R: local constant AWS for irregular (1D/2D) design

aws.irreg {aws} | R Documentation

## 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`.

### Details

Data are first binned (1D/2D), then aws is performed on all datapoints within distance <= henv of nonempty bins.

### 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`

### Author(s)

Joerg Polzehl, polzehl@wias-berlin.de

### References

J. Polzehl, V. 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. DOI:10.1007/978-3-540-33037-0_19.

### See Also

See also `lpaws`, `link{awsdata}`, `lpaws`

### Examples

    require(aws)
    # 1D local constant smoothing
    ## Not run: demo(irreg_ex1)
    # 2D local constant smoothing
    ## Not run: demo(irreg_ex2)

[Package aws version 2.4-0 Index]