Generalized kernel regression estimator for dependent size-biased data

Abstract

This paper considers nonparametric regression estimation in the context of dependent biased non-negative data using a generalized asymmetric kernel. It may be applied to a wider variety of practical situations, such as the length and size biased data. We derive theoretical results using a deep asymptotic analysis of the behavior of the estimator that provides consistency and asymptotic normality in addition to the evaluation of the asymptotic bias term. The asymptotic mean squared error is also derived in order to obtain the optimal value of smoothing parameters required in the proposed estimator. The results are stated under a stationary ergodic assumption, without assuming any traditional mixing conditions. A simulation study is carried out to compare the proposed estimator with the local linear regression estimate.

Linear wavelet estimation of the derivatives of a regression function based on biased data

“…The most popular of them are the kernel methods. Important results on their performances can be found in, e.g., Ahmad (1995), Sköld (1999), Cristóbal and Alcalá (2000), Wu (2000), Cristóbal and Alcalá (2001), Cristóbal et al (2004), Ojeda et al (2007), Ojeda-Cabrera and Van Keilegom (2009) and Chaubey et al (2012). Recently, wavelet methods based on a multiresolution analysis has been developed for the estimation of ϕ.…”

Nonparametric Wavelet Regression Based on Biased Data

“…, (X n , Y n ). This nonparametric estimation problem has already been considered in several studies; see, e.g., Ahmad (1995), Sköld (1999), Cristóbal and Alcalá (2000), Wu (2000), Cristóbal and Alcalá (2001), Cristóbal et al (2004), Ojeda et al (2007), Ojeda-Cabrera and Van Keilegom (2009), and Chaubey et al (2012). It has potential applications in biology, economics and many other fields (see, e.g., the previous references and Patil and Taillie, 1989).…”

Average Derivative Estimation from Biased Data

“…This model has potential applications in biology, economics, and many other fields. Important results on methods and applications can be found in, for example, Ahmad [12], Sköld [13], Cristóbal and Alcalá [14], Wu [15], Cristóbal and Alcalá [16], Cristóbal et al [17], Ojeda et al [18], Cabrera and Van Keilegom [19], and Chaubey et al [20]. Wavelet methods related to this model can be found in Chesneau and Shirazi [21], Chaubey et al [22], and Chaubey and Shirazi [23].…”