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December, 1985 Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions
Craig F. Ansley, Robert Kohn
Ann. Statist. 13(4): 1286-1316 (December, 1985). DOI: 10.1214/aos/1176349739

Abstract

The likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions. This approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations. It is then shown that this method is equivalent to placing a diffuse prior distribution on the unspecified part of the initial state vector, and modified versions of the Kalman filter and smoothing algorithms are derived to give exact numerical procedures for diffuse initial conditions. The results are extended to continuous time models, including smoothing splines and continuous time autoregressive processes.

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Craig F. Ansley. Robert Kohn. "Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions." Ann. Statist. 13 (4) 1286 - 1316, December, 1985. https://doi.org/10.1214/aos/1176349739

Information

Published: December, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0586.62154
MathSciNet: MR811494
Digital Object Identifier: 10.1214/aos/1176349739

Subjects:
Primary: 62M15
Secondary: 60G35, 62M20

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 4 • December, 1985
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