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| 52 |
with state vector \samp{a}, transitions \samp{a <- T a + R e},
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52 |
with state vector \samp{a}, transitions \samp{a <- T a + R e},
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| 53 |
\eqn{e \sim {\cal N}(0, \kappa Q)}{e ~ N(0, kappa Q)} and observation
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53 |
\eqn{e \sim {\cal N}(0, \kappa Q)}{e ~ N(0, kappa Q)} and observation
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| 54 |
equation \samp{y = Z'a + eta},
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54 |
equation \samp{y = Z'a + eta},
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| 55 |
\eqn{(eta\equiv\eta), \eta \sim {\cal N}(0, \kappa h)}{eta ~ N(0, kappa h)}.
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55 |
\eqn{(eta\equiv\eta), \eta \sim {\cal N}(0, \kappa h)}{eta ~ N(0, kappa h)}.
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The likelihood is a profile likelihood after estimation of
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56 |
The likelihood is a profile likelihood after estimation of
|
| 57 |
\eqn{\kappa}{kappa}.
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57 |
\eqn{\kappa}.
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| 58 |
|
58 |
|
| 59 |
The model is specified as a list with at least components
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59 |
The model is specified as a list with at least components
|
| 60 |
\describe{
|
60 |
\describe{
|
| 61 |
\item{\code{T}}{the transition matrix}
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61 |
\item{\code{T}}{the transition matrix}
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| 62 |
\item{\code{Z}}{the observation coefficients}
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62 |
\item{\code{Z}}{the observation coefficients}
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| 92 |
}
|
92 |
}
|
| 93 |
|
93 |
|
| 94 |
\value{
|
94 |
\value{
|
| 95 |
For \code{KalmanLike}, a list with components \code{Lik} (the
|
95 |
For \code{KalmanLike}, a list with components \code{Lik} (the
|
| 96 |
log-likelihood less some constants) and \code{s2}, the estimate of
|
96 |
log-likelihood less some constants) and \code{s2}, the estimate of
|
| 97 |
\eqn{\kappa}{kappa}.
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97 |
\eqn{\kappa}.
|
| 98 |
|
98 |
|
| 99 |
For \code{KalmanRun}, a list with components \code{values}, a vector
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99 |
For \code{KalmanRun}, a list with components \code{values}, a vector
|
| 100 |
of length 2 giving the output of \code{KalmanLike}, \code{resid} (the
|
100 |
of length 2 giving the output of \code{KalmanLike}, \code{resid} (the
|
| 101 |
residuals) and \code{states}, the contemporaneous state estimates,
|
101 |
residuals) and \code{states}, the contemporaneous state estimates,
|
| 102 |
a matrix with one row for each observation time.
|
102 |
a matrix with one row for each observation time.
|