nfcm_nll: Negative approximate log-likelihood of Spline Based Nonlinear...

In samorso/nfcm: Spline Based Nonlinear Factor Copula Model

Negative approximate log-likelihood of Spline Based Nonlinear Factor Copula Model

Description

Compute an upper bound of the negative log-likelihood for a bivariate model. It is defined as

\frac{1}{n}\frac{1}{N}\sum_{i=1}^n\sum_{j=1}^N\Phi^\top\Lambda \psi'(w_{ij}),

where \psi' is the first derivative of a spline basis \psi, \Lambda is a matrix of spline coefficients and \Phi is defined as

\int_0^1\psi(u)du.

It is assumed that the variables have a positive quadrant dependence.

Usage

nfcm_nll(lambda, w, type = "b", splines_control = splines.control())

nfcm_grad_nll(lambda, w, type = "b", splines_control = splines.control())

nfcm_aic(lambda, w, type = "b", splines_control = splines.control())

nfcm_bic(lambda, w, type = "b", splines_control = splines.control())

Arguments

lambda	vector of spline coefficients (\Lambda vectorized).
w	uniform(0,1) n\times N matrix of observations.
type	specify spline basis, either "b" (default), "c", "i" or "m";
splines_control	control (see splines.control).

Value

The approximate negative log-likelihood divided by n and N.

The gradient of the approximate negative log-likelihood divided by n and N.

Akaike information criterion

Bayesian information criterion

samorso/nfcm documentation built on Oct. 13, 2024, 9:35 p.m.