Public API

Functions available to users of shrinkr. More...

Functions
double	C_OAS (const double *const sample_cov, double *const sample_cov_star, size_t n, size_t p)
	Oracle Approximating Shrinkage (OAS) covariance estimator.
void	C_LWAnalytical (const double *const lam, double *const lam_star, size_t n, size_t p, double eps)
	Ledoit-Wolf Analytical (nonlinear) shrinkage of eigenvalues.
double	C_LWLinear (const double *const data, const double *const sample_cov, double *const sample_cov_star, size_t n, size_t p)
	Ledoit-Wolf linear shrinkage estimator.
double	C_DEALObjective (const double *const base_evals, const double *const surr_evals, const double *const z_vec, double gamma, double *start_value, size_t n, size_t p)
	Objective function of DEAL.
double	C_DEAL (const double *const base_evals, const double *const surr_evals, const double *const z_vec, double gamma_min, double gamma_max, size_t n, size_t p)
	DEAL (Deterministic Equivalents for Adaptive LDA) shrinkage.

Detailed Description

Functions available to users of shrinkr.

Function Documentation

C_DEAL()

double C_DEAL	(	const double *const	base_evals,
		const double *const	surr_evals,
		const double *const	z_vec,
		double	gamma_min,
		double	gamma_max,
		size_t	n,
		size_t	p
	)

DEAL (Deterministic Equivalents for Adaptive LDA) shrinkage.

For more information check shrinkr.functional.deal.

Parameters

base_evals	Array of length p of eigenvalues for the objective. Which will be shrunk.
surr_evals	Array of length p of eigenvalues for the objective. Used to compute shrinkage paramters.
z_vec	Array of length p of the vector of interest projected into the eigenvector space.
gamma_min	Minimum value for the gamma bounded search.
gamma_max	Maximum value for the gamma bounded search.
n	Number of effective samples used to compute the sample covariance
p	One of the dimensions of the covariance matrix. Number of features.

C_DEALObjective()

double C_DEALObjective	(	const double *const	base_evals,
		const double *const	surr_evals,
		const double *const	z_vec,
		double	gamma,
		double *	start_value,
		size_t	n,
		size_t	p
	)

Objective function of DEAL.

For more information check shrinkr.functional.deal.

Parameters

base_evals	Array of length p of eigenvalues for the objective. Which will be shrunk.
surr_evals	Array of length p of eigenvalues for the objective. Used to compute shrinkage paramters.
z_vec	Array of length p of the vector of interest projected into the eigenvector space.
gamma	The value of gamma to evaluate. During optimization only this value changes.
start_value	Starting value of delta for the fixed point iteration method used by for the objective.
n	Number of effective samples used to compute the sample covariance
p	One of the dimensions of the covariance matrix. Number of features.

C_LWAnalytical()

void C_LWAnalytical	(	const double *const	lam,
		double *const	lam_star,
		size_t	n,
		size_t	p,
		double	eps
	)

Ledoit-Wolf Analytical (nonlinear) shrinkage of eigenvalues.

Based on Ledoit and Wolf (2018), using the analytic formula that avoids numerical optimization. Handles the high-dimensional setting where p > n.

Parameters

lam	Array of length p containing eigenvalues of the sample covariance matrix
lam_star	Array buffer of length p for shrunk eigenvalues
sample_cov_star	Output buffer for the shurnk covariance (pxp) (C or F contiguous but matching sample_cov)
n	Number of samples used to compute the sample covariance
p	Number of variables. Length of lam and lam_star
eps	Epsilon value for numerical stability

C_LWLinear()

double C_LWLinear	(	const double *const	data,
		const double *const	sample_cov,
		double *const	sample_cov_star,
		size_t	n,
		size_t	p
	)

Ledoit-Wolf linear shrinkage estimator.

Based on the Ledoit-Wolf Lemma. http://www.ledoit.net/ole1a.pdf

Parameters

data	Data matrix (nxp) (C contiguous)
sample_cov	Sample covariance matrix (pxp) (C or F contiguous)
sample_cov_star	Output buffer for the shurnk covariance (pxp) (C or F contiguous but matching sample_cov)
n	Number of samples used to compute the sample covariance
p	One of the dimensions of the covariance matrix

C_OAS()

double C_OAS	(	const double *const	sample_cov,
		double *const	sample_cov_star,
		size_t	n,
		size_t	p
	)

Oracle Approximating Shrinkage (OAS) covariance estimator.

The formulation is based on https://arxiv.org/pdf/0907.4698.pdf.

Parameters

sample_cov	Sample covariance matrix (pxp) (C or F contiguous)
sample_cov_star	Output buffer for the shurnk covariance (pxp) (C or F contiguous but matching sample_cov)
n	Number of samples used to compute the sample covariance
p	One of the dimensions of the matrix

Returns

The value of the linear shrinkage