一次范数最小平差的统计性质

THE STATISTICAL PROPERTY OF LEAST1-NORM ADJUSTMENT

当误差服从Laplace分布时，LA估计量是最或然估计量，因而是渐近有效和一致估计量且渐近正态，此时LA估计优于LS估计。若误差严格服从正态分布，LS估计是最优的。文章深入研究了用ε污染正态分布来作为许多“近似正态”的实际分布模型：Φ（Δ）=（1-ε）Φ_0（Δ）+εΦ_1（Δ），并讨论了在此模型下LA估计优于LS估计的条件。

: When errors obey Laplace distribution, LA estimate will be the most probable one and also a consistent one; it is asymptotically efficient and normal distribution. In this case, LA estimation is superior to LS one. When errors rigorously obey nor mal distribution, LS estimation is optimal. This paper studies in detail the case whe rein the normal distribution contaminated by is taken as practical distribution model of many approximate normal distributions. The condition under which LA estimation is superior to LS one for this model is discussed.