R: Smoothes the given bivariate data using kernel regression.

locally.weighted.polynomial {SiZer} | R Documentation

## Smoothes the given bivariate data using kernel regression.

### Description

Smoothes the given bivariate data using kernel regression.

### Usage

    locally.weighted.polynomial(x, y, h = NA, x.grid = NA, degree = 1,
      kernel.type = "Normal")

### Arguments

`x` | Vector of data for the independent variable
`y` | Vector of data for the dependent variable
`h` | The bandwidth for the kernel
`x.grid` | What x-values should the value of the smoother be calculated at.
`degree` | The degree of the polynomial to be fit at each x-value. The default is to fit a linear regression, ie degree=1.
`kernel.type` | What kernel to use. Valid choices are 'Normal', 'Epanechnikov', 'biweight', and 'triweight'.

### Details

The confidence intervals are created using the row-wise method of Hannig and Marron (2006).

Notice that the derivative to be estimated must be less than or equal to the degree of the polynomial initially fit to the data.

If the bandwidth is not given, the Sheather-Jones bandwidth selection method is used.

### Value

Returns a `LocallyWeightedPolynomial` object that has the following elements:

data

  A structure of the data used to generate the smoothing curve

h

  The bandwidth used to generate the smoothing curve.

x.grid

  The grid of x-values that we have estimated function value and derivative(s) for.

degrees.freedom

  The effective sample size at each grid point

Beta

  A matrix of estimated beta values. The number of rows is degrees+1, while the number of columns is the same as the length of x.grid. Notice that

  \hat{f}(x_i) = β[1,i]

  \hat{f'}(x_i) = β[2,i]*1!

  \hat{f''}(x_i) = β[3,i]*2!

  and so on...

Beta.var

  Matrix of estimated variances for `Beta`. Same structure as `Beta`.

### Author(s)

Derek Sonderegger

### References

Chaudhuri, P., and J. S. Marron. 1999. SiZer for exploration of structures in curves. Journal of the American Statistical Association 94 807-823.

Hannig, J., and J. S. Marron. 2006. Advanced distribution theory for SiZer. Journal of the American Statistical Association 101 484-499.

Sonderegger, D.L., Wang, H., Clements, W.H., and Noon, B.R. 2009. Using SiZer to detect thresholds in ecological data. Frontiers in Ecology and the Environment 7:190-195

### See Also

`SiZer`, `plot.LocallyWeightedPolynomial`, `spm` in package 'SemiPar', `loess`, `smooth.spline`, `interpSpline` in the `splines` package.

### Examples

    data(Arkansas)
    x <- Arkansas$year
    y <- Arkansas$sqrt.mayflies
    layout(cbind(1,2,3))
    model <- locally.weighted.polynomial(x,y)
    plot(model, main='Smoothed Function', xlab='Year', ylab='Sqrt.Mayflies')

    model2 <- locally.weighted.polynomial(x,y,h=.5)
    plot(model2, main='Smoothed Function', xlab='Year', ylab='Sqrt.Mayflies')

    model3 <- locally.weighted.polynomial(x,y, degree=1)
    plot(model3, derv=1, main='First Derivative', xlab='Year', ylab='1st Derivative')

[Package SiZer version 0.1-5 Index]