MINTregression {IndepTest}

MINTregression

Description

Performs a goodness-of-fit test of a linear model by testing whether the errors are independent of the covariates.

Usage

MINTregression(x, y, k, keps, w = FALSE, eps)

Arguments

x

The n \times p design matrix.

y

The response vector of length n.

k

The value of k to be used for estimation of the joint entropy H(X,\epsilon).

keps

The value of k to be used for estimation of the marginal entropy H(\epsilon).

w

The weight vector to be used for estimation of the joint entropy H(X,\epsilon), with the same options as for the KLentropy function.

eps

A vector of null errors which should have the same distribution as the errors are assumed to have in the linear model.

Value

The p-value corresponding the independence test carried out.

References

Berrett, T. B. and Samworth R. J. (2017). “Nonparametric independence testing via mutual information.” ArXiv e-prints. 1711.06642.

Examples

# Correctly specified linear model
x=runif(100,min=-1.5,max=1.5); y=x+rnorm(100)
plot(lm(y~x),which=1) 
MINTregression(x,y,5,10,w=FALSE,rnorm(10000))
# Misspecified mean linear model
x=runif(100,min=-1.5,max=1.5); y=x^3+rnorm(100)
plot(lm(y~x),which=1)
MINTregression(x,y,5,10,w=FALSE,rnorm(10000))
# Heteroscedastic linear model
x=runif(100,min=-1.5,max=1.5); y=x+x*rnorm(100);
plot(lm(y~x),which=1) 
MINTregression(x,y,5,10,w=FALSE,rnorm(10000))
# Multivariate misspecified mean linear model
x=matrix(runif(1500,min=-1.5,max=1.5),ncol=3)
y=x[,1]^3+0.3*x[,2]-0.3*x[,3]+rnorm(500)
plot(lm(y~x),which=1)
MINTregression(x,y,30,50,w=TRUE,rnorm(50000))