Propagation condition for adaptive weights smoothing

The function enables testing of the propagation condition in order to select appropriate values for the parameter lambda in function aws.

awstestprop(dy, hmax, theta = 1, family = "Gaussian", lkern = "Triangle",
            aws = TRUE, memory = FALSE, shape = 2, homogeneous=TRUE, varadapt=FALSE,
            ladjust = 1, spmin=0.25, seed = 1, minlevel=1e-6, maxz=25, diffz=.5,
            maxni=FALSE, verbose=FALSE)
pawstestprop(dy, hmax, theta = 1, family = "Gaussian", lkern = "Triangle",
             aws = TRUE, patchsize=1, shape = 2,
             ladjust = 1, spmin = 0.25, seed = 1, minlevel = 1e-6,
             maxz = 25, diffz = .5, maxni = FALSE, verbose = FALSE)

Arguments

dy	Dimension of grid used in 1D, 2D or 3D. May also be specified as an array of values. In this case data are generated with parameters `dy-mean(dy)+theta` and the propagation condition is testet as if `theta` is the true parameter. This can be used to study properties for a slighty misspecified structural assumption.
hmax	Maximum bandwidth.
theta	Parameter determining the distribution in case of `family %in% c("Poisson","Bernoulli")`
family	`family` specifies the probability distribution. Default is `family="Gaussian"`, also implemented are "Bernoulli", "Poisson", "Exponential", "Volatility", "Variance" and "NCchi". `family="Volatility"` specifies a Gaussian distribution with expectation 0 and unknown variance. `family="Volatility"` specifies that `p*y/theta` is distributed as \(\chi^2\) with `p=shape` degrees of freedom. `family="NCchi"` uses a noncentral Chi distribution with `p=shape` degrees of freedom and noncentrality parameter `theta`.
lkern	character: location kernel, either "Triangle", "Plateau", "Quadratic", "Cubic" or "Gaussian"
aws	logical: if TRUE structural adaptation (AWS) is used.
patchsize	patchsize in case of paws.
memory	logical: if TRUE stagewise aggregation is used as an additional adaptation scheme.
shape	Allows to specify an additional shape parameter for certain family models. Currently only used for family="Variance", that is \(\chi\)-Square distributed observations with `shape` degrees of freedom.
homogeneous	if `homgeneous==FALSE` and `family==Gaussian` then create heterogeneous variances according to a chi-squared distribution with number of degrees of freedom given by `sphere`
varadapt	if `varadapt==TRUE` use inverse of variance reduction instead of sum of weights in definition of statistical penalty.
ladjust	Factor to increase the default value of lambda
spmin	Determines the form (size of the plateau) in the adaptation kernel. Not to be changed by the user.
seed	Seed value for random generator.
minlevel	Minimum exceedence probability to use in contour plots.
maxz	Maximum of z-scale in plots.
diffz	Gridlength in z
maxni	If TRUE use \(max_{l<=k}(N_i^{(l)}\) instead of \((N_i^{(k)}\) in the definition of the statistical penalty.
verbose	If TRUE provide additional information.

Details

Estimates exceedence probabilities

Results for intermediate steps are provided as contour plots. For a good choice of lambda (ladjust) the contours up to probabilities of 1e-5 should be vertical.

Value

A list with components

Sequence of bandwidths used

seq(0,30,.5), the quantiles exceedence probabilities refer to

prob

the matrix of exceedence probabilities, columns corresponding to h

probna

the matrix of exceedence probabilities for corresponding nonadaptive estimates, columns corresponding to h

References

Becker (2013)

Author