Description Usage Arguments Details Value Author(s) References Examples
View source: R/HHG_univariate.R
The p-value computation for the distribution free test of independence between two univariate random variables of Heller et al. (2016) ,using a fixed partition size m
.
1 | hhg.univariate.ind.pvalue(statistic, NullTable, m=min(statistic$mmax,4),l=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. |
l |
For |
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.
For 'DDP'
, 'ADP'
and 'ADP-EQP'
variants, the partition size is described by a single parameter m
(since partition size is m X m). For 'ADP-ML'
and 'ADP-EQP-ML'
variants, partition sizes of data are of sizes m X l, allowing for assymetric tables.
The p-value.
Barak Brill and 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 https://www.jmlr.org/papers/volume17/14-441/14-441.pdf
Brill B. (2016) Scalable Non-Parametric Tests of Independence (master's thesis) http://primage.tau.ac.il/libraries/theses/exeng/free/2899741.pdf
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | ## Not run:
N = 35
data = hhg.example.datagen(N, 'Parabola')
X = data[1,]
Y = data[2,]
plot(X,Y)
#I) Computing test statistics , with default parameters:
#statistic:
hhg.univariate.ADP.Likelihood.result = hhg.univariate.ind.stat(X,Y)
hhg.univariate.ADP.Likelihood.result
#null table:
ADP.null = hhg.univariate.ind.nulltable(N)
#pvalue:
hhg.univariate.ind.pvalue(hhg.univariate.ADP.Likelihood.result, ADP.null)
#II) Computing test statistics , with summation over Data Derived Partitions (DDP),
#using Pearson scores, and partition sizes up to 5:
#statistic:
hhg.univariate.DDP.Pearson.result = hhg.univariate.ind.stat(X,Y,variant = 'DDP',
score.type = 'Pearson', mmax = 5)
hhg.univariate.DDP.Pearson.result
#null table:
DDP.null = hhg.univariate.ind.nulltable(N,mmax = 5,variant = 'DDP',
score.type = 'Pearson', nr.replicates = 1000)
#pvalue , for different partition size:
hhg.univariate.ind.pvalue(hhg.univariate.DDP.Pearson.result, DDP.null, m =2)
hhg.univariate.ind.pvalue(hhg.univariate.DDP.Pearson.result, DDP.null, m =5)
#III) computing P-value for the variants used for large N:
N_Large = 1000
data_Large = hhg.example.datagen(N_Large, 'W')
X_Large = data_Large[1,]
Y_Large = data_Large[2,]
plot(X_Large,Y_Large)
NullTable_ADP_EQP = hhg.univariate.ind.nulltable(N_Large, variant = 'ADP-EQP',
nr.atoms = 30,nr.replicates=200)
NullTable_ADP_EQP_ML = hhg.univariate.ind.nulltable(N_Large,
variant = 'ADP-EQP-ML',nr.atoms = 30,nr.replicates=200)
ADP_EQP_result = hhg.univariate.ind.stat(X_Large,Y_Large,variant = 'ADP-EQP',
nr.atoms =30)
ADP_EQP_ML_result = hhg.univariate.ind.stat(X_Large,Y_Large,variant='ADP-EQP-ML',
nr.atoms = 30)
#P-value for the S_(5X5) statistic, the sum over all 5X5 partitions:
hhg.univariate.ind.pvalue(ADP_EQP_result,NullTable_ADP_EQP,m=5 )
#P-value for the S_(5X3) statistic, the sum over all 5X3 partitions:
hhg.univariate.ind.pvalue(ADP_EQP_ML_result,NullTable_ADP_EQP_ML,m=5,l=3)
## End(Not run)
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