The p-value computation for the K-sample problem using a fixed partition size
The p-value computation for the K-sample test of Heller et al. (2016) using a fixed partition size m.
hhg.univariate.ks.pvalue(statistic, NullTable,m)
statistic |
The value of the computed statistic by the function |
NullTable |
The null table of the statistic, which can be downloaded from the software website (http://www.math.tau.ac.il/~ruheller/Software.html) or computed by the function
|
m |
The partition size. |
For the test statistic, the function extracts the fraction of observations in the null table that are at least as large as the test statistic, i.e. the p-value.
The p-value.
Barak Brill Shachar Kaufman.
Heller, R., Heller, Y., Kaufman S., Brill B, & Gorfine, M. (2016). Consistent Distribution-Free K-Sample and Independence Tests for Univariate Random Variables, JMLR 17(29):1-54
Brill B. (2016) Scalable Non-Parametric Tests of Independence (master's thesis)
http://primage.tau.ac.il/libraries/theses/exeng/free/2899741.pdf
## Not run: #Two groups, each from a different normal mixture: N0=30 N1=30 X = c(c(rnorm(N0/2,-2,0.7),rnorm(N0/2,2,0.7)),c(rnorm(N1/2,-1.5,0.5),rnorm(N1/2,1.5,0.5))) Y = (c(rep(0,N0),rep(1,N1))) plot(Y,X) #I)p-value for fixed partition size using the sum aggregation type hhg.univariate.Sm.Likelihood.result = hhg.univariate.ks.stat(X,Y) hhg.univariate.Sm.Likelihood.result sum.nulltable = hhg.univariate.ks.nulltable(c(N0,N1), nr.replicates=100) #default nr. of replicates is 1000, but may take several seconds. #For illustration only, we use 100 replicates, but it is highly recommended #to use at least 1000 in practice. #p-value for m=4 (the default): hhg.univariate.ks.pvalue(hhg.univariate.Sm.Likelihood.result, sum.nulltable, m=4) #p-value for m=2: hhg.univariate.ks.pvalue(hhg.univariate.Sm.Likelihood.result, sum.nulltable, m=2) #II) p-value for fixed partition size using the max aggregation type hhg.univariate.Mm.likelihood.result = hhg.univariate.ks.stat(X,Y,aggregation.type = 'max') hhg.univariate.Mm.likelihood.result max.nulltable = hhg.univariate.ks.nulltable(c(N0,N1), aggregation.type = 'max', score.type='LikelihoodRatio', mmin = 3, mmax = 5, nr.replicates = 100) #default nr. of replicates is 1000, but may take several seconds. #For illustration only, we use 100 replicates, #but it is highly recommended to use at least 1000 in practice. #p-value for m=3: hhg.univariate.ks.pvalue(hhg.univariate.Mm.likelihood.result, max.nulltable ,m = 3) #p-value for m=5: hhg.univariate.ks.pvalue(hhg.univariate.Mm.likelihood.result, max.nulltable,m = 5) #III) p-value for sum and max aggregation type, using large data variants: #Two groups, each from a different normal mixture, total sample size is 10^4: X_Large = c(c(rnorm(2500,-2,0.7),rnorm(2500,2,0.7)), c(rnorm(2500,-1.5,0.5),rnorm(2500,1.5,0.5))) Y_Large = (c(rep(0,5000),rep(1,5000))) plot(Y_Large,X_Large) # for these variants, make sure to change mmax so that mmax<= nr.atoms hhg.univariate.Sm.EQP.Likelihood.result = hhg.univariate.ks.stat(X_Large,Y_Large, variant = 'KSample-Equipartition',mmax=30) hhg.univariate.Mm.EQP.likelihood.result = hhg.univariate.ks.stat(X_Large,Y_Large, aggregation.type = 'max',variant = 'KSample-Equipartition',mmax=30) N0_large = 5000 N1_large = 5000 Sm.EQP.null.table = hhg.univariate.ks.nulltable(c(N0_large,N1_large), nr.replicates=200, variant = 'KSample-Equipartition', mmax = 30) Mm.EQP.null.table = hhg.univariate.ks.nulltable(c(N0_large,N1_large), nr.replicates=200, aggregation.type='max', variant = 'KSample-Equipartition', mmax = 30) hhg.univariate.ks.pvalue(hhg.univariate.Sm.EQP.Likelihood.result, Sm.EQP.null.table, m=5) hhg.univariate.ks.pvalue(hhg.univariate.Mm.EQP.likelihood.result, Mm.EQP.null.table, m=5) ## End(Not run)
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