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Abstract:
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Nonparametric estimation of unknown statistical constants gain remarkable popularity among applied researchers. Nonparametric estimation is adaptable to a wide range of problems, which parametric alternatives are unable to accommodate because of strict parametric assumption and unknown functional form of the data. In this paper, we develop three smoothing estimators for nonparametric smoothing quantile estimation and compare their relative performance among themselves as well as with the fitted values from the quantile regression. Estimation is based on a two-step nonparametric procedure, in which we first get the nonparametric estimate of the extreme quantiles at a set of disjoint time points and in second step, we smooth them over entire time range. Estimators obtained in the first step and second step are respectively treated as the raw estimators and smoothing estimators. We call these second step estimators as two-step local polynomial smoothing estimator, two-step kernel smoothing estimator and two-step spline smoothing estimator. By application on temperature data and simulation, we will show that our two step smoothing estimator is better than quantile regression estimator.
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