Uniform rate of strong consistency for a smooth kernel estimator of the conditional mode for censored time series

Asymptotic normality of conditional density and conditional mode in the functional single index model

“…In the case of censoring, Ould-Saïd and Cai (2005) established the strong uniform convergence (with rate) of kernel conditional mode estimator for i.i.d random variables, while Ould-Saïd ( 2006) constructed a kernel estimator of the conditional quantile and establish its strong uniform convergence rate. Next, (Khardani, Lemdani, and Ould-Saïd, 2010) obtained strong consistency with the rate and asymptotic normality of the conditional mode (Khardani, Lemdani, and Ould-Saïd, 2011) established strong consistency with the rate of the conditional mode for the censored dependent case, while (Khardani, Lemdani, and Ould-Saïd, 2014) presented asymptotic normality.…”

Modal regression using kernel density estimation: A review

“…Under the assumptions on conditional density, the covariate is more responsible for the smoothing effect than the response. Various studies have reported the convergence of unimodal regression with dependent covariates (Attaoui, 2014;Collomb et al, 1986;Dabo-Niang & Laksaci, 2010;Khardani et al, 2010Khardani et al, , 2011Ould-Saïd, 1993, 1997Ould-Saïd & Cai, 2005). Strong consistency was investigated in Collomb et al (1986)) and Ould-Saïd (1993, 1997).…”

“…Note that the joint PDF can be estimated by other approaches such as local polynomial estimation as well (Einbeck & Tutz, 2006;Fan, Yao, & Tong, 1996;Fan & Yim, 2004). Equation (4) has been generalized to the case of censored response variables (Khardani, Lemdani, & Saïd, 2010, 2011Ould-Saïd & Cai, 2005). Suppose that instead of observing the response variables Y 1 , Á Á Á, Y n , we observe T i = min {Y i , C i } and an indicator δ i = I(T i = Y i ) that informs whether Y i is observed or not and C i is a random variable that is independent of X i and Y i .…”

“…Strong consistency was investigated in Collomb et al (1986)) and Ould-Saïd (1993, 1997). The convergence rate has also been derived in unimodal regression with functional dependent covariates (Attaoui, 2014;Dabo-Niang & Laksaci, 2010), and with censored response (Khardani et al, 2010(Khardani et al, , 2011Ould-Saïd & Cai, 2005).…”

A strong linear representation for the maximum conditional hazard rate estimator in survival analysis

“…Much research has been devoted to the estimation of the unconditional and conditional mode. We focus on recent papers based on conditional mode estimators to mention [25,29,22,26,4,9,15,16].…”