awstestprop: Propagation condition for adaptive weights smoothing In aws: 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

 ```1 2 3 4``` ```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) ```

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. `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 [email protected]

Becker (2013)

`aws`