sjpi {locfit} R Documentation

## Sheather-Jones Plug-in bandwidth criterion.

### 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

```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

```# Fig 10.2 (S-J parts) from Loader (1999).
data(geyser)
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")

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"))
```

[Package locfit version 1.1-9 Index]