Abstract
An extension of the smoothing polynomial spline to fit bivariate response data is presented. The data are modeled as integrated random walks with observational errors. Correlation can exist in the random walks, the observational errors, or both. The Kalman filter is used to calculate the log likelihood of the data as a function of the unknown parameters in the covariance matrices, and nonlinear optimization is used to obtain maximum likelihood estimates of the parameters. A modification of the Kalman filter is used at the beginning of the data to allow the use of diffuse (noninformative) priors. This model is applied to the problem of characterizing gas exchange time series of exercising subjects.
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