Description Usage Arguments Value References See Also

Runs EM algorithm to compute MLE for the smoothed model of Cao et al. (2000). Uses numerical optimization of Q-function for each M-step with analytic computation of its gradient. This performs estimation for a single time point using output from the previous one.

1 2 | ```
smoothed_EM(Y, A, eta0, sigma0, V, c = 2, maxiter = 1000, tol = 1e-06,
eps.lambda = 0, eps.phi = 0, method = "L-BFGS-B")
``` |

`Y` |
matrix (h x k) of observations in local window; columns correspond to OD flows, and rows are individual observations |

`A` |
routing matrix (m x k) for network being analyzed |

`eta0` |
numeric vector (length k+1) containing value for log(c(lambda, phi)) from previous time (or initial value) |

`sigma0` |
covariance matrix (k+1 x k+1) of log(c(lambda, phi)) from previous time (or initial value) |

`V` |
evolution covariance matrix (k+1 x k+1) for log(c(lambda, phi)) (random walk) |

`c` |
power parameter in model of Cao et al. (2000) |

`maxiter` |
maximum number of EM iterations to run |

`tol` |
tolerance (in relative change in Q function value) for stopping EM iterations |

`eps.lambda` |
numeric small positive value to add to lambda for numerical stability; typically 0 |

`eps.phi` |
numeric small positive value to add to phi for numerical stability; typically 0 |

`method` |
optimization method to use (in optim calls) |

list with 5 elements: `lambda`

, the estimated value of
lambda; `phi`

, the estimated value of phi;
`iter`

, the number of iterations run; `etat`

,
log(c(lambda, phi)); and sigmat, the inverse of the Q
functions Hessian at its mode

J. Cao, D. Davis, S. Van Der Viel, and B. Yu. Time-varying network tomography: router link data. Journal of the American Statistical Association, 95:1063-75, 2000.

Other CaoEtAl: `Q_iid`

;
`Q_smoothed`

; `R_estep`

;
`grad_iid`

; `grad_smoothed`

;
`locally_iid_EM`

; `m_estep`

;
`phi_init`

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