In this paper we propose a method for nonparametric regression which admits continuous and catego... more In this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels. A data-driven method of bandwidth selection is proposed, and we establish the asymptotic normality of the estimator. We also ...
The optimal sampling problem for the estimation of an integral, based on observations, with rando... more The optimal sampling problem for the estimation of an integral, based on observations, with random and correlated measurement errors is treated. Considering the effect of the quantization of errors, we determine the optimal design, which is constructed by utilizing stochastic algorithms. The efficiency of the Genetic Algorithm is confirmed by comparison with other implemented algorithms, by considering a pharmacokinetic application for a test of bioavailability. A multiobjective approach is proposed for the choice of an optimal compromise design between the variability of the quantization of errors and the integral's estimator..
ABSTRACT The problem of interest is to estimate the concentration curve and the area under the cu... more ABSTRACT The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with an autocorrelated error process. We introduce a simple linear unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from a sampling design generated by an appropriate density is asymptotically optimal in the sense that it has exactly the same asymptotic performance as the best linear unbiased estimator. Moreover, we prove that the optimal design is robust with respect to a minimax criterion. When repeated observations are available, this estimator is consistent and has an asymptotic normal distribution. Finally, a simulated annealing algorithm is applied to a pharmacokinetic model with correlated errors.
ABSTRACT We consider the problem of predicting integrals of second order processes whose covarian... more ABSTRACT We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.
In this paper we propose a method for nonparametric regression which admits continuous and catego... more In this paper we propose a method for nonparametric regression which admits continuous and categorical data in a natural manner using the method of kernels. A data-driven method of bandwidth selection is proposed, and we establish the asymptotic normality of the estimator. We also ...
The optimal sampling problem for the estimation of an integral, based on observations, with rando... more The optimal sampling problem for the estimation of an integral, based on observations, with random and correlated measurement errors is treated. Considering the effect of the quantization of errors, we determine the optimal design, which is constructed by utilizing stochastic algorithms. The efficiency of the Genetic Algorithm is confirmed by comparison with other implemented algorithms, by considering a pharmacokinetic application for a test of bioavailability. A multiobjective approach is proposed for the choice of an optimal compromise design between the variability of the quantization of errors and the integral's estimator..
ABSTRACT The problem of interest is to estimate the concentration curve and the area under the cu... more ABSTRACT The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with an autocorrelated error process. We introduce a simple linear unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from a sampling design generated by an appropriate density is asymptotically optimal in the sense that it has exactly the same asymptotic performance as the best linear unbiased estimator. Moreover, we prove that the optimal design is robust with respect to a minimax criterion. When repeated observations are available, this estimator is consistent and has an asymptotic normal distribution. Finally, a simulated annealing algorithm is applied to a pharmacokinetic model with correlated errors.
ABSTRACT We consider the problem of predicting integrals of second order processes whose covarian... more ABSTRACT We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.
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Papers by Karim Benhenni