Stabilized determination of geopotential coefficients by the mixed hom-BLUP approach

For the determination of geopotential coefficients, data can be used from rather different sources, e.g., satellite tracking, gravimetry, or altimetry. As each data type is particularly sensitive to certain wavelengths of the spherical harmonic coefficients it is of essential importance how they are treated in a combination solution. For example the longer wavelengths are well described by the coefficients of a model derived by satellite tracking, while other observation types such as gravity anomalies, delta g, and geoid heights, N, from altimetry contain only poor information for these long wavelengths. Therefore, the lower coefficients of the satellite model should be treated as being superior in the combination. In the combination a new method is presented which turns out to be highly suitable for this purpose due to its great flexibility combined with robustness

The Impact of Missing Values on the Reliability Measures in a Linear Model

Reliability measures in linear models are used in geodetic science and elsewhere to quantify the potential to detect outliers and to suppress their impact on the regression estimates. Here we shall study the effect of missing values on these reliability measures with the idea that, under a proper design, they should not change drastically when such a situation occurs

Approximate Confidence Regions for Minimax-Linear Estimators

Minimax estimation is based on the idea, that the quadratic risk function for the estimate β is not minimized over the entire parameter space R^K, but only over an area B(β) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(β) = { β : β' Tβ ≤ r }. The ellipsoid has a larger volume than the cuboid. Hence, the transition to an ellipsoid as a priori information represents a weakening, but comes with an easier mathematical handling. Deriving the linear Minimax estimator we see that it is biased and non-operationable. Using an approximation of the non-central χ^2-distribution and prior information on the variance, we get an operationable solution which is compared with OLSE with respect to the size of the corresponding confidence intervals

Efficiency properties of weighted mixed regression estimation

This paper considers the estimation of the coefficient vector in a linear regression model subject to a set of stochastic linear restrictions binding the regression coefficients, and presents the method of weighted mixed regression estimation which permits to assign possibly unequal weights to the prior information in relation to the sample information. Efficiency properties of this estimation procedure are analyzed when disturbances are not necessarily normally distributed