MECfda (version 0.2.1)

ME.fcQR_CLS: 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
)

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

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.

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)
# \donttest{
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)
# }