We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (`q constraint with 0 < q ≤ 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic ...

This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou navigation satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth orbit satellites, sky-view coverage can be achieved over the entire elevat...

In this paper, a generalized Adams-Moulton method that is a m-step method derived by using the Taylor’s series is proposed to solve the satellite orbit determination problem. We show that our proposed method has produced much smaller error than the original Adams-Moulton method. Finally, the accuracy performance is demonstrated in the satellite orbit correction problem by giving a numerical exa...

recently, gasimov and yenilmez proposed an approach for solving two kinds of fuzzy linear programming (flp) problems. through the approach, each flp problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. then, the crisp problem is solved by the use of the modified subgradient method. in this paper we will have another look at the earlier defuzzifi...

In this paper a new class of Instrumental Variables estimators for linear processes and in particular ARMA models is developed. Previously, IV estimators based on lagged observations as instruments have been used to account for unmodelled MA(q) errors in the estimation of the AR parameters. Here it is shown that these IV methods can be used to improve efficiency of linear time series estimators...

In this paper, a new control chart to monitor multi-binomial processes is first proposed based on a transformation method. Then, the maximum likelihood estimators of change points designed for both step changes and linear-trend disturbances are derived. At the end, the performances of the proposed change-point estimators are evaluated and are compared using some Monte Carlo simulation experimen...

A method is defined for simultaneous atmospheric density calibration and satellite orbit determination for a satellite constellation, and a linearized observability analysis is performed to evaluate the feasibility of the approach. Such an estimation scheme will provide data-based estimates of upper atmosphere density that improve on existing models, e.g. the Jacchia models, along with enhanced...

This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In this sense, pace regression outperforms existing procedures for fitting linear models. Dimensionali...

We consider the problem of structurally constrained high-dimensional linear regression. This has attracted considerable attention over the last decade, with state of the art statistical estimators based on solving regularized convex programs. While these typically non-smooth convex programs can be solved by the state of the art optimization methods in polynomial time, scaling them to very large...

The orbit determination of a satellite in a geostationary orbit is usually based on optical observations. Telescopes all around the Earth are observing the geostationary ring to obtain periodically new measurements in order to update the estimation of the objects’ orbits. One critical aspect of the orbit determination process is the initial orbit determination because no a priori information ar...