robflreg (version 1.3)

fpqr: Function-on-function partial quantile regression

Description

This function is used to perform function-on-function linear quantile regression model $$ Q_{\tau}[Y(u)|X(v)] = \int X(v) \beta_{\tau}(u,v) dv$$ based on the functional partial quantile regression.

Usage

fpqr(y, x, h, tau, nby, nbx, gpy, gpx, qc.type = c("dodge","choi","li"),
hs, nbys, nbxs, nfold, CV)

Value

fitted.values

An matrix containing the fitted values of the functional response.

b0.hat

A vector containing the estimate of intersecp parameter.

b.hat

A matrix containing the estimate of bivariate regression coefficient coducted between the functional response and functional predictor.

mdts

A numeric value containing the estimated intercept parameter.

pqr.coefs

A vector containing the estimated regression parameter for the regression problem of scalar response on the partial quantile regression components.

V

A matrix whose rows are the eigenvectors

model.details

A list object containing model details, such as number of basis functions, number of partial quantile components, and grid points used for the functional variables.

Arguments

y

An matrix containing the observations of function response \(Y(u)\).

x

A matrix containing the observations of functional predictor \(X(v)\).

h

A numeric value denoting the number of functional partial quantile regression components to be computed.

tau

Quantile level.

nby

A numeric value denoting the number of B-spline basis expansion functions to be used to approximate the functional response variable.

nbx

A numeric value denoting the number of B-spline basis expansion functions to be used to approximate the functional predictor variable.

gpy

A vector containing the grid points of the functional response \(Y(u)\).

gpx

A vector containing the grid points of the functional predictor \(X(v)\).

qc.type

Method type used to estimate the quantile covariance. Possibilities are "dodge", "choi", and "li".

hs

A vector containing the candidate elements for the h.

nbys

A vector containing the candidate elements for the nby.

nbxs

A vector containing the candidate elements for the nbx.

nfold

An integer denoting the number of folds used in the k-fold cross validation. Default value is 5.

CV

Logical. If TRUE, then nfold cross-validation is used to find optimum values of h, nby, and nbx. If FALSE, then the specified h, nby, and nbx values are used in the model.

Author

Muge Mutis, Ufuk Beyaztas, Filiz Karaman, and Han Lin Shang

Details

If qc.type = "dodge", then, the quantile covariance proposed by Dodge and Whittaker (2009) is used in the functional partial quantile regression decomposition.

If qc.type = "choi", then, the quantile covariance proposed by Choi and Shin (2018) is used in the functional partial quantile regression decomposition.

If qc.type = "li", then, the quantile covariance proposed by Li et al. (2015) is used in the functional partial quantile regression decomposition.

References

Y. Dodge and J. Whittaker (2009), "Partial quantile regression", Metrika, 70(1), 35-57. J. E.. Choi and D. W. Shin (2018), "Quantile correlation coefficient: A new tail dependence measure", Statistical Papers, 63, 1075-1104. G. Li and Y. Li and C. L. Tsai (2015), "Quantile correlations and quantile autoregressive modeling" Journal of American Statistical Association: Theory and Methods, 110(509), 246-261.

Examples

if (FALSE) {
  gpx <- (1:50)/50
  gpy <- (1:60)/60
  data <- fpqr_dgp(n = 100, gpy = gpy, gpx = gpx, err.dist = "normal")
  y <- data$y
  x <- data$x

  fpqr.model.dodge <- fpqr(y=y, x=x, tau = 0.5, gpx = gpx, gpy = gpy,
                           qc.type = "dodge")

  fpqr.model.choi <- fpqr(y=y, x=x, tau = 0.5, gpx = gpx, gpy = gpy,
                          qc.type = "choi")

  fpqr.model.li <- fpqr(y=y, x=x, tau = 0.5, gpx = gpx, gpy = gpy,
                        qc.type = "li")
}