LPRelevance (version 3.3)

LASER: Generates Artificial RELevance Samples.

Description

This function generates the artificial relevance samples (LASER).These are "sharpened" z-samples manufactured by the relevance-function \(d_x(z)\).

Usage

LASER( X,z, X.target, m=c(4,6), nsample=length(z), lp.reg.method='lm',
       coef.smooth='BIC', centering=TRUE,parallel=FALSE,...)

Arguments

X

A \(n\)-by-\(d\) matrix of covariate values

z

A length \(n\) vector containing observations of z values.

X.target

A \(k\)-by-\(d\) matrix providing k sets of target points for which the LASERs are required.

m

An ordered pair. First number indicates how many LP-nonparametric basis to construct for each \(X\), second number indicates how many to construct for \(z\). Default: m=c(4,6)

nsample

Number of relevance samples to generate for each case.

lp.reg.method

Method for estimating the relevance function and its conditional LP-Fourier coefficients. We currently support thee options: lm (inbuilt with subset selection), glmnet, and knn.

centering

Whether to perform regression-adjustment to center the data, default is TRUE.

coef.smooth

Specifies the method to use for LP coefficient smoothing (AIC or BIC). Uses BIC by default.

parallel

Use parallel computing for obtaining the relevance samples, mainly used for very huge nsample, default is FALSE.

...

Extra parameters to pass to other functions. Currently only supports the arguments for knn().

Value

A list containing the following items:

data

The relevant samples at X.target.

LPcoef

Parameters of the relevance function \(d_x(x)\).

References

Mukhopadhyay, S., and Wang, K (2021) "On The Problem of Relevance in Statistical Inference". <arXiv:2004.09588>

Examples

# NOT RUN {
data(funnel)
X<-funnel$x
z<-funnel$z
z.laser.x30<-LASER(X,z,X.target=30,m=c(4,8))$data
hist(z.laser.x30,50)
# }