LocalPolyRegMain {npDoseResponse}

The main function of the (partial) local polynomial regression.

Description

This function implements the main part of the (partial) local polynomial regression for estimating the conditional mean outcome function and its partial derivatives.

Usage

LocalPolyRegMain(
  Y,
  X,
  x_eval = NULL,
  degree = 2,
  deriv_ord = 1,
  h = NULL,
  b = NULL,
  kernT = "epanechnikov",
  kernS = "epanechnikov"
)

Arguments

Y

The input n-dimensional outcome variable vector.

X

The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.

x_eval

The n*(d+1) matrix for evaluating the local polynomial regression estimates. (Default: x_eval = NULL. Then, x_eval = X.)

degree

Degree of local polynomials. (Default: degree = 2.)

deriv_ord

The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1.)

h, b

The bandwidth parameters for the treatment/exposure variable and confounding variables (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)

kernT, kernS

The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)

Value

The estimated conditional mean outcome function or its partial derivatives evaluated at points x_eval.

Author(s)

Yikun Zhang, [e-mail]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman & Hall/CRC.