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Dive into the research topics where Abdelaati Daouia is active.

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Featured researches published by Abdelaati Daouia.


Econometric Theory | 2005

NONPARAMETRIC FRONTIER ESTIMATION: A CONDITIONAL QUANTILE-BASED APPROACH

Yves Aragon; Abdelaati Daouia; Christine Thomas-Agnan

In frontier analysis, most of the nonparametric approaches (free disposal hull [FDH], data envelopment analysis [DEA]) are based on envelopment ideas, and their statistical theory is now mostly available. However, by construction, they are very sensitive to outliers. Recently, a robust nonparametric estimator has been suggested by Cazals, Florens, and Simar (2002, Journal of Econometrics 1, 1–25). In place of estimating the full frontier, they propose rather to estimate an expected frontier of order m. Similarly, we construct a new nonparametric estimator of the efficient frontier. It is based on conditional quantiles of an appropriate distribution associated with the production process. We show how these quantiles are interesting in efficiency analysis. We provide the statistical theory of the obtained estimators. We illustrate with some simulated examples and a frontier analysis of French post offices, showing the advantage of our estimators compared with the estimators of the expected maximal output frontiers of order m.We thank J.P. Florens for helpful discussions and C. Cazals for providing the post office data set. We also are very grateful to the referees for useful suggestions.


Bernoulli | 2013

On kernel smoothing for extremal quantile regression

Abdelaati Daouia; Laurent Gardes; Stéphane Girard

Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from the tails of the conditional distribution. The purpose of this paper is to extend their asymptotic theory far enough into the tails. We focus on extremal quantile regression estimators of a response variable given a vector of covariates in the general setting, whether the conditional extreme-value index is positive, negative, or zero. Specifically, we elucidate their limit distributions when they are located in the range of the data or near and even beyond the sample boundary, under technical conditions that link the speed of convergence of their (intermediate or extreme) order with the oscillations of the quantile function and a von-Mises property of the conditional distribution. A simulation experiment and an illustration on real data were proposed. The real data are the American electric data where the estimation of conditional extremes is found to be of genuine interest.


Bernoulli | 2010

Frontier estimation and extreme values theory

Abdelaati Daouia; Jean-Pierre Florens; Léopold Simar

In this paper we investigate the problem of nonparametric monotone frontier estimation from an extreme-values theory perspective. This allows to revisit the asymptotic theory of the popular Free Disposal Hull estimator in a general setup, to derive new and asymptotically Gaussian estimators and to provide useful asymptotic confidence bands for the monotone boundary function. The finite sample behavior of the suggested estimators is explored through Monte-Carlo experiments. We also apply our approach to a real data set on the production activity of the French postal services.


Econometric Reviews | 2017

Measuring Firm Performance Using Nonparametric Quantile-type Distances

Abdelaati Daouia; Léopold Simar; Paul W. Wilson

ABSTRACT When faced with multiple inputs and outputs , traditional quantile regression of Y conditional on X = x for measuring economic efficiency in the output (input) direction is thwarted by the absence of a natural ordering of Euclidean space for dimensions q (p) greater than one. Daouia and Simar (2007) used nonstandard conditional quantiles to address this problem, conditioning on Y ≥ y (X ≤ x) in the output (input) orientation, but the resulting quantiles depend on the a priori chosen direction. This article uses a dimensionless transformation of the (p + q)-dimensional production process to develop an alternative formulation of distance from a realization of (X, Y) to the efficient support boundary, motivating a new, unconditional quantile frontier lying inside the joint support of (X, Y), but near the full, efficient frontier. The interpretation is analogous to univariate quantiles and corrects some of the disappointing properties of the conditional quantile-based approach. By contrast with the latter, our approach determines a unique partial-quantile frontier independent of the chosen orientation (input, output, hyperbolic, or directional distance). We prove that both the resulting efficiency score and its estimator share desirable monotonicity properties. Simple arguments from extreme-value theory are used to derive the asymptotic distributional properties of the corresponding empirical efficiency scores (both full and partial). The usefulness of the quantile-type estimator is shown from an infinitesimal and global robustness theory viewpoints via a comparison with the previous conditional quantile-based approach. A diagnostic tool is developed to find the appropriate quantile-order; in the literature to date, this trimming order has been fixed a priori. The methodology is used to analyze the performance of U.S. credit unions, where outliers are likely to affect traditional approaches.


