Idir Ouassou

Cadi Ayyad University | UCAM · Department of Mathematics

We study the problem of estimating the mean vector \(\theta = (\theta _{1}, \ldots , \theta _{d})\) of a random vector \(X \in \mathbb {R}^{d}\) that obeys a spherically symmetric distribution. We consider two types of modified balanced loss functions to overcome this problem: (1) The first type of loss function is defined as \(L_{\omega ,\delta _{...

In this paper, we have introduced a functional approach for approximating nonparametric functions and coefficients in the presence of multivariate and functional predictors. By utilizing the Fisher scoring algorithm and the cross-validation technique, we derived the necessary components that allow us to explain scalar responses, including the funct...

Thispaperaimstoestimatetheconditionalcumulativedistribution function of a surrogate scalar response given a functional random response. We construct the conditional cumulative distribution function using both the available (true) response data and the surrogate data. Subsequently, we es- tablish the almost complete uniform convergence rate of the e...

We construct an estimator for the regression operator of a functional response variable using surrogate data, given a functional random variable. The almost complete uniform convergence rate of the estimator is then established. Finally, to demonstrate the predictive utility and superiority of the estimator when dealing with incomplete data, we app...

In this paper we develop and generalize the estimator of regression function for surrogate scalar response variable given a functional random one. Then, we build up some asymptotic properties in terms of the almost complete convergences, depending in the result we show the superiority of our estimator in term of prediction. Keywords: surrogate res...

This paper presents the estimator of the conditional density function of surrogated scalar response variable given a functional random one. We construct a conditional density function by using the available (true) response data and the surrogate data. Then, we build up some asymptotic properties of the constructed estimator in terms of the almost c...

The COVID-19 pandemic continues to spread and already shows a recurrence in many countries, despite several social distancing and vaccination measures implemented all around the world. Epidemiological data are available, and we use the Auto-Regressive Integrated Moving Average (ARIMA) model to analyze incidence pattern and to generate short-term fo...

We study the non-parametric estimation of partially linear generalized single-index functional models, where the systematic component of the model has a flexible functional semi-parametric form with a general link function. We suggest an efficient and practical approach to estimate (I) the single-index link function, (II) the single-index coefficie...

We develop new estimation results for the functional relationship between a regressor and a response which are functions indexed by time or by spatial locations. The regressor is assumed to belong to a semi-metric space (E, d) whereas the responses belongs to a Hilbert space F. First, we build a double-kernel estimator of the conditional density fu...

Single-index models are potentially important tools for multivariate nonparametric regression analysis. They generalize linear regression models by replacing the linear combination $\alpha_0^T X$ with a nonparametric component $\eta_0\left(\alpha_0^T X\right)$, where $\eta_0(\cdot)$ is an unknown univariate link function. Wang and Cao (2018) studie...

We present a consistent nonparametric test statistic for heteroscedas- ticity in functional data. First we construct the test by evaluating the difference between conditional and unconditional variances. Then we show the asymptotic normality of this test statistic under the null hy- pothesis. In addition, we prove that this test is also consistent...

We consider the problem of estimating the mean vector θ of a d-dimensional spherically symmetric distributed X based on balanced loss functions of the forms: (i) ωρ(‖δ−δ0‖2)+(1−ω)ρ(‖δ−θ‖2) and (ii) ℓω‖δ−δ0‖2+(1−ω)‖δ−θ‖2, where δ0 is a target estimator, and where ρ and ℓ are increasing and concave functions. For d≥4 and the target estimator δ0(X)=X,...

Let $T>0,~\alpha>\frac12$. In this work we consider the problem of estimating the drift parameter of the $\alpha$-Brownian bridge defined as $dX_t=-\alpha\frac{X_t}{T-t}dt+dW_t,~ 0\leq t< T$, where $W$ is a standard Brownian motion. Assume that the process X is observed equidistantly in time with the step size $\Delta_n:=\frac{T}{n+1}$, $t_i=i\Delt...

Epidemiological Modeling supports the evaluation of various disease management activities. The value of epidemiological models lies in their ability to study various scenarios and to provide governments with a priori knowledge of the consequence of disease incursions and the impact of preventive strategies. A prevalent method of modeling the spread...

In this article, we study the problem of estimation of the drift θ of a Gaussian process (Xt)t∈[0,T]. We give a class of estimators of James-Stein type whose risk is lower than the risk of the maximum likelihood estimator (MLE) θ̂:=(Xt)t∈[0,T] under the balanced loss function. Moreover, in the multidimensional case we give a class of Baranchik-type...

We consider the problem of estimating the mean vector $\theta$ of a $d$-dimensional spherically symmetric distributed $X$ based on balanced loss functions of the forms: {\bf (i)} $\omega \rho(\|\de-\de_{0}\|^{2}) +(1-\omega)\rho(\|\de - \theta\|^{2})$ and {\bf (ii)} $\ell\left(\omega \|\de - \de_{0}\|^{2} +(1-\omega)\|\de - \theta\|^{2}\right)$, wh...

Interpretable epidemiological modeling supports the evaluation of various disease management. There is the models' value in their capability to account for variable scenarios and provide governments with a priori knowledge of disease cases' growth. Consequently, an epidemiological model offers the impact of preventive strategies. A prevalent method...

We extend the classical approach in supervised classification based on the local likelihood estimation to the functional covariates case. The estimation procedure of the functional parameter (slope parameter) in the linear model when the covariate is of functional kind is investigated. We show, on simulated as well on real data, that classification...

We develop new estimation results for the functional relationship between a regressor and a response which are functions indexed by time or by spatial locations. The regressor is assumed to belong to a semi-metric space (E, d) whereas the responses belongs to a Hilbert space F. First, we build a double-kernel estimator of the conditional density fu...

