A nonparametric conditional mode estimate

Abstract

This paper proposes a new nonparametric estimate of the conditional mode. This mode estimate is obtained from kernel smoothing of the first derivative of the conditional density function with location adaptive bandwidth. We give the rates of convergence of this estimate under general dependence conditions on the sample that make our results valid for nonparametric prediction of time series. As a by-products, we also get rate of convergence of the usual mode of a density function under dependence, and we give some extensions to local bandwidth of recent results on kernel estimation under mixing conditions.

Regression towards the mode

“…Also, as noted in Section 2, our assumptions can be modified to allow for some dependency in the data, as is typically found in time-series applications. This extension can be very useful, for example in applications involving forecasting (see, e.g., Collomb et al, 1987;Quintela-Del-Rio and Vieu, 1997;Wallis, 1999). A related area for possible future research is the consideration of functional data as in the recent papers by Ezzahrioui and Ould Saïd (2010) and Ferraty et al (2012).…”

“…Likewise, non-parametric estimation of the conditional mode is the subject of many papers in statistical journals (e.g., Collomb et al, 1987;Samanta and Thavaneswarn, 1990;Quintela-Del-Rio and Vieu, 1997). 1 Less attention, however, has been devoted to the case that is most likely to be useful in econometric applications, that is, the semi-parametric case in which the conditional mode is specified ✩ We are very grateful to the Associate Editor and to four referees for their many constructive and helpful comments.…”

Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models

“…The literature on conditional mode estimation is quite important when the explanatory variable X is real (see for instance Collomb et al [8], for previous works and Quintela and Vieu [24], Berlinet et al [2], or Louani and OuldSaïd [21], for recent advances and references). Concerning the functional case, Gasser et al [17] proposed an estimate of the mode of a distribution of random curves (i.e.…”

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].…”