lspkselect implements data-driven procedures to select the Integrated Mean Squared Error (IMSE) optimal number of partitioning knots for partitioning-based least squares regression estimators. Three series methods are supported: B-splines, compactly supported wavelets, and piecewise polynomials.
See Cattaneo and Farrell (2013) and Cattaneo, Farrell and Feng (2019a) for complete details.
Companion commands: lsprobust for partitioning-based least squares regression estimation and inference; lsprobust.plot for plotting results; lsplincom for multiple sample estimation and inference.
A detailed introduction to this command is given in Cattaneo, Farrell and Feng (2019b).
For more details, and related Stata and R packages useful for empirical analysis, visit https://sites.google.com/site/nppackages/.
lspkselect(y, x, m = NULL, m.bc = NULL, smooth = NULL,
bsmooth = NULL, deriv = NULL, method = "bs", ktype = "uni",
kselect = "imse-dpi", proj = TRUE, bc = "bc3", vce = "hc2",
subset = NULL, rotnorm = TRUE)# S3 method for lspkselect
print(x, ...)
# S3 method for lspkselect
summary(object, ...)
Outcome variable.
Independent variable. A matrix or data frame.
Order of basis used in the main regression. Default is m=2.
Order of basis used to estimate leading bias. Default is m.bc=m+1.
Smoothness of B-splines for point estimation. When smooth=s, B-splines have s-order
continuous derivatives. Default is smooth=m-2.
Smoothness of B-splines for bias correction. Default is bsmooth=m.bc-2.
Derivative order of the regression function to be estimated. A vector object of the same
length as ncol(x). Default is deriv=c(0,...,0).
Type of basis used for expansion. Options are "bs" for B-splines,
"wav" for compactly supported wavelets (Cohen, Daubechies and Vial, 1993),
and "pp" for piecewise polynomials. Default is method="bs".
Knot placement. Options are "uni" for evenly spaced knots over the
support of x and "qua" for quantile-spaced knots. Default is ktype="uni".
Method for selecting the number of inner knots used by lspkselect. Options
are "imse-rot" for a rule-of-thumb (ROT) implementation of IMSE-optimal number of knots,
"imse-dpi" for second generation direct plug-in (DPI) implementation of IMSE-optimal number
of knots, and "all" for both. Default is kselect="imse-dpi".
If TRUE, projection of leading approximation error onto the lower-order approximating space
is included for bias correction (splines and piecewise polynomial only). Default is proj=TRUE.
Bias correction method. Options are "bc1" for higher-order-basis bias correction,
"bc2" for least squares bias correction, and "bc3" for plug-in bias correction.
Defaults are "bc3" for splines and piecewise polynomials and "bc2"
for wavelets.
Procedure to compute the heteroskedasticity-consistent (HCk) variance-covariance matrix estimator with plug-in residuals. Options are
"hc0" for unweighted residuals (HC0).
"hc1" for HC1 weights.
"hc2" for HC2 weights. Default.
"hc3" for HC3 weights.
Optional rule specifying a subset of observations to be used.
If TRUE, ROT selection is adjusted using normal densities.
further arguments
class lspkselect objects.
ksA matrix may contain k.rot (IMSE-optimal number of knots for
the main regression through ROT implementation), k.bias.rot
(IMSE-optimal number of knots for bias correction through ROT
implementation), k.dpi (IMSE-optimal number of knots for the
main regression through DPI implementation), k.bias.dpi (IMSE-optimal
number of knots for bias correction through DPI implementation)
optA list containing options passed to the function.
print: print method for class "lspkselect".
summary: summary method for class "lspkselect".
Cattaneo, M. D., and M. H. Farrell (2013): Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators. Journal of Econometrics 174(2): 127-143.
Cattaneo, M. D., M. H. Farrell, and Y. Feng (2019a): Large Sample Properties of Partitioning-Based Series Estimators. Annals of Statistics, forthcoming. arXiv:1804.04916.
Cattaneo, M. D., M. H. Farrell, and Y. Feng (2019b): lspartition: Partitioning-Based Least Squares Regression. Working paper.
Cohen, A., I. Daubechies, and P.Vial (1993): Wavelets on the Interval and Fast Wavelet Transforms. Applied and Computational Harmonic Analysis 1(1): 54-81.
# NOT RUN {
x <- data.frame(runif(500), runif(500))
y <- sin(4*x[,1])+cos(x[,2])+rnorm(500)
est <- lspkselect(y, x)
summary(est)
# }
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