Bernstein estimator for unbounded density copula

We study the asymptotic properties of the Bernstein estimator for unbounded density copula functions. We show that the estimator converges to infinity at the corner. We establish its relative convergence when the copula is unbounded and we provide the uniform strong consistency of the estimator on every compact in the interior region. We also check the finite simple performance of the estimator via an extensive simulation study and we compare it with other well known nonparametric methods. Finally, we consider an empirical application where the asymmetric dependence between international equity markets (US, Canada, UK, and France) is re-examined

Designing and modeling of a multi-agent adaptive learning system (MAALS) using incremental hybrid case-based reasoning (IHCBR)

Several researches in the field of adaptive learning systems has developed systems and techniques to guide the learner and reduce cognitive overload, making learning adaptation essential to better understand preferences, the constraints and learning habits of the learner. Thus, it is particularly advisable to propose online learning systems that are able to collect and detect information describing the learning process in an automatic and deductive way, and to rely on this information to follow the learner in real time and offer him training according to his dynamic learning pace. This article proposes a multi-agent adaptive learning system to make a real decision based on a current learning situation. This decision will be made by performing a hypride cycle of the Case-Based Reasonning approach in order to follow the learner and provide him with an individualized learning path according to Felder Silverman learning style model and his learning traces to predict his future learning status. To ensure this decision, we assign at each stage of the Incremental Hybrid Case-Based Reasoning at least one active agent performing a particular task and a broker agent that collaborates between the different agents in the system

Nonparametric estimation and inference for Granger causality measures

We propose a nonparametric estimator and a nonparametric test for Granger causality measures that quantify linear and nonlinear Granger causality in distribution between random variables. We first show how to write the Granger causality measures in terms of copula densities. We suggest a consistent estimator for these causality measures based on nonparametric estimators of copula densities. Further, we prove that the nonparametric estimators are asymptotically normally distributed and we discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and test for our causality measures. A simulation study reveals that the bias-corrected bootstrap estimator of causality measures behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, we illustrate the practical relevance of nonparametric causality measures by quantifying the Granger causality between S&P500 Index returns and many exchange rates (US/Canada, US/UK and US/Japen exchange rates)

Hybrid approach of the fuzzy C-Means and the K-Nearest neighbors methods during the retrieve phase of dynamic case based reasoning for personalized Follow-up of learners in real time

The goal of adaptive learning systems is to help the learner achieve their goals and guide their learning. These systems make it possible to adapt the presentation of learning resources according to learners' needs, characteristics and learning styles, by offering them personalized courses. We propose an approach to an adaptive learning system that takes into account the initial learning profile based on Felder Silverman's learning style model in order to propose an initial learning path and the dynamic change of his behavior during the learning process using the Incremental Dynamic Case Based Reasoning approach to monitor and control its behavior in real time, based on the successful experiences of other learners, to personalize the learning. These learner experiences are grouped into homogeneous classes at the behavioral level, using the Fuzzy C-Means unsupervised machine learning method to facilitate the search for learners with similar behaviors using the supervised machine learning method K- Nearest Neighbors

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator

Nonparametric statistical inference for dependent censored data

A frequent problem that appears in practical survival data analysis is censoring. A censored observation occurs when the observation of the event time (duration or survival time) may be prevented by the occurrence of an earlier competing event (censoring time). Censoring may be due to different causes. For example, the loss of some subjects under study, the end of the follow-up period, drop out or the termination of the study and the limitation in the sensitivity of a measurement instrument. The literature about censored data focuses on the i.i.d. case. However in many real applications the data are collected sequentially in time or space and so the assumption of independence in such case does not hold. Here we only give some typical examples from the literature involving correlated data which are subject to censoring. In the clinical trials domain it frequently happens that the patients from the same hospital have correlated survival times due to unmeasured variables like the quality of the hospital equipment. Censored correlated data are also a common problem in the domain of environmental and spatial (geographical or ecological) statistics. In fact, due to the process being used in the data sampling procedure, e.g. the analytical equipment, only the measurements which exceed some thresholds, for example the method detection limits or the instrumental detection limits, can be included in the data analysis. Many other examples can also be found in other fields like econometrics and financial statistics. Observations on duration of unemployment e.g., may be right censored and are typically correlated. When the data are not independent and are subject to censoring, estimation and inference become more challenging mathematical problems with a wide area of applications. In this context, we propose here some new and flexible tools based on a nonparametric approach. More precisely, allowing dependence between individuals, our main contribution to this domain concerns the following aspects. First, we are interested in developing more suitable confidence intervals for a general class of functionals of a survival distribution via the empirical likelihood method. Secondly, we study the problem of conditional mean estimation using the local linear technique. Thirdly, we develop and study a new estimator of the conditional quantile function also based on the local linear method. In this dissertation, for each proposed method, asymptotic results like consistency and asymptotic normality are derived and the finite sample performance is evaluated in a simulation study.(STAT 3)--UCL, 200

Nonparametric regression with dependent censored data

Let (Xi , Yi ) (i = 1,..., n) be n replications of a random vector (X, Y ), where Y is supposed to be subject to random right censoring. The data (Xi , Yi ) are assumed to come from a stationary α-mixing process. We consider the problem of estimating the function m(x) = E(φ(Y )|X = x), for some known transformation φ. Particular choices of φ lead to the conditional moment function of Y given X , or the conditional distribution of Y given X . This problem is approached in the following way : first, we introduce a transformed variable Y ∗ i , that is not subject to censoring and satisfies the relation E(φ(Yi |Xi = x) = E(Y ∗ i |Xi = x), and then we estimate m(x) by applying local linear regression techniques to the pseudo-data (Xi , ˆ Y ∗ i ), where ˆ Y ∗ i is a certain estimator of Y ∗ i . The asymptotic properties of the proposed estimator are established. We investigate the performance of the estimator for small samples through a simulation study, and we discuss the optimal choice of the transformation Y ∗ i . As a by-product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions. This result is of independent interest, and can be applied in a wide variety of contexts