Repository Mirror for your Cloud Server and Webhosting

Title:

Shrinkage for Extreme Partial Least-Squares (SEPaLS)

Date:

2023-10-11

Type:

Package

Version:

0.1.0

Description:

Regression context for the Partial Least Squares framework for Extreme values. Estimations of the Shrinkage for Extreme Partial Least-Squares (SEPaLS) estimators, an adaptation of the original Partial Least Squares (PLS) method tailored to the extreme-value framework. The SEPaLS project is a joint work by Stephane Girard, Hadrien Lorenzo and Julyan Arbel. R code to replicate the results of the paper is available at https://github.com/hlorenzo/SEPaLS_simus. Extremes within PLS was already studied by one of the authors, see M Bousebeta, G Enjolras, S Girard (2023) <doi:10.1016/j.jmva.2022.105101>.

License:

MIT + file LICENSE

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.2.0

NeedsCompilation:

Packaged:

2023-10-23 21:11:42 UTC; hlorenzo

Author:

Stephane Girard [aut], Julyan Arbel [aut], Hadrien Lorenzo [aut, cre, cph]

Maintainer:

Hadrien Lorenzo <hadrien.lorenzo@univ-amu.fr>

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2023-10-24 18:20:06 UTC

Function to estimate SEPaLS estimators

Description

Function to estimate SEPaLS estimators

Usage

SEPaLS(
  X,
  Y,
  yn,
  type = c("vMF", "Laplace"),
  mu0 = NULL,
  kappa0 = NULL,
  lambda = NULL
)

Arguments

X

(n\times p)-dimensional matrix of the covariates.

Y

(n)-dimensional vector of the response.

yn

y_n the quantile correponding to lowest values of Ys to put in th e tail.

type

character, wether vMF for von Mises-Fisher prior or Laplace for Laplace prior. See details.

mu0

\mu_0, unitary (p)-dimensional vector. The direction parameter for the vMF prior.

kappa0

\kappa_0, positive. The concentration parameter for the vMF prior.

lambda

\lambda, positive. The concentration parameter for the Laplace prior.

Details

The SEPaLS estimators are built depending on the value given to type:

vMF: then the estimator is proportional to

\hat{\beta}_{ml}(y_n) + \kappa_0\mu_0,

where \hat{\beta}_{ml}(y_n) is the EPLS estimator, which coincides with the maximum-likelihood estimator of SEPaLS for a threshold y_n.
Laplace: then the estimator is proportional to

S_\lambda\left(\hat{\beta}_{ml}(y_n)\right),

where S_\lambda is the soft-thresholding operator of threshold \lambda.

Value

A SEPaLS estimator

Examples

set.seed(1)
n <- 3000
p <- 10
X <- matrix(rnorm(n*p),n,p)
beta <- c(5:1,rep(0,p-5)) ; beta <- beta/sqrt(sum(beta^2))
Y <- (X%*%beta)^3 + rnorm(n,sd=1/3)
mu0 <- rnorm(p) ; mu0 <- mu0/sqrt(sum(mu0^2))
sepals_vMF <- SEPaLS(X,Y,yn=1,type="vMF",mu0=mu0,kappa0=1)
sepals_Laplace <- SEPaLS(X,Y,yn=1,type="Laplace",lambda=0.01)

Bootstrap function for SEPaLS estimator.

Description

Bootstrap function for SEPaLS estimator.

Usage

bootstrap.SEPaLS(
  X,
  Y,
  yn,
  type = c("vMF", "Laplace"),
  mu0 = NULL,
  kappa0 = NULL,
  lambda = NULL,
  B = 20
)

Arguments

X

(n\times p)-dimensional matrix of the covariates.

Y

(n)-dimensional vector of the response.

yn

y_n the quantile corresponding to lowest values of Ys to put in the tail.

type

character, whether vMF for von Mises-Fisher prior or Laplace for Laplace prior. See details.

mu0

\mu_0, unitary (p)-dimensional vector. The direction parameter for the vMF prior.

kappa0

\kappa_0, positive. The concentration parameter for the vMF prior.

lambda

\lambda, positive. The concentration parameter for the Laplace prior.

B

positive integer. The number of bootstrap samples on which estimate the SEPaLS directions. Default to 20.

Value

A list with two elements:

ws: A (B\times p)-dimensional matrix with each row corresponding to the SEPaLS direction estimated on each bootstrap sample.
cor: The correlation of each estimate direction on the Out-Of-Bag (OOB) sample with the response.

Examples

set.seed(5)
n <- 3000
p <- 10
X <- matrix(rnorm(n*p),n,p)
beta <- c(5:1,rep(0,p-5)) ; beta <- beta/sqrt(sum(beta^2))
Y <- (X%*%beta)^3 + rnorm(n)
boot.sepals_Laplace <- bootstrap.SEPaLS(X,Y,yn=1,type="Laplace",lambda=0.01,
B=100)
boxplot(boot.sepals_Laplace$ws);abline(h=0,col="red",lty=2)

Maximum Likelihood estimator

Description

Maximum Likelihood estimator

Usage

maximum_Likelihood_SEPaLS(X, Y, yn)

Arguments

X

(n\times p)-dimensional matrix of the covariates.

Y

(n)-dimensional vector of the response.

yn

the quantile corresponding to the lowest values of Ys to put in the tail.

Value

The maximum likelihood estimator.

Examples

n <- 3000
p <- 10
X <- matrix(rnorm(n*p),n,p)
beta <- c(5:1,rep(0,p-5)) ; beta <- beta/sqrt(sum(beta^2))
Y <- X%*%beta + rnorm(n,sd=1/3)
estimators <- do.call(rbind,lapply(seq(0,1,length.out=100),function(pp){
  yn <- quantile(Y,probs = pp)
  maximum_Likelihood_SEPaLS(X,Y,yn)
}))
matplot(estimators,type="l",lty=1,col=c(rep(2,5),rep(1,p-5)))
abline(h=beta/sqrt(sum(beta^2)),col=c(rep(2,5),rep(1,p-5)))

The RICA dataset describing the production of carrots (open field) (in quintals) from 2000 to 2015.

Description

A subset of data from the 'agreste' French governmental website <https://agreste.agriculture.gouv.fr/agreste-web/servicon/I.2/listeTypeServicon/>.

Usage

data(ricaCarrots)

Format

'ricaCarrots'

A List of 3 objects:

Y: a vector. The production of carrots (open field) (in quintals) for 598 French farms.
X: a matrix. The 259 covariates describing the same 598 French farms.
description: a matrix. Description of the 259 covariates.

Source

<https://agreste.agriculture.gouv.fr/agreste-web/servicon/I.2/listeTypeServicon/>

Function to estimate SEPaLS estimators

Description

Usage

Arguments

Details

Value

See Also

Examples

Bootstrap function for SEPaLS estimator.

Description

Usage

Arguments

Value

See Also

Examples

Maximum Likelihood estimator

Description

Usage

Arguments

Value

Examples

The RICA dataset describing the production of carrots (open field) (in quintals) from 2000 to 2015.

Description

Usage

Format

Source