cvpvs: Cross-Validated P-Values

In pvclass: P-Values for Classification

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data.

Usage

cvpvs(X, Y, method = c('gaussian','knn','wnn', 'logreg'), ...)

Arguments

X	matrix containing training observations, where each observation is a row vector.
Y	vector indicating the classes which the training observations belong to.
method	one of the following methods: 'gaussian': plug-in statistic for the standard Gaussian model, 'knn': k nearest neighbors, 'wnn': weighted nearest neighbors, 'logreg': multicategory logistic regression with l1-penalization.
...	further arguments depending on the method (see cvpvs.gaussian, cvpvs.knn, cvpvs.wnn, cvpvs.logreg).

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that Y[i] = b.
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using a plug-in statistic for the Gaussian model, 'k nearest neighbors', 'weighted nearest neighbors' or multicategory logistic regression with l1-penalization (see cvpvs.gaussian, cvpvs.knn, cvpvs.wnn, cvpvs.logreg) with estimated prior probabilities N(b)/n. Here N(b) is the number of observations of class b and n is the total number of observations.

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that Y[i] = b.

Author(s)

Niki Zumbrunnen [e-mail]
Lutz Dümbgen [e-mail]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

See Also

cvpvs.gaussian, cvpvs.knn, cvpvs.wnn, cvpvs.logreg, pvs, analyze.pvs

Examples

X <- iris[,1:4]
Y <- iris[,5]

cvpvs(X,Y,method='k',k=10,distance='d')

pvclass documentation built on May 1, 2019, 10:17 p.m.