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 2.5-1 Index]