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Second, the performance of filtering drops off when we incorrectly specify the variance of the sampling error, and especially when we overestimate it.
It makes a priori assumptions about the variance of the sampling error that would not usually be made and does so in a way that violates an important property of the Kalman filter.
Through simulations we assess whether and to what extent filtering: reliably detects the characteristics of time series; does so across series with different rates of autoregressive decay; and does so when the variance of the sampling error is unknown.
We set the power transmitted over each basis function to be 0.7 and the variance of the sampling noise to be 0.004.
If the variance of the prior information is smaller than the variance of the sampling information, then a higher weight is assigned to the prior information.
Similarly, Maravall (2003) derived expressions for the asymptotic variance of the sampling variances and autocorrelations of the smoothed components using classic results for linear stationary Gaussian processes (see e.g. Lomnicki and Zaremba 1959 or Anderson and Walker 1964).
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When the sampling variation is considered, the variance of the sample sensitivity is slightly inflated, but its confidence interval width becomes widely dispersed.
Previous studies on the characterization of solids mixtures have shown that the variance of the sample composition can be related to the structure of t.
In this paper, a methodology is proposed to weight data pairs in order to compensate for redundancies between clustered data values and to minimize the fluctuation variance of the sample variogram.
The sample variance of the sample is defined as (1.2).
From both sets we calculated the mean and variance of the sampled data.
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Justyna Jupowicz-Kozak
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