ME.fcQR_CLS: Bias correction method of applying quantile linear regression...

In MECfda: Scalar-on-Function Regression with Measurement Error Correction

Bias correction method of applying quantile linear regression to dataset with one functional covariate with measurement error using corrected loss score method.

Description

Zhang et al. proposed a new corrected loss function for a partially functional linear quantile model with functional measurement error in this manuscript. They established a corrected quantile objective function of the observed measurement that is an unbiased estimator of the quantile objective function that would be obtained if the true measurements were available. The estimators of the regression parameters are obtained by optimizing the resulting corrected loss function. The resulting estimator of the regression parameters is shown to be consistent.

Usage

ME.fcQR_CLS(
  data.Y,
  data.W,
  data.Z,
  tau = 0.5,
  t_interval = c(0, 1),
  t_points = NULL,
  grid_k,
  grid_h,
  degree = 45,
  observed_X = NULL
)

Arguments

data.Y	Response variable, can be an atomic vector, a one-column matrix or data frame, recommended form is a one-column data frame with column name.
data.W	A 3-dimensional array, represents W, the measurement of X. Each row represents a subject. Each column represent a measurement (time) point. Each layer represents an observation.
data.Z	Scalar covariate(s), can be not input or NULL (when there's no scalar covariate), an atomic vector (when only one scalar covariate), a matrix or data frame, recommended form is a data frame with column name(s).
tau	Quantile \tau\in(0,1), default is 0.5.
t_interval	A 2-element vector, represents an interval, means the domain of the functional covariate. Default is c(0,1), represent interval [0,1].
t_points	Sequence of the measurement (time) points, default is NULL
grid_k	An atomic vector, of which each element is candidate number of basis.
grid_h	A non-zero-value atomic vector, of which each element is candidate value of tunning parameter.
degree	Used in computation for derivative and integral, defult is 45, large enough for most scenario.
observed_X	For estimating parametric variance. Default is NULL.

Value

Returns a ME.fcQR_CLS class object. It is a list that contains the following elements.

estimated_beta_hat	Estimated coefficients from corrected loss function (including functional part)
estimated_beta_t	Estimated functional curve
SE_est	Estimated parametric variance. Returned only if observed_X is not NULL.
estimated_Xbasis	The basis matrix we used
res_naive	results of naive method

References

Zhang, Mengli, et al. "PARTIALLY FUNCTIONAL LINEAR QUANTILE REGRESSION WITH MEASUREMENT ERRORS." Statistica Sinica 33 (2023): 2257-2280.

Examples

data(MECfda.data.sim.0.1)

res = ME.fcQR_CLS(data.Y = MECfda.data.sim.0.1$Y,
                data.W = MECfda.data.sim.0.1$W,
               data.Z = MECfda.data.sim.0.1$Z,
               tau = 0.5,
               grid_k = 4:7,
               grid_h = 1:2)

MECfda documentation built on April 3, 2025, 10:07 p.m.