# Univariate implementation of the test of Fan (1994) in the form proposed by Li and Racine (2007).

### Description

Given a sample of a continuous univariate random variable and a density
function `fun.den`

with support in the interval (`lower`

, `upper`

)),
`fan.test`

considers the test whose null hypothesis is that the sample has `fun.den`

as density function
and the test statistic and the corresponding p-value of the test based on the integral of the squared difference between
the null hypothesis density function and a kernel smoothing approximation.
To properly run, the `KernSmooth`

package needs to be
installed, as in its default option it depends on the `dpik`

function to estimate the bandwidth.

### Usage

1 2 |

### Arguments

`x` |
a numeric vector of data values for which the null hypothesis is tested. |

`fun.den` |
an actual density distribution function, such as |

`par` |
list of (additional) parameters of the density function under the null hypothesis, default NULL. |

`lower` |
lower end point of the support of the random variable defined by |

`upper` |
upper end point of the support of the random variable defined by |

`kernel` |
a character string with the kernel to be used, either "normal" (a N(0,1) density), "box" (a uniform in -1 to 1) or "epanech" (a Epanechnikov quadratic kernel), default "normal". |

`bw` |
a number indicating the bandwidth to be used in the empirical kernel estimate of the data,
default NULL. In its default option, the bandwidth is estimated using the |

### Details

The Fan's test is based on a normal approximation of the integral of the squared difference between the null hypothesis density function and a kernel smoothing approximation. In Li and Racine's form it is obtained as the aggregation of (i) a sampling component, (ii) the integrate of the square of the kernel convolution of the density null function and (iii) the sum of the convolution of the density in the sampled values, see Li and Racine (2007, pp.380-1) for details.

### Value

The output is an object of the class `htest`

exactly like for the Kolmogorov-Smirnov
test, `ks.test`

.
A list containing the following components:

`statistic` |
the value of the test statistic. |

`p.value` |
the p-value of the test. |

`method` |
the character string "Geometric test". |

`data.name` |
a character string giving the name of the data. |

### Warning

`fan.test`

calls the `dpik`

function of `KernSmooth`

### Note

To properly run the function requires the package `KernSmooth`

to be installed to estimate the bandwidth.

### Author(s)

Jose M. Pavia

### References

Fan, Y (1994) "Testing the goodness-of-fit of a parametric density function by kernel method", Econometric Theory, 10, 316–356.

Li, O. and Racine, J.F. (2007) "Nonparametric Econometrics", Princeton niversity Press, New Jersey.

### See Also

`dgeometric.test`

, `integrate`

and `dpik`

.

### Examples

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