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3.4.3 High-dimensional Empirical Linear Prediction
Hung-kung Liu
William F. Guthrie Statistical Engineering Division, ITL
J.T. Gene Hwang Cornell University
Michael T. Souders
Gerard N. Stenbakken Electricity Division, EEEL Many engineering problems involve high-dimensional observations with mean vectors sitting in a lower dimensional space. Exhaustive measurement of all the elements of an observation is often time consuming and expensive. Applying a traditional multivariate linear model, one can incorporate a small number of the elements of the observation with a known design matrix to predict the rest of the elements. However, for a complicated engineering system, the design matrix is often hard to be fully determined. We investigate an empirical linear model, in which we allow ourselves to use the data to determine the size of the design matrix and to estimate the unknown part of the design matrix. This estimated model is then used to construct point and interval estimates for the future observation. This technique is called HELP (High-dimensional Empirical Linear Prediction).
As an example, for a 13 bit A/D converter,
to be absolutely sureof performance,
one needs to test 8192 outputs, corresponding
to transition levels (usually voltage levels) for the conversion
of the analog signals to the digital signals.
By using the exhaustive measurements of 88 converters and the measurement
of only 64 transition levels of a future converter,
HELP predicts well the behavior of the rest 8128
transition levels. In manufacturing
converters, testing cost constitutes 20% to 50% of the total
manufacturing cost.
Obviously, a reduction from 8192 measurements down to 64 measurements,
less than one percent, can reduce production cost tremendously.
Figure 27: This figure shows 18 of the 88 vectors we analyzed, each corresponding to the 8192 error transition levels of a 13 bit converter.
Date created: 7/20/2001 |