estimate_parameters: estimate_parameters

In EMLI: Computationally Efficient Maximum Likelihood Identification of Linear Dynamical Systems

estimate_parameters

Description

Calculates maximum likelihood estimates of the statistical measures of the output-differenced version of the one-dimensional cumulative structural equation model with shock-error output measurement equation and assumptions of normality and independence.

Usage

estimate_parameters(dat, tol)

Arguments

dat	An (n + 1) x (m + 1) data frame of finite numeric elements (possibly except for row 1 columns 1 to m) containing observed input (columns 1 to m) and output (column m + 1) data of the original model.
tol	A tolerance parameter of the golden section search algorithm used for minimizing the one-dimensional likelihood function (vector of length 1, finite positive numeric element).

Value

A list consisting of 3 elements: 1) estimate of the covariance at lag 0 of the data that result from the output-differenced model (Sigma; (m + 1) x (m + 1) matrix of numeric elements); 2) estimate of the only non-zero element of the negative covariance at lag 1 of the data that result from the output-differenced model (sigma_y^2; vector of length 1, numeric element); 3) estimate of the mean of the data that result from the output-differenced model (mu; (m + 1) x 1 matrix of numeric elements).

Examples

set.seed(1)

m <- 4
k <- 2

L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)

data <- generate_data(100, L, sigma, mu)

estimate_parameters(data, 0.00001)

EMLI documentation built on Nov. 21, 2022, 1:06 a.m.