### Table 1 The e ect of constant on the bias components Estimator Asymptotic Bias

"... In PAGE 15: ... It is not obvious whether the magnitude of the higher order terms in the earlier results would remain negligible if the estimation window h were to decrease faster than the order p t. Table1 shows that assuming constant , ^ lt; Z; Z gt;t will be the best choice among the three. When is random, none of the estimation schemes in Section 2.... ..."

### Table 1: Asymptotic Bias of the Yule-Walker Estimator of .

2005

### Table 2: Asymptotic Bias of the Yule-Walker Estimator of 2.

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### Table I. Asymptotic values of the maximum and mimmum internal

### Table 5: Maximum Likelihood Estimates

### Table 6: Maximum Likelihood Estimates

### Table 3: Approximate Asymptotic Bias J B-spl Freq Cnt Kern

"... In PAGE 22: ... To check the validity of this, we ran the above examples once on a sample size of 1,000,000 for the cases of J = 10; 22. Given that the relative variance is small with such a large sample, we call the associated l2 estimates the approximate asymptotic bias, and they are provided in Table3 . In each case, the weighted B-spline clearly outperforms the frequency estimators.... ..."

### Table 3. Maximum bias and random errors allowable for the measurement data. Measurement Bias error Random error

"... In PAGE 17: ... Based on the accuracy and resolution specifications stated earlier, the Monte Carlo analyses MOS were used to assess the maximum bias and random errors allowable to meet the ultrahigh altitude flight program requirements. Table3 shows estimates of these data for the fully stable system. Measurement latency limitations have yet to be established, but based on the simulation runs, these requirements are very relaxed and can be easily achieved with conventional instrumentation methods.... ..."

### Table 11. Recall that the asymptotic variance 2 I tends to be inversely proportional to . In contrast, formula (75) implies that the asymptotic bias tends to be independent of . Hence, the bias becomes relatively more important as system size grows. Formulas (73) and (75) can be used to estimate the remaining bias if we eliminate an initial portion of the run of length t0. Let I(t0) be this remaining bias. Then

1996

"... In PAGE 31: ... Hence, we can numerically investigate the M/M/s/0 model and more complicated Markov loss models. For example, Table11 displays the asymptotic bias for the... In PAGE 33: ... Hence, for the experiments in Section 2 we deleted an initial portion of length 5 from each run. Table11 gives an idea of the bias reduction. For example, this phenomenon occurs when s = 104.... In PAGE 53: ...2 0.52 0:0005 0:30 0:0087 Table11 . The asymptotic bias for the indirect and time-congestion estimators in the M/M/s/0 model with s = 400, starting empty or full, discussed in Section 11.... ..."

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### Table 2: Achievable Asymptotic Messaging Bandwidth Per Processor and Transmis- sion Overhead Per Byte, tp. Machine Asymptotic

"... In PAGE 11: ... The parameter tp determines the asymptotic message injection bandwidth o ered by a communication library on a given system. Table2 provides representative values of tp obtained on di erent ma- chines and messaging platforms [11]. It can be observed that on most systems the asymptotic messaging bandwidth achieved is signi cantly lower than the theoretical channel maximum, in- dicating relatively high messaging overheads on such systems.... ..."