The Study Of A Quick Algorithm Of Least Absolute Deviation Estimator

This paper brings forward a quick algorithm theory of Least Absolute Deviation Estimator(LAD) in order to solve the difficult problem of the calculation of LAD. It divides into three chapters to expatiate this algorithm theory by two sides : theory and algorithm realization. First chapter introduces the history background and development of the problem of LAD. The second chapter defines the concept of basic point,polar point,best polar point,stable polar point,degenerate polar point and non-degenerate polar point. It also points out that this algorithm theory is discussed under the degenerate complexion that is:,,then call is Non-degenerate Polar Point. It also discussed the solution of the best polar point and put forward this quick algorithm theory and prove its convergence under all polar points are Non-degenerate Polar Points. Then it gave out a significant conclusion: the stable polar point is the LAD. It also described the realization frame of this arithmetic. In third chapter, it gave out the linear programming method of LAD and two examples. To the first example it gave out its linear programming result by Lindo6.01. Of course the result proves its accuracy and rapidity by comparing with Lindo6.01 and testing with random data. The last chapter described the algorithm in detail with its realization in computer. Then it defined three concepts of solution point group ,same solution group set and different solution group set. It also gave out the algorithm of finding all the solution point sets. It extended the adaptability of this algorithm. At the end it also did some pilot study about the same solution group set.The series of point group calculated by this algorithm theory is strictly descending and converging to the stable polar point. This theory is very efficiency in solving the problem of LAD for its simplicity,rapid speed and high adaptability.