Description Usage Arguments Details Value Side Effects Note References See Also Examples

This function uses the technique of cross-validation to select a smoothing parameter suitable for constructing a density estimate or nonparametric regression curve in one or two dimensions.

1 |

`x` |
a vector, or two-column matrix of data. If |

`y` |
a vector of response values for nonparametric regression. |

`hstart` |
the smallest value of the grid points to be used in an initial grid search for the value of the smoothing parameter. |

`hend` |
the largest value of the grid points to be used in an initial grid search for the value of the smoothing parameter. |

`...` |
other optional parameters are passed to the |

See Sections 2.4 and 4.5 of the reference below.

The two-dimensional case uses a smoothing parameter derived from a single value, scaled by the standard deviation of each component.

This function does not employ a sophisticated algorithm and some
adjustment of the search parameters may be required for different sets
of data. An initial estimate of the value of h which minimises the
cross-validatory criterion is located from a grid search using values
which are equally spaced on a log scale between `hstart`

and
`hend`

. A quadratic approximation is then used to refine this
initial estimate.

the value of the smoothing parameter which minimises the cross-validation criterion over the selected grid.

If the minimising value is located at the end of the grid of search positions,
or if some values of the cross-validatory criterion cannot be evaluated,
then a warning message is printed. In these circumstances altering the
values of `hstart`

and `hend`

may improve performance.

As from version 2.1 of the package, a similar effect can be
obtained with the new function `h.select`

, via
`h.select(x, method="cv")`

. Users are encouraged to adopt
this route, since `hcv`

might be not accessible directly
in future releases of the package. When the
sample size is large `hcv`

uses the raw data while
`h.select(x, method="cv")`

uses binning. The latter is
likely to produce a more stable choice for `h`

.

Bowman, A.W. and Azzalini, A. (1997).
*Applied Smoothing Techniques for Data Analysis:*
*the Kernel Approach with S-Plus Illustrations.*
Oxford University Press, Oxford.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# Density estimation
x <- rnorm(50)
par(mfrow=c(1,2))
h.cv <- hcv(x, display="lines", ngrid=32)
sm.density(x, h=hcv(x))
par(mfrow=c(1,1))
# Nonparametric regression
x <- seq(0, 1, length = 50)
y <- rnorm(50, sin(2 * pi * x), 0.2)
par(mfrow=c(1,2))
h.cv <- hcv(x, y, display="lines", ngrid=32)
sm.regression(x, y, h=hcv(x, y))
par(mfrow=c(1,1))
``` |

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