We propose a root n consistent estimator for β0 when the qth conditional quantile of Y given X=x and Z=z takes the semi linear form g(x)+z′β0 where g(.) is an unknown real valued function,β0 a finite dimensional parameter and (X,Z)a couple of explanatory variables.Importantly, our estimator attains,under homoscedasticity,the semi parametric efficiency bound.This estimation is conducted in two s...

A lot of time series analysis in economics and nance is to determine whether a unit root and/or seasonal unit root is present in the data. These tests are usually based on unit root tests orginally developed by Dickey & Fuller(1981). Testing for the presence of a seasonal root has been considered by Dickey, Hasza & Fuller (1984). Li(1991) considered tests for the existence of a seasonal and a r...

Exponential Smooth Transition Autoregressive (ESTAR) models can capture non-linear adjustment of the deviations from equilibrium conditions which may explain the economic behavior of many variables that appear non stationary from a linear viewpoint. Many researchers employ the Kapetanios test which has a unit root as the null and a stationary nonlinear model as the alternative. However this tes...

This paper considers nonparametric estimation of first-price auction models under the monotonicity restriction on the bidding strategy. Based on an integrated-quantile representation of the first-order condition, we propose a tuning-parameter-free estimator for the valuation quantile function. We establish its cube-root-n consistency and asymptotic distribution under weaker smoothness assumptio...

We congratulate Koenker and Xiao on their interesting and important contribution to the quantile autoregression (QAR). The paper provides a comprehensive overview on the QAR model, from probabilistic aspects, to model identification, statistical inferences, and empirical applications. The attempt to integrate the quantile regression and the QAR process is intriguing. It demonstrates surprisingl...

Sustainable development remains unattainable unless we move to reduce the negative impact of economic factors on environmental quality. It is noteworthy provide new evidence whether and how empirical association between export diversification, agricultural value-addition, renewable energy, regulatory quality with greenhouse gas (GHG) emissions evolved in Asian countries from 1996 2014. The stud...

sample standard deviation, is the square root of sample variance. • R book, page 50: The th quantile is at position in the sorted data. If this is not an integer, a weighted average is used. For example, as the median is the 0.5 quantile, if is even, the position is a fraction, and hence an average is used as shown above in the definition of median. The th quantile splits the dataset so that 10...