kdbwselect: Bandwidth Selection Procedures for Kernel Density Estimation...

In nprobust: Kernel Density and Local Polynomial Regression Methods

Bandwidth Selection Procedures for Kernel Density Estimation and Inference

Description

kdbwselect implements bandwidth selectors for kernel density point estimators and inference procedures developed in Calonico, Cattaneo and Farrell (2018). See also Calonico, Cattaneo and Farrell (2022) for related optimality results. It also implements other bandwidth selectors available in the literature.

Companion commands are: kdrobust for kernel density point estimation and inference procedures.

A detailed introduction to this command is given in Calonico, Cattaneo and Farrell (2019). For more details and related software useful for empirical analysis, visit https://nppackages.github.io/.

Usage

kdbwselect(x, eval = NULL, neval = NULL, kernel = "epa",
bwselect = "mse-dpi", bwcheck=21, imsegrid=30, subset = NULL, data = NULL)

Arguments

x	independent variable.
eval	vector of evaluation point(s). By default it uses 30 quantile-spaced points (deciles 0.1 to 0.9 in equal steps) over the support of x.
neval	number of quantile-spaced evaluation points on the support of x. Default is neval=30.
kernel	kernel function used to construct the kernel estimators. Options are epa for the epanechnikov kernel, and uni for the uniform kernel. Default is kernel = epa.
bwselect	bandwidth selection procedure to be used. Options are: mse-dpi second-generation DPI implementation of MSE-optimal bandwidth. Default option. imse-dpi second-generation DPI implementation of IMSE-optimal bandwidth (computed using grid of evaluation points selected). imse-rot ROT implementation of IMSE-optimal bandwidth (computed using grid of evaluation points selected). ce-dpi second generation DPI implementation of CE-optimal bandwidth. ce-rot ROT implementation of CE-optimal bandwidth. all reports all available bandwidth selection procedures. Note: MSE = Mean Square Error; IMSE = Integrated Mean Squared Error; CE = Coverage Error; DPI = Direct Plug-in; ROT = Rule-of-Thumb. For details on implementation see Calonico, Cattaneo and Farrell (2019).
bwcheck	if a positive integer is provided, then the selected bandwidth is enlarged so that at least bwcheck effective observations are available at each evaluation point. Default is bwcheck = 21.
imsegrid	number of evaluations points used to compute the IMSE bandwidth selector. Default is imsegrid = 30.
subset	optional rule specifying a subset of observations to be used.
data	an optional data frame. When supplied, x and subset may be given as bare variable names referring to columns of data.

Value

bws	A matrix containing eval (grid points), h and b (selected bandwidths) for each evaluation point. When bwselect="all", the matrix is widened to include both MSE and CER bandwidths from each of the DPI and ROT estimators.
bws.imse	IMSE-optimal bandwidths returned when bwselect="all"; NULL otherwise.
opt	A list containing options passed to the function.

Author(s)

Sebastian Calonico, University of California, Davis, CA. [e-mail].

Matias D. Cattaneo, Princeton University, Princeton, NJ. [e-mail].

Max H. Farrell, University of California, Santa Barbara, CA. [e-mail].

References

Calonico, S., M. D. Cattaneo, and M. H. Farrell. 2018. On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference. Journal of the American Statistical Association, 113(522): 767-779. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2017.1285776")}.

Calonico, S., M. D. Cattaneo, and M. H. Farrell. 2019. nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference. Journal of Statistical Software, 91(8): 1-33. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v091.i08")}.

Calonico, S., M. D. Cattaneo, and M. H. Farrell. 2022. Coverage Error Optimal Confidence Intervals for Local Polynomial Regression. Bernoulli, 28(4): 2998-3022.

See Also

kdrobust

Examples

x   <- rnorm(500)
est <- kdbwselect(x)
summary(est)

nprobust documentation built on May 19, 2026, 9:07 a.m.