npscoefbw computes a bandwidth object for a smooth
coefficient kernel regression estimate of a one (1) dimensional
dependent variable on
$p+q$-variate explanatory data, using the model
$Y_i = W_{i}^{\prime} \gamma (Z_i) + u_i$ where $W_i'=(1,X_i')$
given training points (consisting of explanatory data and dependent
data), and a bandwidth specification, which can be a rbandwidth
object, or a bandwidth vector, bandwidth type and kernel type.npscoefbw(...)## S3 method for class 'formula':
npscoefbw(formula, data, subset, na.action, call, \dots)
## S3 method for class 'NULL':
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
...)
## S3 method for class 'default':
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
nmulti,
random.seed,
cv.iterate,
cv.num.iterations,
backfit.iterate,
backfit.maxiter,
backfit.tol,
bandwidth.compute = TRUE,
bwmethod,
bwscaling,
bwtype,
ckertype,
ckerorder,
ukertype,
okertype,
optim.method,
optim.maxattempts,
optim.reltol,
optim.abstol,
optim.maxit,
...)
## S3 method for class 'scbandwidth':
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
nmulti,
random.seed = 42,
cv.iterate = FALSE,
cv.num.iterations = 1,
backfit.iterate = FALSE,
backfit.maxiter = 100,
backfit.tol = .Machine$double.eps,
bandwidth.compute = TRUE,
optim.method = c("Nelder-Mead", "BFGS", "CG"),
optim.maxattempts = 10,
optim.reltol = sqrt(.Machine$double.eps),
optim.abstol = .Machine$double.eps,
optim.maxit = 500,
...)
as.data.frame) containing the variables
in the model. If not found in data, the variables are taken from
np when a bandwidth search has been implied by a call to
another function. It is not recommended that the user set this.zdat, will also correspond to
$Z$ from the model eqxdat.xdat.scbandwidth
object returned from a previous invocation, or as a vector of
bandwidths, with each element $i$ corresponding to the bandwidth
for column $i$ in xdat. In eitFALSE, a scbandwidth object
will be returned with bandwidths set to those specified
in bws. Defaults to cv.ls
specifies least-squares cross-validation, which is all that is
currently supported. Defaults to cv.ls.TRUE the
supplied bandwidths are interpreted as `scale factors'
($c_j$), otherwise when the value is FALSE they are
interpreted as `raw bandwidths' ($h_j$ for continuous data
typesfixed. Option summary:
fixed: fixed bandwidths or scale factors
generalized_nn: generagaussian, epanechnikov, or
uniform. Defaults to gaussian.(2,4,6,8)). Kernel order specified along with a
uniform continuous kernel type will be ignored. Defaults to
2.aitchisonaitken or liracine. Defaults to
aitchisonaitken.wangvanryzin or liracine. Defaults to
wangvanryzin.min(5,ncol(xdat)).optim for minimization of
the objective function. See ?optim for references. Defaults
to "Nelder-Mead".the default method is an implementation of that of
optim. Defaults to 100.optim. Only useful
for non-negative functions, as a tolerance for reaching
zero. Defaults to .Machine$double.eps.optim. The algorithm
stops if it is unable to reduce the value by a factor of 'reltol *
(abs(val) + reltol)' at a step. Defaults to
sqrt(.Machine$douoptim. Defaults
to 500.FALSE.1.FALSE.100..Machine$double.eps.bwtype is set to fixed, an object containing
bandwidths (or scale factors if bwscaling = TRUE) is
returned. If it is set to generalized_nn or adaptive_nn,
then instead the $k$th nearest neighbors are returned for the
continuous variables while the discrete kernel bandwidths are returned
for the discrete variables. Bandwidths are stored in a vector under the
component name bw. Backfitted bandwidths are stored under the
component name bw.fitted. The functions predict, summary, and
plot support
objects of this class.
