R: Propagation condition for adaptive weights smoothing

awstestprop {aws}

R Documentation

Propagation condition for adaptive weights smoothing

Description

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

Usage

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

`h`	Sequence of bandwidths used
`z`	`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`

Author(s)

Joerg Polzehl polzehl@wias-berlin.de

References

S. Becker, P. Mathe, Electron. J. Statist. (2013), 2702-2736, doi:10.1214/13-EJS860