Archive | 2011

Estimating Frontier Cost Models Using Extremiles

Abdelaati Daouia; Irène Gijbels

In the econometric literature on the estimation of production technologies, there has been considerable interest in estimating so called cost frontier models that relate closely to models for extreme non-standard conditional quantiles (Aragon et al. Econ Theor 21:358–389, 2005) and expected minimum input functions (Cazals et al. J Econometrics 106:1–25, 2002). In this paper, we introduce a class of extremile-based cost frontiers which includes the family of expected minimum input frontiers and parallels the class of quantile-type frontiers. The class is motivated via several angles, which reveals its specific merits and strengths. We discuss nonparametric estimation of the extremile-based costs frontiers and establish asymptotic normality and weak convergence of the associated process. Empirical illustrations are provided.


Annals of economics and statistics | 2006

Efficiency Measurement: A Nonparametric Approach

Yves Aragon; Abdelaati Daouia; Christine Thomas-Agnan

The aim of the paper is to present a statistical methodology allowing a meaningful comparison of the production performance of firms without resorting to the usual concept of production frontier. We introduce an efficiency measure based on a nonstandard conditional distribution and propose a two-stage estimation procedure with a smoothing step followed by an isotonization step. We illustrate the approach through a simulated example and an analysis of the performance of Spanish electricity distributors.


Archive | 2011

Nadaraya’s Estimates for Large Quantiles and Free Disposal Support Curves

Abdelaati Daouia; Laurent Gardes; Stéphane Girard

A new characterization of partial boundaries of a free disposal multivariate support, lying near the true support curve, is introduced by making use of large quantiles of a simple transformation of the underlying multivariate distribution. Pointwise empirical and smoothed estimators of the full and partial support curves are built as extreme sample and smoothed quantiles. The extreme-value theory holds then automatically for the empirical frontiers and we show that some fundamental properties of extreme order statistics carry over to Nadaraya’s estimates of upper quantile-based frontiers. The benefits of the new class of partial boundaries are illustrated through simulated examples and a real data set, and both empirical and smoothed estimates are compared via Monte Carlo experiments. When the transformed distribution is attracted to the Weibull extreme-value type distribution, the smoothed estimator of the full frontier outperforms frankly the sample estimator in terms of both bias and Mean-Squared Error, under optimal bandwidth. In this domain of attraction, Nadaraya’s estimates of extreme quantiles might be superior to the sample versions in terms of MSE although they have a higher bias. However, smoothing seems to be useless in the heavy tailed case.


Statistics | 2009

Large deviation properties for empirical quantile-type production functions

Abdelaati Daouia; Cyrille Joutard

In standard microeconomic theory of the firm, the production frontier is used to describe the geometric locus of the optimal production. Most limitations of the conventional estimators of this efficient frontier stem from its reliance on estimation of the upper surface of the joint support of (X, Y), where X∈ℝ p + represents the inputs-usage and Y∈ℝ+ is the produced output. Instead, a recent approach involving the estimation of a partial quantile-type frontier of the joint support, lying close to its full boundary, has emerged in the literature as an attractive alternative. In this paper, we present a new and simple proof of the asymptotic normality of the resulting nonparametric frontier estimators and provide an estimate for the accuracy of the normal approximation. We also propose a Kiefer-type asymptotic representation for these estimators. The main results concern the study of some weak, moderate and strong large deviation properties of the quantile-based frontier estimators.


Journal of the American Statistical Association | 2018

Extremiles: A new perspective on asymmetric least squares

Abdelaati Daouia; Irène Gijbels; Gilles Stupfler

ABSTRACT Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. This article considers a valuable alternative class to expectiles, called extremiles, which parallels the class of quantiles and includes the family of expected minima and expected maxima. The new class is motivated via several angles, which reveals its specific merits and strengths. Extremiles suggest better capability of fitting both location and spread in data points and provide an appropriate theory that better displays the interesting features of long-tailed distributions. We discuss their estimation in the range of the data and beyond the sample maximum. A number of motivating examples are given to illustrate the utility of estimated extremiles in modeling noncentral behavior. There is in particular an interesting connection with coherent measures of risk protection. Supplementary materials for this article are available online.


Annals of Operations Research | 2010

Mass transportation and the consistency of the empirical optimal conditional locations

Florent Bonneu; Abdelaati Daouia

We consider the problem of finding the optimal locations of new facilities given the locations of existing facilities and clients. We analyze the general situation where the locations of existing facilities are deterministic while the locations of clients are stochastic with the same unknown marginal distribution. We show how this conditional location-allocation problem can be modeled as a variation of the standard Monge-Kantorovich mass transference problem. We provide a probabilistic formulation of the optimal locations of the new facilities and derive consistent estimators of these theoretical locations from a sample of identically distributed random clients. The integrity of our method is illustrated through some simulation experiments and a real case study.

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Léopold Simar

Université catholique de Louvain

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Laurent Gardes

University of Strasbourg

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Irène Gijbels

Katholieke Universiteit Leuven

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Yves Aragon

University of Toulouse

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Hohsuk Noh

Université catholique de Louvain

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