In this dissertation, we devote to the robust representation of combined signals in sparse data condition in terms of the formulation of JCGM expression and take advantage to the unified pdf of coverage interval for uncertainty measurement.
However, this unified pdf expression of coverage interval shows that the shortest coverage interval is good enough to represent the whole distribution of coverage interval when the pdf of population is asymptotically symmetric. Due to the fact that the two endpoints of coverage interval are decided in one step, we reverse the traditional procedure, which finds the endpoints after the mean estimation, to estimate the mean value of population after finding the endpoints of coverage interval. We find that given with an accurate coverage interval is capable of improving the mean estimation by the way of regarding the coverage interval as a result of variably truncated normal distribution. Besides the improvement on the mean estimation, a robust estimation for truncated normal pdf is also reached when we take the quantile-based estimation combined with the output of unified pdf of coverage interval. The result is better as compared with the model derived by Cohen.
We also use quantile to derive a nonlinear equation for mean estimation. Simulation results demonstrate that it performs well. We last try a novel algorithm, named “The robust statistical principle of minimax optimization”, to use the unified pdf of coverage interval in mean estimation. It is a convex optimization method for the general mean estimation. The optimization process converges exactly to the true mean direction so that it may be considered as a new search algorithm as well as the steepest gradient descent algorithm without the quadratic object function. Finally, we apply the new mean estimator, QMLE-QSQ, to the application of signal activity detection in terms of finding the upper bound of eigenvalues. We find that the QMLE-QSQ can replace the classical sample mean to obtain a more accurate correlation matrix estimate, which in turn leads to a more efficient representation of the maximum eigenvalue. Thus, our study extend the previous UBE finding studies, which use deterministic correlation matrix, to employ stochastic correlation matrix
via introducing the uncertainty of mean estimation on spare data condition. And our solution can obtain better UBE for improving signal activity detection..
Our work still leaves several warm topics about CI which are worthy of studying in the future. For instance, “the shortest CI” should be replaced with “the probably shortest CI” whenever the pdf is skew. But we don’t know how the skewness of signal pdf affects the pdf shape of CI. Secondly, we have proved some properties of endpoints of quantiles based on the QMI principle. They include the structure of left endpoint mapping to the quantile of 1/ (n+ , the right endpoint mapping to the 1) quantile of / (n n+ , and coverage being equal to (1) n−1) / (n+ which is the 1) expectation E c shown in Eq.(3-11). Hence, the endpoint-decision with the QMI c n| [ ] principle is deterministic. So, this criterion can not support the exploration of the random effects of endpoints. We suspect that the quantile-based mean estimation ought to be suffered from the random effects of the endpoints expression.
Publication List
Journal Papers
[1] Wen-Hui Lo and Sin-Horng Chen, “The analytical estimator for sparse data”, IAENG International journal of applied Mathematics, vol. 39, iss. 1, 2009, pp.
71-81.
[2] Wen-Hui Lo and Sin-Horng Chen, “The uncertainty reduction for the refined sample mean of combined quantities,” IAENG International journal of applied Mathematics, vol. 39, iss. 3, 2009, pp. 192-197.
Submitted Papers
[1] Wen-Hui Lo and Sin-Horng Chen, “The Probability Distribution Function of Coverage Interval and Its Optimal Expression for Sparse Data Condition,” IEEE Transaction on Instrumentation and Measurement, Revised, 2009.
[2] Wen-Hui Lo and Sin-Horng Chen, “An efficient representation for combined signal activity detection in sparse data condition,” IEEE Transaction on Instrumentation and Measurement, Revised, 2010.
Conference Papers
Wen-Hui Lo and Sin-Horng Chen, “The wide-sense parametric coverage estimator against the distribution mismatch problem for sparse data”, World Congress on Engineering, (The best student paper award), London, U.K., 2008, pp.1005-1010.
Wen-Hui Lo and Sin-Horng Chen, “The coverage-based estimator for sparse data”, The 2008 Asian International Workshop on Advanced Reliability Modeling, Taichung, Taiwan., 2008, pp. 382-389.
Wen-Hui Lo and Sin-Horng Chen, “Robust estimation for sparse data”, IEEE 19th International Conference on Pattern Recognition, Tampa Bay, Florida, USA., 2008, pp.1-5.
Wen-Hui Lo and Sin-Horng Chen, “Theoretical and practical realization for the uncertainty measurement by coverage interval,” IEEE International Conference on Instrumentation and Measurement Technology (The best paper award), Singapore, 2009, pp. 1562-1567.
Wen-Hui Lo and Sin-Horng Chen, “The mean estimation of the combined quantities by the asymptotic minimax optimization,” IEEE International Workshop on
Advanced Methods for Uncertainty Estimation in Measurement, Bucharest, Romania, 2009, pp. 63-68.
博士候選人資料
姓 名 ：羅文輝
性 別 ： 男
出生年月日 ： 民國 58 年 3 月 30 日
出生地 ： 台灣新竹
學 歷 ：
台灣省立新竹師範專科學校普通科數學組畢業(73 年 9 月～79 年 6 月)
私立逢甲大學交通工程與管理學系暨電子工程輔學系畢業(79 年 9 月
～82 年 6 月)
國立台灣大學土木工程研究所交通工程組碩士畢業(82 年 9 月～85 年 1 月)
國立交通大學電機資訊學院碩士在職專班電信學程畢業(88 年 9 月～
95 年 7 月)
國立交通大學電信工程研究所博士畢業(90 年 9 月～99 年 7 月)
論文題目 ：
稀少取樣下之組合式訊號測不準表示法研究與其在訊號平均值估計 之應用
An Efficient Representation of Uncertainty Measurement for Combined Signals on Small Sampling Size Condition and its Application to Signal Mean Estimation
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