Stein’s result has transformed common belief in statistical world that the maximum likelihood estimator, which is in common use for more than a century, is optimal. Charles Stein showed in 1955 that it is possible to uniformly improve the maximum likelihood estimator (MLE) for the Gaussian model in terms of total squared error risk when several parameters are estimated simultaneously from indep...

Researchers are currently developing new value-added uses for almond shells, an abundant agricultural by-product. Almond varieties are distinguished by processors as being either hard or soft shelled, but these two broad classes of almond also exhibit varietal diversity in shell morphology and physical characters. By defining more precisely the physical and chemical characteristics of almond sh...

In this paper we prove rates of uniform strong convergence, convergence rates of the mean square error and the asymptotic normality of the kernel estimator for the transition density of a geometrically ergodic Markov chain. The assumptions on the Markov chain are closely related to absolute regularity. We allow the initial distribution of the Markov chain to be arbitrary.

The main purpose of this work is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the consta...

We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive theoretical results by giving a deep asymptotic study of the behaviour of the estimate, including mean squared convergence (with rates and precise evaluation of ...

Considering the possibility of the harmful side effects of synthetic antioxidants, it is necessary to substitute the synthetic antioxidants by the natural ones, the antioxidants that have been consumed by man for years. The mango seeds were washed and air dried and the kernels were removed manually from the seeds. Mango seed kernel oil was extracted by hexane using soxhlet extraction apparatus....

Small or shrivelled wheat kernels (screenings) that reduce crop value are commonly produced in terminal drought environments. The aim of this study was to establish whether the incorporation of the tiller inhibition (tin) gene would contribute to maintenance of kernel weight and reductions in screenings under terminal water deficit. Five Silverstar near-isogenic lines contrasting in high and lo...

In this paper, we establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator.

Measuring the diffusion properties of crossing fibers is very challenging due to the high number of model parameters involved and the intrinsically low SNR of Diffusion Weighted MR Images. Noise filtering aims at suppressing the noise while pertaining the data distribution. We propose an adaptive version of the Linear Minimum Mean Square Error (LMMSE) estimator to achieve this. Our filter appli...