation by delta-sequences method for functional data and its applications

In this paper, we introduce a somewhat more general class of nonparametric estimators (delta-sequences estimators) for estimating an unknown regression operator from noisy data. The regressor is assumed to take values in an infinite-dimensional separable Banach space, when the response variable is a scalar. Under some general conditions, we establish the uniform almost-complete convergence with the rates of these estimators. Moreover, we give some particular cases of our results, which can also be considered as novel in the finite-dimensional setting. Moreover, after giving some examples of the impact of our results, we show how to use them in some statistical applications (prediction procedure and curve discrimination).