aws (version 1.8-0)

awstestprop: 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, ladjust = 1, seed = 1)

Arguments

dy

Dimension of grid used in 1D, 2D or 3D

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" and "Variance". family="Volatility" specifies a Gaussian distri

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 $\chi$-Square distributed observations with shape degrees of freedom.

ladjust

Factor to increase the default value of lambda

seed

Seed value for random generator.

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
• pofalpha
  the matrix of exceedence probabilities with respect to a grid of alpha for the direct propagation condition

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.

References

Becker (2013)

See Also

aws