This study aims to examine the impact of coal energy consumption on economic progress in Pakistan by using annual time series data during 1972–2019. Three-unit root tests were employed rectify variables’ stationarity. The quantile regression approach with extension cointegration test was utilized check variables interaction progress. outcomes uncover that power sector and brick kilns have adver...

Abstract The conditional quantile function m(X) of response variable Y given the value of covariate X is modeled through a single-index model, i.e. m(X) = m(θ 0 X) for some unknown parameter vector θ0. An iterated algorithm is proposed to estimate θ0. To establish the root-n consistency of the estimator, we prove a convexity lemma for almost sure convergence, parallel to the results by Pollard ...

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulatio...

the main idea of this paper is to study the dependence between the probability of default and the recovery rate on credit portfolio and to seek empirically this relationship. we examine the dependence between pd and rr by theoretical approach. for the empirically methodology, we use the bootstrapped quantile regression and the simultaneous quantile regression. these methods allow to determinate...

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse p...

Local-to-unity and moderate-deviations specifications have been popular alternatives to unit root modeling. This article considers another kind of departures from a root, the form c v t / T β , where is random determines distance root. We classify stochastic into two types: local moderate. classification task completed by investigating asymptotic behavior tests that assume (STUR) processes as a...

• Central properties of geometric quantiles have been well-established in the recent statistical literature. In this study, we try to get a grasp of how extreme geometric quantiles behave. Their asymptotics are provided, both in direction and magnitude, under suitable moment conditions, when the norm of the associated index vector tends to one. Some intriguing properties are highlighted: in par...

Abstract Based on the quantile regression, we extend Koenker and Xiao (2004) Ling McAleer (2004)’s works from finite-variance innovations to infinite-variance innovations. A robust t -ratio statistic test for unit-root a re-sampling method approximate critical values of are proposed in this paper. It is shown that limit distribution functional stable processes Brownian bridge. The finite sample...