In this paper we propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm in the case of length-biased data...
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In this paper we propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm in the case of length-biased data. We compared our proposed plug-in method with the cross-validation method and the so-called smooth bootstrap bandwidth selector via simulations as well as a real data set. Results showed that, using the selected plug-in bandwidth and some special stepsizes, the proposed recursive estimators will be very competitive to the non-recursive one in terms of estimation error and much better in terms of computational costs.
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the...
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Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. This model was introduced by Benaim, Benjamini, Chen, and Lima. When G is not balanced bipartite, Chen and Lucas proved that the proportion of balls in the bins converges to a point w(G) almost surely. We prove almost sure convergence for balanced bipartite graphs: the possible limit is either a single point w(G) or a closed interval J(G).
In the present paper, we are mainly concerned with the kernel type estimators for the moment generating function. More precisely, we establish the central limit theorem together with the characterization of the bias a...
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In the present paper, we are mainly concerned with the kernel type estimators for the moment generating function. More precisely, we establish the central limit theorem together with the characterization of the bias and the variance for the nonparametric recursive kernel-type estimators for the moment generating function under some mild conditions. Finally, we investigate the performance of the methodology for small samples through a short simulation study.(c) 2022 Elsevier B.V. All rights reserved.
In this paper, we extend the work of Slaoui (J Probab Stat, http://***/10.1155/2014/739640, 2014) to the case of strong mixing data. Then, we study the properties of these estimators and compare them with Rosemblatt&#...
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In this paper, we extend the work of Slaoui (J Probab Stat, http://***/10.1155/2014/739640, 2014) to the case of strong mixing data. Then, we study the properties of these estimators and compare them with Rosemblatt's nonrecursive estimator. The bias, variance and MISE are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the nonrecursive density estimator under alpha-mixing condition in terms of estimation error and much better in terms of computational costs.
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