RPB {RobustANOVA}

Robust Parametric Bootstrap Test based on MML estimators

Description

Computes the p-value of the robust parametric bootstrap (RPB) test for the equality of means of several long-tailed symmetric (LTS) distributions when the variances are unknown and arbitrary.

Usage

RPB(formula, data, alpha , verbose = TRUE, p_shape, repn)

Arguments

formula

a formula of the form left-hand-side(lhs) ~ right-hand-side(rhs). lhs shows the observed values and rhs shows the group corresponding to the observed values.

data

data frame containing the variables in the formula.

alpha

the level of significance. Default is set to alpha = 0.05.

verbose

a logical for printing output to R console.

p_shape

shape parameter of the LTS distribution.

repn

replication number for performing the RPB test.

Details

RPB test based on modifed maximum likelihood (MML) estimators is proposed as a robust alternative to parametric bootstrap (PB) test proposed by Krishnamoorthy et. al (2007). See also Tiku (1967, 1968) for the details of MML estimators. The p-value for the RPB test is based on the replication number in the algorithm given by Guven et. al (2022).

Value

A list with class "htest" containing the following components:

p.value

the p-value for the RPB test.

alpha

the level of significance.

method

a character string "Robust Parametric Bootstrap Test based on MML Estimators" indicating which test is used.

data

a data frame containing the variables.

formula

a formula of the form left-hand-side(lhs) ~ right-hand-side(rhs). lhs shows the observed values and rhs shows the group corresponding to the observed values.

Author(s)

Gamze Guven <[e-mail]>

References

G. Guven, S. Acitas, and B. Senoglu, B. RobustANOVA: An R Package for one-way ANOVA under heteroscedasticity and nonnormality. Under review, 2022.

K. Krishnamoorthy, F. Lu, and T. Mathew. A parametric bootstrap approach for anova with unequal variances: Fixed and random models. Computational Statistics & Data Analysis, 51(12): 5731-5742,2007.

M. L. Tiku. Estimating the mean and standard deviation from a censored normal sample. Biometrika, 54:155-165, 1967.

M. L. Tiku. Estimating the parameters of log-normal distribution from censored samples. Journal of the American Statistical Association, 63(321): 134-140, 1968.

Examples

library(RobustANOVA)

RPB(obs ~ methods, data = peak_discharge, alpha = 0.05, verbose = TRUE, p_shape=2.3, repn=5000)