# sjpi: Sheather-Jones Plug-in bandwidth criterion. In locfit: Local Regression, Likelihood and Density Estimation

## Description

Given a dataset and set of pilot bandwidths, this function computes a bandwidth via the plug-in method, and the assumed ‘pilot’ relationship of Sheather and Jones (1991). The S-J method chooses the bandwidth at which the two intersect.

The purpose of this function is to demonstrate the sensitivity of plug-in methods to pilot bandwidths and assumptions. This function does not provide a reliable method of bandwidth selection.

## Usage

 `1` ```sjpi(x, a) ```

## Arguments

 `x` data vector `a` vector of pilot bandwidths

## Value

A matrix with four columns; the number of rows equals the length of `a`. The first column is the plug-in selected bandwidth. The second column is the pilot bandwidths `a`. The third column is the pilot bandwidth according to the assumed relationship of Sheather and Jones. The fourth column is an intermediate calculation.

## References

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. JRSS-B 53, 683-690.

`locfit`, `locfit.raw`, `lcvplot`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# Fig 10.2 (S-J parts) from Loader (1999). data(geyser, package="locfit") gf <- 2.5 a <- seq(0.05, 0.7, length=100) z <- sjpi(geyser, a) # the plug-in curve. Multiplying by gf=2.5 corresponds to Locfit's standard # scaling for the Gaussian kernel. plot(gf*z[, 2], gf*z[, 1], type = "l", xlab = "Pilot Bandwidth k", ylab = "Bandwidth h") # Add the assumed curve. lines(gf * z[, 3], gf * z[, 1], lty = 2) legend(gf*0.05, gf*0.4, lty = 1:2, legend = c("Plug-in", "SJ assumed")) ```

### Example output

```locfit 1.5-9.1 	 2013-03-22
```

locfit documentation built on March 25, 2020, 5:07 p.m.