MAMSE-package: Minimum Averaged Mean Squared Error (MAMSE) Weights.
In MAMSE: Calculation of Minimum Averaged Mean Squared Error (MAMSE) Weights

Description Details Author(s) References See Also Examples

This package provides algorithms to calculate the nonparametric adaptive MAMSE weights. The MAMSE weights can be used for the weighted likelihood (see references below), or as mixing probabilities to define mixtures of empirical distributions. They provide a framework to borrow strenght with minimal assumptions.

Package:	MAMSE
Type:	Package
Version:	0.2
Date:	2016-01-20
License:	GPL-2

Function MAMSE calculates the MAMSE weights for univariate data, right-censored data, or for the copula underlying the distribution of multivariate data. The function WKME is used to compute the MAMSE-weighted Kaplan-Meier estimate with (optional) bootstrap confidence intervals. The function roc calculates MAMSE-weighted ROC curves.

Jean-Francois Plante, <jfplante(at)hec.ca>.

Maintainer: Jean-Francois Plante, <jfplante(at)hec.ca>.

J.-B. Débordès & J.-F. Plante (2009). Combining ROC curves using MAMSE weighted distributions. Cahier du GERAD G-2015-69.

F. Hu and J. V. Zidek (2002). The weighted likelihood, The Canadian Journal of Statistics, 30, 347–371.

J.-F. Plante (2007). Adaptive Likelihood Weights and Mixtures of Empirical Distributions. Unpublished doctoral dissertation, University of British Columbia.

J.-F. Plante (2008). Nonparametric adaptive likelihood weights. The Canadian Journal of Statistics, 36, 443-461.

J.-F. Plante (2009). Asymptotic properties of the MAMSE adaptive likelihood weights. Journal of Statistical Planning and Inference, 139, 2147-2161.

J.-F. Plante (2009). About an adaptively weighted Kaplan-Meier estimate. Lifetime Data Analysis, 15, 295-315.

X. Wang (2001). Maximum weighted likelihood estimation, unpublished doctoral dissertation, Department of Statistics, The University of British Columbia.

MAMSE, WKME, roc.

set.seed(2009)

# MAMSE weights for univariate data
x=list(rnorm(25),rnorm(250,.1),rnorm(100,-.1))
wx=MAMSE(x)

# Weighted Likelihood estimate for the mean (Normal model)
sum(wx*sapply(x,mean))

#MAMSE weights for copulas
rho=c(.25,.3,.15,.2)
r=2*sin(rho*pi/600)
y=list(0,0,0,0)
for(i in 1:4){
  sig=matrix(c(1,r,r,1),2,2)
  y[[i]]=matrix(rnorm(150),nc=2)
}
wy=MAMSE(y)

# Weighted coefficient of correlation
sum(wy*sapply(y,cor,method="spearman")[2,])

#MAMSE weights for right-censored data

z=list(0,0,0)
for(i in 1:3){  
  zo=rexp(100)
  zc=pmin(rexp(100),rexp(100),rexp(100))
  z[[i]]=cbind(pmin(zo,zc),zo<=zc)
}

MAMSE(z,.5,surv=TRUE)

allz=pmin(.5,c(z[[1]][z[[1]][,2]==1,1],z[[2]][z[[2]][,2]==1,1],
   z[[3]][z[[3]][,2]==1,1]))
K=WKME(z,.5,time=sort(unique(c(0,.5,allz,allz-.0001))))
plot(K$time,K$wkme,type='l',col="blue",xlab="x",ylab="P(X<=x)",
   ylim=c(0,.5))
lines(K$time,K$kme[,1],col="red")
legend(0,.5,c("Weighted Kaplan-Meier","Kaplan-Meier"),
   col=c("blue","red"),lty=c(1,1))

# MAMSE-weighted ROC curve

set.seed(2016)
nh=c(50,25,70,100)
nd=c(40,20,50,80)
muh=c(1.5,1,1.7,1.2)
mud=c(0,.2,.5,.4)

# Target curve
FPR=seq(0,1,.01)
TPR=pnorm(qnorm(FPR,mean=muh[1]),mean=mud[1])

simh=list()
simd=list()

for(i in (1:length(nh))){
  simh[[i]]=rnorm(nh[i],mean=muh[i])
  simd[[i]]=rnorm(nd[i],mean=mud[i])
}

par(mfrow=c(1,2))
plot(roc(simh,simd),col="red")
lines(roc(simh[[1]],simd[[1]]),col="blue")
lines(FPR,TPR,col="gray")
title("Empirical ROC curves")

plot(roc(simh,simd,method="normal"),col="red")
lines(roc(simh[[1]],simd[[1]],method="normal"),col="blue")
lines(FPR,TPR,col="gray")
title("Parametric ROC curves")