approxMleWnPairs: Approximate MLE of the WN diffusion in 2D from a sample of...

In sdetorus: Statistical Tools for Toroidal Diffusions

Approximate MLE of the WN diffusion in 2D from a sample of initial and final pairs of angles.

Description

Approximate Maximum Likelihood Estimation (MLE) for the Wrapped Normal (WN) diffusion, using the wrapped Ornstein–Uhlenbeck diffusion and assuming initial stationarity.

Usage

approxMleWnPairs(data, delta, start = c(0, 0, 1, 1, 0, 1, 1),
  alpha = rep(NA, 3), mu = rep(NA, 2), sigma = rep(NA, 2), rho = NA,
  lower = c(-pi, -pi, 0.01, 0.01, -25, 0.01, 0.01, -0.99), upper = c(pi,
  pi, 25, 25, 25, 25, 25, 0.99), maxK = 2, expTrc = 30, ...)

Arguments

data	a matrix of dimension c(n, p).
delta	discretization step.
start	starting values, a matrix with p columns, with each entry representing a different starting value.
alpha	vector of length 3 parametrizing the A matrix as in alphaToA.
mu	a vector of length 2 giving the mean.
sigma	vector of length 2 containing the square root of the diagonal of \Sigma, the diffusion matrix.
rho	correlation coefficient of \Sigma.
lower, upper	bound for box constraints as in method "L-BFGS-B" of optim.
maxK	maximum absolute value of the windings considered in the computation of the WN.
expTrc	truncation for exponential: exp(x) with x <= -expTrc is set to zero. Defaults to 30.
...	further parameters passed to mleOptimWrapper.

Value

Output from mleOptimWrapper.

Examples

mu <- c(0, 0)
alpha <- c(1, 2, 0.5)
sigma <- c(1, 1)
rho <- 0.5
set.seed(4567345)
begin <- rStatWn2D(n = 200, mu = mu, alpha = alpha, sigma = sigma)
end <- t(apply(begin, 1, function(x) rTrajWn2D(x0 = x, alpha = alpha,
                                               mu = mu, sigma = sigma,
                                               rho = rho, N = 1,
                                               delta = 0.1)[2, ]))
data <- cbind(begin, end)
approxMleWnPairs(data = data, delta = 0.1,
                 start = c(2, pi/2, 2, 0.5, 0, 2, 1, 0.5))

sdetorus documentation built on June 22, 2024, 6:58 p.m.