aws (version 1.6-2)

lpaws: Local polynomial smoothing by AWS

Description

The function allows for structural adaptive smoothing using a local polynomial (degree

Usage

lpaws(y, degree = 1, hmax = NULL, aws = TRUE, memory = FALSE, lkern = "Triangle", homogen = TRUE, earlystop = TRUE, aggkern = "Uniform", sigma2 = NULL, hw = NULL, ladjust = 1, u = NULL, graph = FALSE, demo = FALSE)

Arguments

y

Response, either a vector (1D) or matrix (2D). The corresponding design is assumed to be a regular grid in 1D or 2D, respectively.

degree

Polynomial degree of the local model

hmax

maximal bandwidth

aws

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

memory

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

lkern

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

homogen

logical: if TRUE the function tries to determine regions where weights can be fixed to 1. This may increase speed.

earlystop

logical: if TRUE the function tries to determine points where the homogeneous region is unlikely to change in further steps. This may increase speed.

aggkern

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

sigma2

Error variance, the value is estimated if not provided.

hw

Regularisation bandwidth, used to prevent from unidentifiability of local estimates for small bandwidths.

ladjust

factor to increase the default value of lambda

u

a "true" value of the regression function, may be provided to report risks at each iteration. This can be used to test the propagation condition with u=0

graph

logical: If TRUE intermediate results are illustrated graphically. May significantly slow down the computations in 2D. Please avoid using the default X11() on systems build with cairo, use X11(type="Xlib") inst

demo

logical: if TRUE wait after each iteration

Value

• returns anobject of class aws with slots
• y = "numeric"
  y
• dy = "numeric"
  dim(y)
• x = "numeric"
  numeric(0)
• ni = "integer"
  integer(0)
• mask = "logical"
  logical(0)
• theta = "numeric"
  Estimates of regression function and derivatives, length: length(y)*(degree+1)
• mae = "numeric"
  Mean absolute error for each iteration step if u was specified, numeric(0) else
• 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"
  numeric(0)
• xmax = "numeric"
  numeric(0)
• wghts = "numeric"
  numeric(0)
• degree = "integer"
  degree
• 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"
  homogen
• earlystop = "logical"
  eralustop
• varmodel = "character"
  "Constant"
• vcoef = "numeric"
  numeric(0)
• call = "function"
  the arguments of the call to lpaws

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

link{awsdata},aws, aws.irreg

Examples

library(aws)
# 1D local polynomial smoothing
demo(lpaws_ex1)
# 2D local polynomial smoothing
demo(lpaws_ex2)