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Overview of Process Control
Published in Robert Doering, Yoshio Nishi, Handbook of Semiconductor Manufacturing Technology, 2017
These two metrics are influenced by how centered a process is and the variability of the process. MISE is the analog of the standard deviation, but with the average replaced with the target. In other words, MISE can be considered the standard deviation around the target. MIAE is the analog of the Mean Absolute Deviation, and just like Mean Absolute Deviation, is less sensitive to outliers. Thus, process modifications improve MISE greater fraction than MIAE if the modifications remove outliers (“spikes”). These two metrics do not convey information on yield, but they do indicate impact of process and equipment modifications. The goal is to continuously shrink the values of MIAE and MISE.
Density estimation
Published in José E. Chacón, Tarn Duong, Multivariate Kernel Smoothing and its Applications, 2018
The MISE is a non-stochastic quantity that describes the performance of the kernel density estimator with respect to a typical sample from the true density. This is due to the expected value included in its definition. However, in some situations it is of interest to measure how the kernel estimator performs, not for an average sample, but for the data that we have at hand. This is the case, for instance, when the goal is to compare the kernel estimator based on different data-based methods to select the bandwidth matrix. To that end, a stochastic discrepancy measure depending on the data at hand is the integrated squared error (ISE), defined as ISE{f^(·;H)}=∫Rd{f^(x;H)-f(x)}2dx. $$ \mathrm ISE \{\hat{f}(\cdot ; \mathbf{H})\}=\int _{ \mathbb R ^d}\{\hat{f}({\boldsymbol{x}};\mathbf{H})-f({\boldsymbol{x}})\}^2d{\boldsymbol{x}}. $$
Link dynamic vehicle count estimation based on travel time distribution using license plate recognition data
Published in Transportmetrica A: Transport Science, 2023
Chunguang He, Dianhai Wang, Mengwei Chen, Guomin Qian, Zhengyi Cai
We test the accuracy of KDE with different sample sizes. The mean-integrated square error (MISE) is chosen to evaluate the discrepancy between the ‘true' density function drawn with a large sample size and its estimator drawn with the sample data. The MISE of 50 runs at each sample size is plotted to illustrate the trend in accuracy as the sample size increased. A not unreasonable aim would be to ensure that the MISE is fairly small, say less than 0.01. Figure 9(a) shows the sample size required to achieve this object is 10.
Safety assessment of automated vehicles: how to determine whether we have collected enough field data?
Published in Traffic Injury Prevention, 2019
Erwin de Gelder, Jan-Pieter Paardekooper, Olaf Op den Camp, Bart De Schutter
The measure for completeness proposed in this article can be regarded as an approximation of the MISE of Eq. (1). To minimize the MISE, the approximated pdf should be similar to the real pdf. However, it might be that one is not interested in the exact likelihoods of certain values of the parameters but in all possible values that the parameters can have. In this case, one might be interested in the support of the real pdf, because the support of the pdf defines all possible values for which the likelihood is larger than zero; see, for example, Schölkopf et al. (2001).