In these cases, the least squares estimate amplifies the measurement noise and may be grossly inaccurate.
2.
In particular, least squares estimates for regression models are highly sensitive to ( not robust against ) outliers.
3.
In general, they may be estimated using the unrestricted least squares estimates obtained from the original full model.
4.
Univariate normality is not needed for least squares estimates of the regression parameters to be meaningful ( see Gauss-Markov theorem ).
5.
This filter uses MRI signal models to implement an approximate maximum likelihood or least squares estimate of each pixel gray level from the gray levels.
6.
The simplest methods of estimating parameters in a regression model that are less sensitive to outliers than the least squares estimates, is to use least absolute deviations.
7.
When the conditional variance is known, then the inverse variance weighted least squares estimate is BLUE . However, the conditional variance is rarely, if ever, known.
8.
Our goal is to estimate the parameters of the filter \ mathbf { w }, and at each time " n " we refer to the new least squares estimate by \ mathbf { w } _ n.
9.
This can be easily generated for any distribution for which the quantile function can be computed, but conversely the resulting estimates of location and scale are no longer precisely the least squares estimates, though these only differ significantly for small.
10.
Ogwang showed that " G " can be expressed as a function of the weighted least squares estimate of the constant " A " and that this can be used to speed up the calculation of the jackknife estimate for the standard error.
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