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 χ^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 χ-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

Becker (2013)

### See Also

`aws`

[Package aws version 2.4-0 Index]