aws (version 1.6-2)

aws.irreg: local constant AWS for irregular (1D/2D) design

Description

The function implements the propagation separation approach to nonparametric smoothing (formerly introduced as Adaptive weights smoothing) for varying coefficient Gaussian models on a 1D or 2D irregulat design. The function allows for a paramertic (polynomial) mean-variance dependence.

Usage

aws.irreg(y, x, hmax = NULL, aws=TRUE, memory=FALSE, varmodel = "Constant", lkern = "Triangle", aggkern = "Uniform", sigma2 = NULL, nbins = 100, hpre = NULL, henv = NULL, ladjust =1, varprop = 0.1, graph = FALSE)

Arguments

y

The observed response vector (length n)

x

Design matrix, dimension n x d, d %in% 1:2

hmax

hmax specifies the maximal bandwidth. Unit is binwidth in the first dimension.

aws

logical: if TRUE structural adaptation (AWS) is used.

memory

logical: if TRUE stagewise aggregation is used as an additional adaptation scheme.

varmodel

determines the model that relates variance to mean. Either "Constant", "Linear" or "Quadratic".

lkern

character: location kernel, either "Triangle", "Plateau", "Quadratic", "Cubic" or "Gaussian"

aggkern

character: kernel used in stagewise aggregation, either "Triangle" or "Uniform"

sigma2

sigma2 allows to specify the variance in case of varmodel="Constant", estimated if not given.

nbins

numer of bins, can be NULL, a positive integer or a vector of positive integers (length d)

hpre

smoothing bandwidth for initial variance estimate

henv

radius of balls around each observed design point where estimates will be calculated

ladjust

factor to increase the default value of lambda

varprop

exclude the largest 100*varprop% squared residuals when estimating the error variance

graph

If graph=TRUE intermediate results are illustrated after each iteration step. Defaults to graph=FALSE.

Value

• returns anobject of class aws with slots
• y = "numeric"
  y
• dy = "numeric"
  dim(y)
• x = "numeric"
  x
• ni = "integer"
  number of observations per bin
• mask = "logical"
  bins where parameters have been estimated
• theta = "numeric"
  Estimates of regression function, length: length(y)
• mae = "numeric"
  numeric(0)
• var = "numeric"
  approx. variance of the estimates of the regression function. Please note that this does not reflect variability due to randomness of weights.
• xmin = "numeric"
  vector of minimal x-values (bins)
• xmax = "numeric"
  vector of maximal x-values (bins)
• wghts = "numeric"
  relative binwidths
• degree = "integer"
  0
• hmax = "numeric"
  effective hmax
• sigma2 = "numeric"
  provided or estimated error variance
• scorr = "numeric"
  0
• family = "character"
  "Gaussian"
• shape = "numeric"
  numeric(0)
• lkern = "integer"
  integer code for lkern, 1="Plateau", 2="Triangle", 3="Quadratic", 4="Cubic", 5="Gaussian"
• lambda = "numeric"
  effective value of lambda
• ladjust = "numeric"
  effective value of ladjust
• aws = "logical"
  aws
• memory = "logical"
  memory
• homogen = "logical"
  FALSE
• earlystop = "logical"
  FALSE
• varmodel = "character"
  varmodel
• vcoef = "numeric"
  estimated coefficients in variance model
• call = "function"
  the arguments of the call to aws

Details

Data are first binned (1D/2D), then aws is performed on all datapoints within distance

References

Joerg Polzehl, Vladimir Spokoiny, in V. Chen, C.; Haerdle, W. and Unwin, A. (ed.) Handbook of Data Visualization Structural adaptive smoothing by propagation-separation methods Springer-Verlag, 2008, 471-492

See Also

See also lpaws, link{awsdata}, lpaws

Examples

require(aws)
# 1D local constant smoothing
demo(irreg_ex1)
# 2D local constant smoothing
demo(irreg_ex2)