# SemiQRegGALaD: Semiparametric quantile regression in generalized Laplace... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

The local polynomial technique is used to estimate location and scale functions of the quantile-based asymmetric Laplace distribution as discussed in Gijbels et al. (2019c). Using these estimates, the quantile function of the generalized asymmetric Laplace distribution will be estimated. A detailed study can be found in Gijbels et al. (2019b).

## Usage

 1 2 SemiQRegGALaD(beta, x, y, p1 = 1, p2 = 1, h, alpha = NULL, g, lower = -Inf, upper = Inf, m = 101) 

## Arguments

 beta This is a specific probability for estimating βth quantile function. x This is a conditioning covariate. y The is a response variable. p1 This is the order of the Taylor expansion for the location function (i.e.,μ(X)) in local polynomial fitting technique. The default value is 1. p2 This is the order of the Taylor expansion for the log of scale function (i.e., \ln[φ(X)]) in local polynomial fitting technique. The default value is 1. h This is the bandwidth parameter h. alpha This is the index parameter α of the generalized asymmetric Laplace density. The default value of α is NULL in the code SemiQRegGALaD. In this case, the α will be estimated based on the residuals form local linear mean regression. g This is the "link" function. The function g is to be differentiated. Therefore, g must be written as a function. For example, g<-function(y){log(y)} for log link function. lower This is the lower limit of the domain (support of the random variable) f_{α}^g(y;η,φ), default -Inf. upper This is the upper limit of the domain (support of the random variable) f_{α}^g(y;η,φ), default Inf. m This is the number of grid points at which the functions are to be evaluated. The default value is 101.

## Value

The code SemiQRegGALaD provides the realized value of the βth conditional quantile estimator by using semiparametric quantile regression technique discussed in Gijbels et al. (2019b) and Gijbels et al. (2019c).

## References

Gijbels, I., Karim, R. and Verhasselt, A. (2019b). Quantile estimation in a generalized asymmetric distributional setting. To appear in Springer Proceedings in Mathematics & Statistics, Proceedings of ‘SMSA 2019’, the 14th Workshop on Stochastic Models, Statistics and their Application, Dresden, Germany, in March 6–8, 2019. Editors: Ansgar Steland, Ewaryst Rafajlowicz, Ostap Okhrin.

Gijbels, I., Karim, R. and Verhasselt, A. (2019c). Semiparametric quantile regression using quantile-based asymmetric family of densities. Manuscript.

## Examples

  1 2 3 4 5 6 7 8 9 10 data(LocomotorPerfor) x=log(LocomotorPerfor$Body_Mass) y=LocomotorPerfor$MRRS # For log-link function g_log<-function(y){log(y)} h_ROT = 0.9030372 fit<-SemiQRegGALaD(beta=0.90,x,y,p1=1,p2=1,h=h_ROT,g=g_log,lower=0) plot(x,y) lines(fit$x0,fit$qf_g) 

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.