On the consistency of a new kernel rule for spatially dependent data

Strong consistency of a kernel-based rule for spatially dependent data

“…Note that the assumption on the bandwidth, using by [21] to prove the weak consistency, is similar to the classical assumption used by [7] and [8] in the independent case. In addition, the condition on bboldn is minimal compared to that used by [4] and [3] since they have studied the rate of uniform convergence for the estimators.…”

“…Hence, the Gaussian kernel is regular. Assumption 2, used by [21] to prove the weak consistency, is similar to that used by [3]. It is satisfied for example if f and fi,j are uniformly bounded.…”

“…Using Markov’s inequality and Lemma 3.3 together with (7.7), we have for any ϵ>0,where ρ>0 is the constant defined in Lemma 3.3. Since r˜ is bounded and p→∞ as n→∞, so p−r˜≥p/2 for truen^ large enough.…”

“…This nonparametric classifier allows for the classification of missing spatially dependent data. The weak consistency of the classifier has been studied by Younso (2017). The purpose of this paper is to establish strong consistency of this classifier under mild conditions.…”

On Nonparametric Conditional Quantile Estimation for Non-stationary Random

“…For the recent review in nonparametric regression context, one can refer to Dabo-Niang et al(2014), Ternynck (2014b), Younso (2017). Attouch et al(2017) proposed an alternative kernel of regression function based on the minimization of the mean square error.…”