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Spectral Estimation and Modeling
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
S. Unnikrishna Pillai, Theodore I. Shim, Stella N. Batalama, Dimitri Kazakos, Ping Xiong, David D. Sworder, John E. Boyd
The unbiased estimator that has minimum variance is called the minimum variance unbiased estimator (MVUE). An MVUE does not always exist. Under certain conditions, an MVUE can be found either as the solution that maximizes the likelihood function or through the use of sufficient statistics. In particular, if an efficient estimator exists, then it is also MVUE and can be found as the unique solution that maximizes the likelihood function (the maximum likelihood estimator will be discussed in detail in the next section). However, if an efficient estimate does not exist, the ML estimator is not MVUE. An alternative way to find an MVUE, provided it exists, is through the use of sufficient statistics.
Fuzzy assessment model to judge quality level of machining processes involving bilateral tolerance using crisp data
Published in Journal of the Chinese Institute of Engineers, 2021
Chien-Che Huang, Tsang-Chuan Chang, Bae-Ling Chen
In general, the two estimates and are asymptotically equivalent. It is worth mentioning that and are the MLEs of and , respectively. For this reason, is the MLE of . Additionally, the denominator of is the uniformly minimum variance-unbiased estimator of the denominator of because and . For the sake of reliability, it is reasonable to use to calculate in assessing the process quality level of a machining process. Thus, the MLE of with and can be shown in Equation (6):
Testing process quality of wire bonding with multiple gold wires from viewpoint of producers
Published in International Journal of Production Research, 2019
Tsang-Chuan Chang, Kuen-Suan Chen
Let , then . Under the assumption of normality, is distributed as the chi-square distribution with degrees of freedom (i.e. ). Therefore, can be re-expressed as follows: Since and are mutually independent under the normality assumption, so the expected value of can be shown as follows: where and (see Appendix 1 for details). From Equation (23), it can easily be seen that the estimator will be unbiased (i.e. ). Furthermore, is the sufficient statistic for , and is only the function of . Obviously, is a uniformly minimum variance unbiased estimator (UMVUE) of (see Appendix 2).
Estimation of P(Y<X) for lognormal distribution
Published in Quality Technology & Quantitative Management, 2022
Yogesh Mani Tripathi, C. Petropoulos, Mayank Kumar Jha
Let follow distribution and follow distributions, respectively. Here, we obtain uniformly minimum variance unbiased estimator of . An unbiased estimator of is given by