Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions
type: Item
instance of: scholarly article
title: Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions
zbMATH Open document ID: 0586.62154
author: Craig F. Ansley
author: Robert Kohn
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 3940539
zbMATH Keywords: likelihood
zbMATH Keywords: state space model
zbMATH Keywords: incompletely specified initial conditions
zbMATH Keywords: predictors
zbMATH Keywords: interpolators
zbMATH Keywords: missing observations
zbMATH Keywords: diffuse prior
zbMATH Keywords: Kalman filter
zbMATH Keywords: smoothing algorithms
zbMATH Keywords: exact numerical procedures
zbMATH Keywords: diffuse initial conditions
zbMATH Keywords: continuous time models
zbMATH Keywords: smoothing splines
zbMATH Keywords: continuous time autoregressive processes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349739
OpenAlex ID: W2016115088
DOI: 10.1214/AOS/1176349739
description: scientific article; zbMATH DE number 3940539