Application of Monte Carlo method to statistical testing in deformation analysis based on robust M-estimation. Issue 348 (3rd May 2016) - Nowel, K.
Abstract : In deformation analysis of geodetic control networks, it is important to know whether the estimated displacement value of a given point is the effect of displacement or only the effect of random measurement errors. The F-test of statistical significance is used to answer this question. This test is applied both in conventional deformation analysis (CDA) based on least square (LS) estimation and in deformation analysis based on robust M-estimation. Unfortunately, the F-test is strongly flawed in the latter case. As a consequence, its results are significantly different here than assumed/expected. This paper analyses how flawed the F-test is and proposes a new solution. First, the algorithm of the global and local F-tests was derived. It was then demonstrated that for deformation analysis based on robust M-estimation, this algorithm has theoretical flaws. Next, it was shown how these problems can be solved numerically. The basis of the solutions proposed involves the use of stochastic simulations and, more specifically, the Monte Carlo (MC) method. Moreover, it was noted that other statistical test problems which also occur in deformation analysis based on robust M-estimation can be solved using present-day computers. The numerical approach can be a good support here in the selection of the proper significance level as well as in the correct performance of the test sensitivity analysis. All theoretical discussions were verified on an example simulated control network.