data.frame function to construct your input data and not
cbind, since cbind will typically not work as
intended on mixed data types and will coerce the data to the same
type. Caution: multivariate data-driven bandwidth selection methods are, by
their nature, computationally intensive. Virtually all methods
require dropping the $i$th observation from the data set,
computing an object, repeating this for all observations in the
sample, then averaging each of these leave-one-out estimates for a
given value of the bandwidth vector, and only then repeating
this a large number of times in order to conduct multivariate
numerical minimization/maximization. Furthermore, due to the potential
for local minima/maxima, restarting this procedure a large
number of times may often be necessary. This can be frustrating for
users possessing large datasets. For exploratory purposes, you may
wish to override the default search tolerances, say, setting
optim.reltol=.1 and conduct multistarting (the default is to restart
min(5,ncol(zdat)) times). Once the procedure terminates, you can restart
search with default tolerances using those bandwidths obtained from
the less rigorous search (i.e., set bws=bw on subsequent calls
to this routine where bw is the initial bandwidth object). A
version of this package using the Rmpi wrapper is under
development that allows one to deploy this software in a clustered
computing environment to facilitate computation involving large
datasets.
Support for backfitted bandwidths is experimental and is limited in functionality. The code does not support asymptotic standard errors or out of sample estimates with backfitting.
npscoefbw implements a variety of methods for semiparametric
regression on multivariate ($p+q$-variate) explanatory data defined
over a set of possibly continuous data. The approach is based on Li and
Racine (2003) who employ Three classes of kernel estimators for the continuous data types are available: fixed, adaptive nearest-neighbor, and generalized nearest-neighbor. Adaptive nearest-neighbor bandwidths change with each sample realization in the set, $x_i$, when estimating the density at the point $x$. Generalized nearest-neighbor bandwidths change with the point at which the density is estimated, $x$. Fixed bandwidths are constant over the support of $x$.
npscoefbw may be invoked either with a formula-like
symbolic description of variables on which bandwidth selection is to be
performed or through a simpler interface whereby data is passed
directly to the function via the xdat, ydat, and
zdat parameters. Use of these two interfaces is mutually
exclusive.
Data contained in the data frame xdat may be continuous and in
zdat may be of mixed type. Data can be entered in an arbitrary
order and data types will be detected automatically by the routine (see
np for details).
Data for which bandwidths are to be estimated may be specified
symbolically. A typical description has the form dependent
data ~ parametric explanatory data
| nonparametric explanatory data, where
dependent data is a univariate response, and
parametric explanatory data and
nonparametric explanatory data are both series of
variables specified by name, separated by the separation character
'+'. For example, y1 ~ x1 + x2 | z1 specifies that the
bandwidth object for the smooth coefficient model with response
y1, linear parametric regressors x1 and x2, and
nonparametric regressor (that is, the slope-changing variable)
z1 is to be estimated. See below for further examples. In the
case where the nonparametric (slope-changing) variable is not
specified, it is assumed to be the same as the parametric variable.
A variety of kernels may be specified by the user. Kernels implemented for continuous data types include the second, fourth, sixth, and eighth order Gaussian and Epanechnikov kernels, and the uniform kernel. Unordered discrete data types use a variation on Aitchison and Aitken's (1976) kernel, while ordered data types use a variation of the Wang and van Ryzin (1981) kernel.
Cai Z. (2007),
Hastie, T. and R. Tibshirani (1993),
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2010),
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics,
Cambridge University Press.
Racine, J.S. and D. Ouyang and Q. Li (2010),
Wang, M.C. and J. van Ryzin (1981),
npregbw, npreg# EXAMPLE 1 (INTERFACE=FORMULA):
set.seed(42)
n <- 100
x <- runif(n)
z <- runif(n, min=-2, max=2)
y <- x*exp(z)*(1.0+rnorm(n,sd = 0.2))
bw <- npscoefbw(formula=y~x|z)
summary(bw)
# EXAMPLE 1 (INTERFACE=DATA FRAME):
n <- 100
x <- runif(n)
z <- runif(n, min=-2, max=2)
y <- x*exp(z)*(1.0+rnorm(n,sd = 0.2))
bw <- npscoefbw(xdat=x, ydat=y, zdat=z)
summary(bw)Run the code above in your browser using DataLab