returnCutoff: Estimates the statistic cutoff for a target alpha

In dbEmpLikeGOF: Goodness-of-fit and two sample comparison tests using sample entropy

Description

estimates the test statistic cutoff for significance

Usage

returnCutoff(sample.size,
              testcall=c("uniform", "normal", "distribution.equality"),
              targetalpha=.05,
              num.mc=200,
              delta=0.5,
              delta.equality=0.10,
              pvl.Table=FALSE,
              random.seed.flag=TRUE)

Arguments

sample.size	number of observations
testcall	Type of distribution: either uniform, normal, or distribution.equality
targetalpha	The significance level for the test.
num.mc	number of simulations to estimate distribution of statistic
delta	an option for changing the minimizing range for the EL ratio test statistic for the normal and uniform distribution.
delta.equality	an option for changing the minimizing range for the EL ratio test statistic for the two sample distribution equality
pvl.Table	logical indicating if value should be calculated based on estimates from data table or by using monte carlo techniques
random.seed.flag	logical if set seed should be set

Details

This function is designed to return the cut-off for significance for the statistics obtained from the density-based EL tests described in Vexler and Gurevich, 2010 and Gurevich and Vexler, 2011. The significance level for the associated cutoffs are specified by the user in 'targetalpha'.

Note 'sample.size' should be a scalar for the normal and uniform tests, but a vector of length two for 'testcall=distribution.equality' denoting the number of observations for each sample.

The 'delta' value should remain at the default value of 0.50. The 'delta' value corresponds to the 'delta' in equation 2.10 (normal) or equation 2.3.2 (uniform) in Vexler and Gurevich, 2010. Essentially this setting controls the range over which a minimum is taken to produce the EL ratio test statistic The range is from 1 to n^(1-'delta') where 'n' represents the number of observations in 'x'.

The 'delta.equality' option specifies the range over which a minimum is taken to produce the EL ratio test statistic for the two sample distribution equality test. The lower endpoint in the range is n^(0.5+delta) and upper endpoint is min(n^(1-delta),n/2) where 'n' corresponds to the number of observations. Acceptable delta values are in the interval (0,0.25).From our experiences, the two sample distribution test is rather robust to the choice of 'delta.equality'.

The 'pvl.Table' is a binary option where when TRUE, the test statistic is determined by imputation from a stored table of test statistics and significance levels for common sample sizes. If 'pvl.Table' is FALSE, then the test statistic is determined from a Monte-Carlo simulation where the number of resamplings is controlled by 'num.mc'.

Value

Returns a statistical cutoff value to assess significance at level 'targetalpha'

Author(s)

Jeffrey C. Miecznikowski, Lori A. Shepherd

References

Jeffrey C. Miecznikowski, Albert Vexler, Lori A. Shepherd (2013). dbEmpLikeGOF: An R Package for Nonparametric Likelihood Ratio Tests for Goodness-of-Fit and Two-Sample Comparisons Based on Sample Entropy. Journal of Statistical Software, 54(3), 1-19. http://www.jstatsoft.org/v54/i03/

Examples

 returnCutoff(sample.size=50, testcall="normal")
 returnCutoff(sample.size=50, testcall="uniform")
 returnCutoff(sample.size=10, testcall="distribution.equality")
 returnCutoff(sample.size=c(10,15), testcall="distribution.equality")

dbEmpLikeGOF documentation built on May 2, 2019, 4:04 p.m.