Single-index models are potentially important tools for multivariate nonparametric regression analysis. They generalize linear regression models by replacing the linear combination \(\alpha^T_0\) with a nonparametric component \(\eta_0({\alpha^T_0})X\), where \(\eta_0(\cdot)\) is an unknown univariate link function. [7] studied generalized partiall...

The COVID-19 epidemic continues to spread outside of China and has some recurrence inside China, despite several social distancing measures implemented by the Chinese government. Limited epidemiological data are available, and recent changes in case definition and reporting further complicate our understanding of the impact of the epidemic, particu...

In this paper we consider a decision-theoretical study of predictive density estimators of multivariate observables measured by the frequentist risk corresponding to Density Power Divergences (DPD) as a set of loss functions (for every α∈[0,1]). The main themes, revolve about the inefficiency of MRE (Minimum Risk Equivariant) predictors in high eno...

We consider the problem of the nonparametric estimation in a functional regression model Y=r(X)+ε, with Y a real random variable response and X representing a functional variable taking values in a semi-metric space. The aim of this note is to find conditions of admissibility of Stein-type estimators of such a model under a class of balanced loss f...

Data in the form of time series of counts appear in a number of important applications such as health care services, financial markets, disease surveillance, and internet traffic modeling. One of the attractive models for this type of data is the so-called autoregressive conditional Poisson model (ACP). In this work, we propose a Stein-type shrinka...

In this paper, we consider the study of the efficiency of predictive density estimators of multivariate observables measured by the frequentist risk corresponding to S-Hellinger distances as a set of loss functions (for every � 2 [0; 1]). The main themes, revolve around the inefficiency of MRE predictors in high enough dimensions and about the inef...

We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the L1 approach. Under standard assumptions, we prove the almost complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulate...

We consider adaptive Ridge regression estimators in the general linear model with homogeneous spherically symmetric errors. A restriction on the parameter of regression is considered. We assume that all components are nonnegative (i.e. on the positive orthant ). For this setting, we produce under general quadratic loss such estimators whose risk fu...

We investigate the local linear kernel estimator of the regression function of a stationary and strongly mixing real random field observed over a general subset of the lattice . Assuming that is differentiable with derivative , we provide a new criterion on the mixing coefficients for the consistency and the asymptotic normality of the estimators o...

▶ Features original research contributions on functional statistics ▶ Shows applications in queuing theory, signal processing and epidemiology This volume, which highlights recent advances in statistical methodology and applications, is divided into two main parts. The first part presents theoretical results on estimation techniques in functional s...

As the problem of prediction is of great interest, several tools based on different methods and devoted to various contexts, have been developed in the statistical literature. The contribution of this paper is to focus on the study of the local linear nonparametric estimation of the quantile of a scalar response variable given a functional covariat...

The aim of this paper is first to find interactions between compartments of hosts in the Ross-Macdonald Malaria transmission system. So, to make clearer this association we introduce the concordance measure and then the Kendall’s tau and Spearman’s rho. Moreover, since the population compartments are dependent, we compute their conditional distribu...

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 establi...

We consider the problem of estimating the quadratic loss ∥δ-θ∥ 2 of an estimator δ of the location parameter θ=(θ 1 ,...,θ p ) when a subset of the components of θ are restricted to be nonnegative. First, we assume that the random observation X is a Gaussian vector and, secondly, we suppose that the random observation has the form (X,U) and has a s...

We consider the problem of estimating the quadratic loss ‖δ−θ‖2 of point estimators δ of a location parameter θ=(θ1,…,θp) for family of symmetric distributions with known scale parameter, when a subset of the components of θ are restricted to be nonnegative and when a residual vector U is available. In the normal case, we give a class of estimators...

We consider the problem of estimating the regression operator r when the explanatory variables are of functional type. Specifically, we assume that Y=r(X)+ε, where X is of functional fixed-design type, the response Y is a real random variable and the errors consist of independent and identically distributed variables. Then, we prove the existence a...

We consider the problem of efficient estimation for the drift of fractional Brownian motion with hurst parameter H less than . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

Let X=(X1,…,Xp) be a p-variate normal random vector with unknown mean θ=(θ1,…,θp) and identity covariance matrix. Estimators δ=(δ1,…,δp) of θ are considered under the quartic loss . For p⩾3, we develop sufficient conditions on δ(X)=X+g(X) to improve upon the usual estimator δ0(X)=X. To this end, we yield an unbiased estimator Og(X) of the risk diff...

´For estimating the median θ of a spherically symmetric univariate distribution under squared error loss, when θ is known to be restricted to an interval [−m, m], m known, we derive sufficient conditions for estimators δ to dominate the maximum likelihood estimator δmle. Namely: (i) we identify a large class of models where for sufficiently small m...

We consider the problem of estimating a p-dimensional parameter θ=(θ1,…,θp) when the observation is a p+k vector (X,U) where and where U is a residual vector with . The distributional assumption is that (X,U) has a spherically symmetric distribution around (θ,0). Two restrictions on the parameter θ are considered. First we assume that θi⩾0 for i=1,...

We study estimation of a location vector restricted to a convex cone when the dimension, p, is at least 3. We find estimators which improve on the "usual" estimator (the MLE in the normal case) in the general case of a spherically symmetric distribution with unknown scale. The improved estimators may be viewed as Stein-type shrinkage estimators on...

In this paper, we consider the problem of estimating the quadratic loss of point estimators of a location parameter \(\theta\), for a family of symmetric distribution with known scale parameter, subject to different constraints to be satisfied by the norm of \(\theta\) and when a residual vector U is available. We compare the robust and non-robust...