Generalised kernel smoothing for non-negative stationary ergodic processes

Abstract

In this paper, we consider a generalized kernel smoothing estimator of the regression function with non-negative support, using gamma probability densities as kernels, which are nonnegative and have naturally varying shapes. It is based on a generalization of Hille's lemma and a perturbation idea that allows us to deal with the problem at the boundary. Its uniform consistency and asymptotic normality are obtained at interior and boundary points, under a stationary ergodic process assumption, without using traditional mixing conditions. The asymptotic mean squared error of the estimator is derived and the optimal value of smoothing parameter is also discussed. Graphical illustrations of the proposed estimator are provided for simulated as well as for real data. A simulation study is also carried out to compare our method with the competing local linear method.

Response of a boreal forest to canopy opening: assessing vertical and lateral tree growth with multi-temporal lidar data

“…In fact, interior hardwood trees grow at a consistent rate of 0.1, i.e., 10% of their initial height over five years, which is slower than gap edge and gap island hardwood trees over the entire range of height. However, it should be noted that although no samples of interior hardwood trees were found below 13.9 m in height, the estimated regression models are expected to be unbiased near the boundaries (Chaubey et al 2010). Comparatively, gap island hardwood trees have the highest average growth rate with nearly 75% of the trees having a growth over 0.25 over the five years.…”

“…Nonparametric regression is a form of regression analysis where the predictor does not take a predetermined form but is constructed according to information derived from the data. To predict the maximum rate of growth over five years for a given initial height we used a nonparametric regression estimator for nonnegative random variables proposed by Chaubey et al (2010), which converges to the true regression function m ( x ) defined as The nonparametric regression estimator is of the form which is of the form of a weighted average ∑ Y i W i ( x ), ∑ W i ( x ) = 1. Here is a gamma density function with mean x + ε n and variance ( x + ε n ) 2 .…”

“…Nonparametric regression is a form of regression analysis where the predictor does not take a predetermined form but is constructed according to information derived from the data. To predict the maximum rate of growth over five years for a given initial height we used a nonparametric regression estimator for nonnegative random variables proposed by Chaubey et al (2010), which converges to the true regression function m(x) defined as…”

Generalized kernel regression estimator for dependent size-biased data

“…Ordinary kernel regression does not provide admissible values of the regression, or its functionals at the boundaries for restricted support regressions (see, e.g., Chaubey et al (2010) for further discussion). In this paper consider the setting of biased data that typically features non-negative observations.…”

“…In this paper consider the setting of biased data that typically features non-negative observations. We extend the methodology given in Chaubey et al (2010) to this setup, for constructing a nonparametric regression estimator that allows to deal with the boundary bias problem. In this setup the density of biased data is given by a target density weighted by some function of the observations.…”