We consider a class of stochasticapproximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locall...
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We consider a class of stochasticapproximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locally Lipschitz continuous. Here, we show that this condition can be relaxed to the extent that the estimating functions are bounded and continuous almost everywhere. As a consequence, the use of the SA algorithm can be extended to some problems with irregular estimating functions. Our theoretical results are illustrated by solving an estimation problem for exponential power mixture models.
In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandw...
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In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non-recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.
We propose a recursive distribution estimator using Robbins-Monro's algorithm and Bernstein polynomials. We study the properties of the recursive estimator, as a competitor of Vitale's distribution estimator. ...
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We propose a recursive distribution estimator using Robbins-Monro's algorithm and Bernstein polynomials. We study the properties of the recursive estimator, as a competitor of Vitale's distribution estimator. We show that, with optimal parameters, our proposal dominates Vitale's estimator in terms of the mean integrated squared error. Finally, we confirm theoretical result throught a simulation study.
We apply the stochasticapproximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil [1994. On the efficiency of on-line densi...
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We apply the stochasticapproximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil [1994. On the efficiency of on-line density estimators. IEEE Trans. Inform. Theory 40, 1504-1512]. We study the properties of these estimators and compare them with Rosenblatt's nonrecursive estimator. It turns out that, for pointwise estimation, it is preferable to use the nonrecursive Rosenblatt's kernel estimator rather than any recursive estimator. A contrario, for estimation by confidence intervals, it is better to use a recursive estimator rather than Rosenblatt's estimator. (C) 2008 Elsevier B.V. All rights reserved.
In the present paper, we are mainly concerned with a family of kernel type estimators based upon spatial data. More precisely, we establish large and moderate deviations principles for the recursive kernel estimators ...
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In the present paper, we are mainly concerned with a family of kernel type estimators based upon spatial data. More precisely, we establish large and moderate deviations principles for the recursive kernel estimators of a regression function for spatial data defined by the stochastic approximation algorithm. (C) 2019 Elsevier B.V. All rights reserved.
We apply the stochasticapproximation method to construct a large class of recursive kernel estimators of a distribution function. We study the properties of these estimators and compare them with Nadaraya's distr...
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We apply the stochasticapproximation method to construct a large class of recursive kernel estimators of a distribution function. We study the properties of these estimators and compare them with Nadaraya's distribution estimator. It turns out that, with an adequate choice of the stepsize of the proposed algorithm, the MWISE (Mean Weighted Integrated Squared Error) of the proposed estimator is smaller than that of Nadaraya's estimator. We corroborate these theoretical results by simulations and a real dataset.
In this research paper, we apply the stochasticapproximation method to define a class of recursive kernel estimator of the conditional extreme value index. We investigate the properties of the proposed recursive esti...
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In this research paper, we apply the stochasticapproximation method to define a class of recursive kernel estimator of the conditional extreme value index. We investigate the properties of the proposed recursive estimator and compare them to those pertaining to Hill's non-recursive kernel estimator. We show that using some optimal parameters, the proposed recursive estimator defined by the stochastic approximation algorithm proves to be very competitive to Hill's non-recursive kernel estimator. Finally, the theoretical results are confirmed through simulation experiments and illustrated using a real dataset about Malaria in Senegalese children.
In this paper we show how one can implement in practice the bandwidth selection in deconvolution recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm. We cons...
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In this paper we show how one can implement in practice the bandwidth selection in deconvolution recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm. We consider the so called super smooth case where the characteristic function of the known distribution decreases exponentially. We show that, using the proposed bandwidth selection and some special stepsizes, the proposed recursive estimator will be very competitive to the nonrecursive one in terms of estimation error and much better in terms of computational costs. We corroborate these theoretical results through simulations and a real dataset.
Important information concerning a multivariate data set, such as modal regions, is contained in the derivatives of the probability density or regression functions. Despite this importance, nonparametric estimation of...
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Important information concerning a multivariate data set, such as modal regions, is contained in the derivatives of the probability density or regression functions. Despite this importance, nonparametric estimation of higher order derivatives of the density or regression functions have received only relatively scant attention. The main purpose of the present work is to investigate general recursive kernel type estimators of function derivatives. We establish the central limit theorem for the proposed estimators. We discuss the optimal choice of the bandwidth by using the plug in methods. We obtain also the pointwise MDP of these estimators. Finally, we investigate the performance of the methodology for small samples through a short simulation study.
The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered *** authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the syst...
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The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered *** authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the systems,adaptive regulators are directly designed based on the event-triggered observations on the regulation *** adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions,the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically *** authors also testify the theoretical results through simulation studies.
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