lprobust: Local Polynomial Methods with Robust Bias-Corrected Inference

In nprobust: Kernel Density and Local Polynomial Regression Methods

Local Polynomial Methods with Robust Bias-Corrected Inference

Description

lprobust implements local polynomial regression point estimators, with robust bias-corrected confidence intervals 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 estimation and inference procedures available in the literature.

Companion commands: lpbwselect for local polynomial data-driven bandwidth selection, and nprobust.plot for plotting results.

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

lprobust(y, x, eval = NULL, neval = NULL, p = NULL, deriv = NULL,
h = NULL, b = NULL, rho = 1, kernel = "epa", bwselect = NULL,
bwcheck = 21, bwregul = 1, imsegrid = 30, vce = "nn", covgrid = FALSE,
cluster = NULL, nnmatch = 3, level = 95, interior = FALSE, subset = NULL,
weights = NULL, masspoints = "check", data = NULL)

Arguments

y	dependent variable.
x	independent variable.
eval	vector of evaluation point(s). By default it uses 30 equally spaced points over the support of x.
neval	number of equally spaced evaluation points on the support of x. Default is neval=30.
p	polynomial order used to construct point estimator; default is p = 1 (local linear regression).
deriv	derivative order of the regression function to be estimated. Default is deriv=0 (regression function).
h	main bandwidth used to construct local polynomial point estimator. Can be either scalar (same bandwidth for all evaluation points), or vector of same dimension as eval. If not specified, bandwidth h is computed by the companion command lpbwselect.
b	bias bandwidth used to construct the bias-correction estimator. Can be either scalar (same bandwidth for all evaluation points), or vector of same dimension as eval. By default it is set equal to h. If rho is set to zero, b is computed by the companion command lpbwselect.
rho	Sets b=h/rho. Default is rho = 1.
kernel	kernel function used to construct local polynomial estimators. Options are epa for the epanechnikov kernel, tri for the triangular kernel, uni for the uniform kernel and gau for the gaussian kernel. Default is kernel = epa.
bwselect	bandwidth selection procedure to be used via lpbwselect. By default it computes h and sets b=h/rho (with rho=1 by default). It computes both h and b if rho is set equal to zero. Options are: mse-dpi second-generation DPI implementation of MSE-optimal bandwidth. Default option if only one evaluation point is chosen. mse-rot ROT implementation of MSE-optimal bandwidth. imse-dpi second-generation DPI implementation of IMSE-optimal bandwidth (computed using a grid of evaluation points). Default option if more than one evaluation point is chosen. imse-rot ROT implementation of IMSE-optimal bandwidth (computed using a grid of evaluation points). ce-dpi second generation DPI implementation of CE-optimal bandwidth. ce-rot ROT implementation of CE-optimal bandwidth. Use lpbwselect with bwselect="all" to report 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.
bwregul	specifies scaling factor for the regularization term added to the denominator of bandwidth selectors. Setting bwregul = 0 removes the regularization term from the bandwidth selectors. Default is bwregul = 1.
imsegrid	number of evaluations points used to compute the IMSE bandwidth selector. Default is imsegrid = 30.
vce	procedure used to compute the variance-covariance matrix estimator. Options are: nn heteroskedasticity-robust nearest neighbor variance estimator with nnmatch the (minimum) number of neighbors to be used. Default choice (when cluster is not supplied). hc0 heteroskedasticity-robust plug-in residuals variance estimator without weights. hc1 heteroskedasticity-robust plug-in residuals variance estimator with hc1 weights. hc2 heteroskedasticity-robust plug-in residuals variance estimator with hc2 weights. hc3 heteroskedasticity-robust plug-in residuals variance estimator with hc3 weights. cr1 cluster-robust variance estimator with ((n-1)/(n-k)) * (G/(G-1)) multiplier (Stata-style CR1). Default choice when cluster is supplied. Requires cluster. cr2 cluster-robust variance estimator with Bell-McCaffrey block-adjusted residuals. Requires cluster. cr3 cluster-robust variance estimator with block jackknife-style adjustment and (G-1)/G multiplier. Requires cluster. When cluster is supplied, vce=hc0 or vce=hc1 is remapped to cr1, vce=hc2 to cr2, and vce=hc3 to cr3 (with a warning). vce=nn with cluster silently defaults to cr1.
covgrid	if TRUE, it computes two covariance matrices (cov.us and cov.rb) for classical and robust covariances across point estimators over the grid of evaluation points.
cluster	indicates the cluster ID variable used for cluster-robust variance estimation. When supplied, the default vce becomes cr1; cr2 and cr3 are also available.
nnmatch	to be combined with for vce=nn for heteroskedasticity-robust nearest neighbor variance estimator with nnmatch indicating the minimum number of neighbors to be used. Default is nnmatch=3

.

level	confidence level used for confidence intervals; default is level = 95.
interior	if TRUE, all evaluation points are assumed to be interior points. This option affects only data-driven bandwidth selection via lpbwselect. Default is interior = FALSE.
subset	optional rule specifying a subset of observations to be used.
weights	optional vector of non-negative observation weights of the same length as x. User weights multiply the kernel weights in estimation, bandwidth selection, and variance computation (weighted least squares interpretation).
masspoints	how to handle evaluation points whose bandwidth window contains few unique x values (the local polynomial may become unreliable in that case). Options: "check" (default) warns when there are fewer than p+5 unique values inside the main bandwidth; "off" disables the check.
data	an optional data frame. When supplied, y, x, cluster, weights, and subset may be given as bare variable names referring to columns of data.

Value

Estimate	A matrix containing eval (grid points), h, b (bandwidths), N (effective sample sizes), tau.us (point estimates with p-th order local polynomial), tau.bc (bias-corrected point estimates with (p+1)-th order local polynomial), se.us (standard error corresponding to tau.us), and se.rb (robust standard error).
cov.us	Conventional-estimator covariance matrix across the evaluation grid (neval by neval). Returned only when covgrid=TRUE; NULL otherwise.
cov.rb	Robust-bias-corrected covariance matrix across the evaluation grid (neval by neval). Returned only when covgrid=TRUE; 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

lpbwselect

Examples

x   <- runif(500)
y   <- sin(4*x) + rnorm(500)
est <- lprobust(y,x)
summary(est)

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