Description Usage Arguments Details Value References Examples

Approximate Maximum Likelihood Estimation (MLE) for the Wrapped Normal (WN) in 1D using the wrapped Ornstein–Uhlenbeck diffusion.

1 2 3 |

`data` |
a matrix of dimension |

`delta` |
discretization step. |

`start` |
starting values, a matrix with |

`alpha, mu, sigma` |
if their values are provided, the likelihood function is optimized with respect to the rest of unspecified parameters. The number of elements in |

`lower` |
bound for box constraints as in method "L-BFGS-B" of |

`upper` |
bound for box constraints as in method "L-BFGS-B" of |

`vmApprox` |
flag to indicate von Mises approximation to wrapped normal. See |

`maxK` |
maximum absolute winding number used if |

`...` |
further parameters passed to |

See Section 3.3 in García-Portugués et al. (2019) for details.

Output from `mleOptimWrapper`

.

García-Portugués, E., Sørensen, M., Mardia, K. V. and Hamelryck, T. (2019) Langevin diffusions on the torus: estimation and applications. *Statistics and Computing*, 29(2):1–22. doi: 10.1007/s11222-017-9790-2

1 2 3 4 5 6 7 8 9 10 | ```
alpha <- 0.5
mu <- 0
sigma <- 2
samp <- rTrajWn1D(x0 = 0, alpha = alpha, mu = mu, sigma = sigma, N = 1000,
delta = 0.1)
approxMleWn1D(data = samp, delta = 0.1, start = c(alpha, mu, sigma))
approxMleWn1D(data = samp, delta = 0.1, sigma = sigma, start = c(alpha, mu),
lower = c(0.01, -pi), upper = c(25, pi))
approxMleWn1D(data = samp, delta = 0.1, mu = mu, start = c(alpha, sigma),
lower = c(0.01, 0.01), upper = c(25, 25))
``` |

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