npscoef  R Documentation 
npscoef
computes a kernel regression estimate of a one (1)
dimensional dependent variable on pvariate explanatory data,
using the model Y_i =
t(W_i) * gamma(Z_i) + u_i where
t(W_i)=(1,t(X_i)), given a set of evaluation
points, training points (consisting of explanatory data and dependent
data), and a bandwidth specification. A bandwidth specification can be
a scbandwidth
object, or a bandwidth vector, bandwidth type and
kernel type.
npscoef(bws, ...) ## S3 method for class 'formula' npscoef(bws, data = NULL, newdata = NULL, y.eval = FALSE, ...) ## S3 method for class 'call' npscoef(bws, ...) ## Default S3 method: npscoef(bws, txdat, tydat, tzdat, ...) ## S3 method for class 'scbandwidth' npscoef(bws, txdat = stop("training data 'txdat' missing"), tydat = stop("training data 'tydat' missing"), tzdat = NULL, exdat, eydat, ezdat, residuals = FALSE, errors = TRUE, iterate = TRUE, maxiter = 100, tol = .Machine$double.eps, leave.one.out = FALSE, betas = FALSE, ...)
bws 
a bandwidth specification. This can be set as a 
... 
additional arguments supplied to specify the regression type,
bandwidth type, kernel types, selection methods, and so on.
To do this, you may specify any of 
data 
an optional data frame, list or environment (or object
coercible to a data frame by 
newdata 
An optional data frame in which to look for evaluation data. If omitted, the training data are used. 
y.eval 
If 
txdat 
a pvariate data frame of explanatory data (training data),
which, by default, populates the columns 2 through p+1
of W in the model equation, and in the
absence of 
tydat 
a one (1) dimensional numeric or integer vector of dependent data, each
element i corresponding to each observation (row) i of

tzdat 
an optionally specified qvariate data frame of explanatory data (training data), which corresponds to Z in the model equation. Defaults to the training data used to compute the bandwidth object. 
exdat 
a pvariate data frame of points on which the regression will be
estimated (evaluation data).By default,
evaluation takes place on the data provided by 
eydat 
a one (1) dimensional numeric or integer vector of the true values of the dependent variable. Optional, and used only to calculate the true errors. 
ezdat 
an optionally specified qvariate data frame of points on
which
the regression will be estimated
(evaluation data), which corresponds to Z
in the model equation. Defaults to be the same as 
errors 
a logical value indicating whether or not asymptotic standard errors
should be computed and returned in the resulting

residuals 
a logical value indicating that you want residuals computed and
returned in the resulting 
iterate 
a logical value indicating whether or not backfitted estimates
should be iterated for selfconsistency. Defaults to 
maxiter 
integer specifying the maximum number of times to iterate the
backfitted estimates while attempting to make the backfitted estimates
converge to the desired tolerance. Defaults to 
tol 
desired tolerance on the relative convergence of backfit
estimates. Defaults to 
leave.one.out 
a logical value to specify whether or not to compute the leave one
out estimates. Will not work if 
betas 
a logical value indicating whether or not estimates of the
components of gamma should be returned in the

npscoef
returns a smoothcoefficient
object. The generic
functions fitted
, residuals
, coef
,
se
, and predict
,
extract (or generate) estimated values,
residuals, coefficients, bootstrapped standard
errors on estimates, and predictions, respectively, from
the returned object. Furthermore, the functions summary
and plot
support objects of this type. The returned object
has the following components:
eval 
evaluation points 
mean 
estimation of the regression function (conditional mean) at the evaluation points 
merr 
if 
beta 
if 
resid 
if 
R2 
coefficient of determination (Doksum and Samarov (1995)) 
MSE 
mean squared error 
MAE 
mean absolute error 
MAPE 
mean absolute percentage error 
CORR 
absolute value of Pearson's correlation coefficient 
SIGN 
fraction of observations where fitted and observed values agree in sign 
If you are using data of mixed types, then it is advisable to use the
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.
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.
Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413420.
Cai Z. (2007), “Trending timevarying coefficient time series models with serially correlated errors,” Journal of Econometrics, 136, 163188.
Doksum, K. and A. Samarov (1995), “Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression,” The Annals of Statistics, 23 14431473.
Hastie, T. and R. Tibshirani (1993), “Varyingcoefficient models,” Journal of the Royal Statistical Society, B 55, 757796.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2010), “Smooth varyingcoefficient estimation and inference for qualitative and quantitative data,” Econometric Theory, 26, 131.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.
Li, Q. and D. Ouyang and J.S. Racine (2013), “Categorical semiparametric varyingcoefficient models,” Journal of Applied Econometrics, 28, 551589.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301309.
bw.nrd
, bw.SJ
, hist
,
npudens
, npudist
,
npudensbw
, npscoefbw
## Not run: # EXAMPLE 1 (INTERFACE=FORMULA): n < 250 x < runif(n) z < runif(n, min=2, max=2) y < x*exp(z)*(1.0+rnorm(n,sd = 0.2)) bw < npscoefbw(y~xz) model < npscoef(bw) plot(model) # EXAMPLE 1 (INTERFACE=DATA FRAME): n < 250 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) model < npscoef(bw) plot(model) ## End(Not run)
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