H-square error

We next show in Table 2 the H-square error and the energy lower bound calculated by the modified Temple equation. As the order n of the FC wave function increases, the H-square error gradually decreases and converges towards zero, the exact value. It is as small as 1.29 x 10 at n = 27. When the H-square error becomes zero, it means that the wave function becomes exact. So, this table means that, as the order n increases, the FC wave function approaches the exact wave... 

Order, n K H-square error, a Energy lower bound ... 

LPRINT "WEIGHTED SUN OF SQUARES (ERROR NEASURE, " Q2 IF NB<=10 THEN LPRINT "CHI SQUARE AT 0.05 SIGNIFICANCE LEVEL " CH LPRINT Vt=STRING (53,"-") Ft=, .H llAA LPRINT Vt... 

Figure 3. Reconstructions of (A) diatom-based and (B) chrysophyte-based monomeric Al for Big Moose Lake, and diatom-based monomeric Al for (C) Deep Lake, (D) Upper Wallface Pond, and (E) Windfall Pond in the Adirondack Mountains, New York. Reconstructions are bounded by bootstrapping estimates of the root mean-squared error of prediction for each sample. Bars to the right of each reconstruction indicate historical (H) and Chaoborus-based (C) reconstructions of fishery resources. The historical fish records are not continuous, unlike the paleolimnological records. Intervals older than 1884 are dated by extrapolation. (Reproduced with permission from reference 10.

For both the subdistribution and the GEX fit methods a Marquardt algorithm for constrained non-linear regression was used to minimize the sum of squares error (.10). The FORTRAN program CONTIN was used for the constrained regularization method. All computations were performed on a Harris H-800 super mini computer. 

Swallow, W. H. (1987). Relative mean squared error and cost considerations in choosing group size for group testing to estimate infection rates and probabilities of disease transmission. Phytopathology, 11, 1376-1381. 

The usual procedure is to employ least squares directly on equation 2. However, this results in minimizing the squared error in h, not y. That is, the procedure finds the set b such that the quantity... 

Consequently, the minimum mean square error estimate for y is y = Hm and the associated covariance of this is Cy= HC H + R. 

Fig. 3.2 Correlation coefficient, mean biases, and Root Mean Square Errors(RMSE) for WRF/ Chem, comparing model forecasts of 8-h averaged peak ozone mixing ratios with those observed by surface monitoring stations. The statistics span a time period of 30 days. The model was run once a day at OOOOUTC...

The F-value using 3, 9 degrees of freedom was 3.86, Student s two-tailed t-distribution with 9 degrees of freedom was 2.262, and the mean square error was 2427.8. Suppose the 95% confidence interval for the predicted value at Tmax was needed. At a Tmar of 3 h, the predicted value was 740.03 ng/mL. The Jacobian matrix evaluated at 3 h under the final parameter estimates was... 

All theses 7 parameters were obtained from squared-error minimizations. The data analysis reveals that the best fits for hydrogen follow a very shallow minimum valleys so that the reported 7 parameters obtained from these fits should be taken with a grain of salt. The value 7j = 2 which was tested here is consistent with - and loosely justified by - the virial ratio for H, V e/E = 2. A reasonable explanation for possible distortions of the 7 value is perhaps linked to the basis used for hydrogen. This point is briefly examined with the help of DFT results (Table 5) and SCF computations using enriched bases. 

Minimum mean squared error predictor. For the joint dishibution in Exercise 7, eompute E y - IjvIx]]. Now, find the a and b which minimize the ftmction E y - a - bxf. Given the solutions, verify ih t E y - E y >c]f < E y-a-bxf. The result is fundamental in least squares theory. Verify that the a and h whieh you found satisfy (3-68) and (3-69). 

By this way the parameters which minimize the mean squared error on the test data set were determined for every indicator. They are given in Table 4. For every indicator, best performance could be obtain with a polynomial or a gaussian kernel. In some cases, different h value gives the same performances, then an interval on h is given for the optimal value. 

Root mean square error (RMSE) 0.49138 Correlation coefficient (H) 0.86270... 

Donoho, D.L. 1995. Denoising by soft thresholding. IEEE Trans. Information Theory 41(3) 613-627. Ephraim, Y. 1992. Statistical model based speech enhancement systems. Proc. IEEE 80(10) 1526-1555. Ephraim, Y. and Malah, D. 1984. Speech enhancement using a minimum mean-square error short time spectral amphtude estimator. IEEE Trans. Acoustics, Speech, and Signal Processing 32(6) 1109-1121. Ephraim, Y. and Van Trees, H.L. 1995. A signal subspace approach for speech enhancement. IEEE Trans, on Speech and Audio Processing 3 4) 25l-266. 

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