SemiQRegGAND: Semiparametric quantile regression in generalized normal...
In QBAsyDist: Asymmetric Distributions and Quantile Estimation

Description Usage Arguments Value References Examples

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

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

`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 normal density. The default value of α is NULL in the code `SemiQRegGAND`. In this case, the α will be estimated based on the residuals from 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.

The code SemiQRegGAND 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).

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.

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<-SemiQRegGAND(beta=0.5,x,y,p1=1,p2=1,h=h_ROT,g=g_log,lower=0)
plot(x,y)
lines(fit$x0,fit$qf_g)