MAMSE (version 0.2-1)

MAMSE: Minimum Averaged Mean Squared Error Weights

Description

Computes the MAMSE weights (see references below for their definition).

Usage

MAMSE(x,surv=FALSE,ub=NULL,lb=0,MCint=FALSE,nMC=10000)

Arguments

x

A list of m samples. Elements of the list must be vectors of matrices. If they are vectors, the univariate MAMSE weights are computed. Matrices should have n lines with one p-dimensional datum per line. The data are automatically tranformed into rescaled ranks by the function ranked. The MAMSE weights for copulas are then calculated. For survival MAMSE weights, use the argument surv=TRUE and provide an n by 2 matrix where the second column is an indicator (delta) of whether the time in column 1 is observed (delta=1) or censored (delta=0).

surv

Controls the calculation of the survival MAMSE weights rather that the multivariate version for copulas.

ub

if surv=TRUE, the upper bound for the integral of the MAMSE criterion.

lb

If surv=TRUE, the lower bound for the integral of the MAMSE criterion.

MCint

When MAMSE weights are calculated for copulas, MCint=TRUE allows to proceed with Monte Carlo integration. The laternative MCint=TRUE will estimate the integral on the grid [1/n1,2/n1,...,1]^p which does not scale well with the number of dimensions p.

nMC

When MCint=TRUE, nMC controls the number of samples used to approximate the integral.

Value

p elements containing the MAMSE weights for each of the populations.

Details

Provided a list of samples, this function returns the Minimum Averaged Mean Squared Error weights. The MAMSE weights can be used in a weighted likelihood, or to define mixtures of empirical distributions. In both cases, the methodology is used to infer on Population 1 while borrowing strength from the other samples provided. Refer to the articles below for the exact definition of the MAMSE weights, their asymptotic properties and simulations results, as well as additional information about the weighted likelihood.

References

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 Unpublished doctoral dissertation, University of British Columbia.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.

See Also

MAMSE-package, WKME.

Examples

set.seed(2009)

# MAMSE weights for univariate data
x=list(rnorm(25),rnorm(25,.1),rnorm(25,.2))
MAMSE(x)

#MAMSE weights for copulas
y=list(matrix(rnorm(150),nc=2),matrix(rnorm(150),nc=2),
   matrix(rnorm(150),nc=2))
MAMSE(y)
MAMSE(y,MCint=TRUE)

#MAMSE weights for right-censored data
z=list(cbind(rexp(50),rbinom(50,1,.5)),cbind(rexp(50,1.1),
   rbinom(50,1,.5)),cbind(rexp(50,.9),rbinom(50,1,.5)))
MAMSE(z,3,surv=TRUE)

#For more examples, see help on "MAMSE-package"