# ksEstimator: Generic Function for the Computation of the Kolmogorov... In ROptEstOld: Optimally Robust Estimation - Old Version

## Description

Generic function for the computation of the Kolmogorov(-Smirnov) minimum distance estimator.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```ksEstimator(x, distribution, ...) ## S4 method for signature 'numeric,Binom' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Pois' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Norm' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Lnorm' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Gumbel' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Exp' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ## S4 method for signature 'numeric,Gammad' ksEstimator(x, distribution, param, eps = .Machine\$double.eps^0.5) ```

## Arguments

 `x` sample `distribution` object of class `"Distribution"` `...` additional parameters `param` name of the unknown parameter. If missing all parameters of the corresponding distribution are estimated. `eps` the desired accuracy (convergence tolerance).

## Details

In case of discrete distributions the Kolmogorov distance is computed and the parameters which lead to the minimum distance are returned. In case of absolutely continuous distributions `ks.test` is called and the parameters which minimize the corresponding test statistic are returned.

## Value

The Kolmogorov minimum distance estimator is computed. Returns a list with components named like the parameters of `distribution`.

## Methods

x = "numeric", distribution = "Binom"

Binomial distributions.

x = "numeric", distribution = "Pois"

Poisson distributions.

x = "numeric", distribution = "Norm"

Normal distributions.

x = "numeric", distribution = "Lnorm"

Lognormal distributions.

x = "numeric", distribution = "Gumbel"

Gumbel distributions.

x = "numeric", distribution = "Exp"

Exponential distributions.

x = "numeric", distribution = "Gamma"

Gamma distributions.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

`Distribution-class`
 ```1 2 3 4 5 6 7 8``` ```x <- rnorm(100, mean = 1, sd = 2) ksEstimator(x=x, distribution = Norm()) # estimate mean and sd ksEstimator(x=x, distribution = Norm(mean = 1), param = "sd") # estimate sd ksEstimator(x=x, distribution = Norm(sd = 2), param = "mean") # estimate mean mean(x) median(x) sd(x) mad(x) ```