# Snorm.grad: Gradient of the loglikelihood of a multivariate normal with... In SuperGauss: Superfast Likelihood Inference for Stationary Gaussian Time Series

## Usage

 `1` ```Snorm.grad(X, mu, acf, dmu, dacf) ```

## Arguments

 `X` A length-`N` vector of multivariate normal observations. `mu` A scalar or length-`N` vector of means. If missing defaults to the vector of zeros. `acf` A `Toeplitz` object or length-`N` vector containing the first column of the Toeplitz variance matrix. `dmu` A length-`p` vector or `N x p` matrix of partial derivatives of `mu` along the columns. If missing defaults to a matrix of zeros. `dacf` An `N x p` matrix with the partial derivatives of `acf` along the columns.

## Value

A length-`p` vector containing the gradient of the loglikelihood.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# two parameter inference acf.fun <- function(theta) theta[2]^2 * exp(-theta[1]*(1:N-1)) mu.fun <- function(theta) theta[1] # partial derivatives dacf.fun <- function(theta) { ea <- exp(-theta[1]*(1:N-1)) cbind(-theta[1]*theta[2]^2 * ea, 2*theta[2] * ea) } dmu.fun <- function(theta) c(1, 0) # generate data N <- 300 theta <- rexp(2) X <- rSnorm(n = 1, acf = acf.fun(theta)) + mu.fun(theta) # likelihood gradient Snorm.grad(X = X, mu = mu.fun(theta), dmu = dmu.fun(theta), acf = acf.fun(theta), dacf = dacf.fun(theta)) ```

SuperGauss documentation built on May 1, 2019, 7:58 p.m.