empirical.variance {rQCC}

Empirical variances of robust estimators

Description

This function calculate or estimate the variances of the mean, median, Hodges-Lehmann (HL1, HL2, HL3), standard deviation, range, median absolute deviation (MAD) and Shamos estimators.

Usage

evar (n, estimator=c("mean","median","HL1","HL2","HL3", "sd","range","mad","shamos"),
         poolType=c("A","B","C"), correction=TRUE )

Arguments

n

a vector of sample sizes. For "HL1", "sd", "range" and "shamos", n \ge 2. For others, n \ge 2.

estimator

a character string specifying the estimator, must be one of "mean" (default), "median", "HL1", "HL2", "HL3", "sd", "range", "mad", and "shamos".

poolType

Type for how to pool estimators, must be one of "A" (default), "B", and "C".

correction

logical. A finite-sample bias correction for the estimator with a single sample. TRUE (default) adjusts a finite-sample bias correction for a scale estimator using c4.factor function.

Details

This function calculates or estimates the variance of a specific estimator when a random sample is from the standard normal distribution.

For the mean, standard deviation (sd) and range, their exact variances are calculated, but the others are empirically estimated through the extensive Monte Carlo simulation with 1E07 replicates for n=1,2,\ldots,100. For the case of n > 100, the empirical variances are obtained using the method of Hayes (2014).

Value

It returns a numeric value.

Author(s)

Chanseok Park and Min Wang

References

Park, C., H. Kim, and M. Wang (2022). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, 51, 2619-2645.
doi: 10.1080/03610918.2019.1699114

Hayes, K. (2014). Finite-sample bias-correction factors for the median absolute deviation. Communications in Statistics: Simulation and Computation, 43, 2205–2212.

See Also

RE{rQCC} for the relative efficiency.
n.times.eVar.of.HL1{rQCC} for the empirical variance of the HL1 estimator (times n).
n.times.eVar.of.HL2{rQCC} for the empirical variance of the HL2 estimator (times n).
n.times.eVar.of.HL3{rQCC} for the empirical variance of the HL3 estimator (times n).
n.times.eVar.of.mad{rQCC} for the empirical variance of the MAD estimator (times n).
n.times.eVar.of.median{rQCC} for the empirical variance of the median estimator (times n).
n.times.eVar.of.shamos{rQCC} for the empirical variance of the Shamos estimator (times n).

Examples

# Empirical variance of the Hodges-Lehmann estimator (HL2) under the standard normal distribution.
evar (n=10, estimator="HL2")

# Multiple samples
evar (n=c(4,5), estimator="mad", poolType="C")