ROptEst (version 0.5.0)

ksEstimator: Generic Function for the Computation of the Kolmogorov Minimum Distance Estimator

Description

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

Usage

ksEstimator(x, distribution, ...)

## S3 method for class 'numeric,Binom':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class 'numeric,Pois':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class 'numeric,Norm':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class 'numeric,Lnorm':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class 'numeric,Gumbel':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class 'numeric,Exp':
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)

## S3 method for class '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).

Value

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

concept

• Kolmogorov minimum distance estimator
• minimum distance estimator
• estimator

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.

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

Distribution-class

Examples

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)