Description Usage Arguments Details Value Author(s) References See Also Examples
It implements the functional Nadaraya-Watson estimator to estimate the regression function. It depends on the type of semi-metric used as well as the optimal selection of bandwidth parameter
1 2 | funopare.kernel(Response, CURVES, PRED, bandwidth, ..., kind.of.kernel = "quadratic",
semimetric = "deriv")
|
Response |
A real-valued scalar response of length n |
CURVES |
An (n by p) matrix of discretised data of functional curves |
PRED |
An (n by k) matrix of discretised data of functional curves. |
bandwidth |
A real-valued bandwidth parameter |
... |
Other arguments |
kind.of.kernel |
Type of kernel function. By default, it is the Epanechnikov kernel |
semimetric |
Type of semi-metric. By default, it is the semi-metric based on the qth order derivative, where q is an integer |
The functional NW estimator of the conditional mean can be expressed as a weighted average of response variable: ∑^n_{i=1}K_h(d(x_i,x))y_i/∑^n_{i=1}K_h(d(x_i,x)), where K(\cdot) is a kernel function which integrates to one, it has continuous derivative on the function support range. The semi-metric d is used to measure distances among curves. For a set of smooth curves, the semi-metric based on derivative should be considered. For a set of rough curves, the semi-metric based on functional principal components should be used. The bandwidth h controls the tradeoff between squared bias and variance in the mean squared error
NWweit |
Estimated Nadaraya-Watson weights |
Estimated.values |
Estimated values of the regression function |
Predicted.values |
Predicted values of the regression function |
band |
Bandwidth of the functional NW estimator |
Mse |
In-sample mean squared error |
Han Lin Shang
H. L. Shang (2013) Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density, Computational Statistics, in press.
H. L. Shang (2013) Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density, Computational Statistics and Data Analysis, 67, 185-198.
X. Zhang and R. D. Brooks and M. L. King (2009) A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation, Journal of Econometrics, 153, 21-32.
F. Ferraty, I. Van Keilegom and P. Vieu (2010) On the validity of the bootstrap in non-parametric functional regression, Scandinavian Journal of Statistics, 37, 286-306.
F. Ferraty and P. Vieu (2006) Nonparametric Functional Data Analysis: Theory and Practice, Springer, New York.
F. Ferraty and P. Vieu (2002) The functional nonparametric model and application to spectrometric data, Computational Statistics, 17, 545-564.
bayMCMC_np_global
, bayMCMC_np_local
, bayMCMC_semi_global
, bayMCMC_semi_local
1 2 | funopare.kernel(Response = simresp_np_normerr, CURVES = simcurve_smooth_normerr,
PRED = simcurve_smooth_normerr, bandwidth = 2.0, range.grid=c(0,pi), q=2, nknot=20)
|
Loading required package: splines
$Mse
[1] 0
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