### Table 1. Probability Density functions .

"... In PAGE 96: ...one dimension less and rk = akn; bij = aij ? anj However, the probability distributions are not the same for the elements of A in the replicator equation and for the o -diagonal elements of B in the Lotka-Volterra model. Table1 lists the density functions used in this contribution. The probability for the quadratic form xAx and detA to have a certain sign is clearly 1=2.... ..."

### Table 3. Gaussian selection accuracy as a function of selection beamwidth.

2000

"... In PAGE 4: ... The acoustic models used for this evalua- tion had 6000 senones, with 20 component densities in the mix- ture representing each senone. Table3 shows the selection accuracy as a function of the selection beamwidth. Within each mixture, the selection beamwidth determines the Gaussian density with the worst score (in terms of the quantized parameters) that can be considered to be active, relative to the best scoring density in that mixture.... ..."

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### Table 3. Gaussian selection accuracy as a function of selection beamwidth.

2000

"... In PAGE 4: ... The acoustic models used for this evalua- tion had 6000 senones, with 20 component densities in the mix- ture representing each senone. Table3 shows the selection accuracy as a function of the selection beamwidth. Within each mixture, the selection beamwidth determines the Gaussian density with the worst score (in terms of the quantized parameters) that can be considered to be active, relative to the best scoring density in that mixture.... ..."

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### Table 8: Renormalized Maximum Values of the Probability Density Distribution Functionsa

1448

"... In PAGE 11: ... Table8 lists the maximum values of the probability density distribution function for the various combined-channel MAX data sets and all models considered here. From these numerical values, and from Figure 4, one sees that for all the combined-channel MAX data sets, except 5MP which does not have a detection, the likelihood functions are peaked and very well separated from 0 K.... ..."

### Table 3. Parameter estimates and likelihood scores for the Troponin C gene family under different branch models, sites models, and branch- site models.

"... In PAGE 8: ... Averaging H9275 over all sites and branches yielded the estimate H9275H110050.017 (one ratio model; Table3 ), indi- cating the overwhelming role of purifying selection in this gene family. We relax the assumption of a single H9275 for all branches in the two-ratios model.... In PAGE 8: ... 4, branch A) immediately postdates the Troponon C duplication event. Parameter estimates suggested a higher relative rate of nonsynonymous substitution in branch A ( Table3 ), but the two-ratio model did not provide a significantly better fit to these data (Table 4). We also applied sites models (Nielsen and Yang, 1998; Yang et al.... In PAGE 8: ... We also applied sites models (Nielsen and Yang, 1998; Yang et al., 2000) to Troponoin C ( Table3 ).We employed the following model pairs: (i) one-ratio (M0) and M3; (ii) M1 and M2; and (iii) M7 and M8.... In PAGE 9: ...Table3 ). This finding indicates significant variation in selective constraints among sites, but not by positive Darwinian selection.... In PAGE 9: ... Comparison of model A with its null model (M1), and model B with its null model (M3; kH110052) indicated that the branch-site mod- els provided a significantly better fit to these data (Table 4). Positively selected sites identified by the Bayes method were listed in Table3 . Model B iden- tified fewer sites than model B (Table 3).... ..."

### Table 1 Prospect model parameter mean and standard deviation for the Gaussian distribution, and minimum and maximum for uniform distribution Model parameter Gaussian distribution Uniform distribution

in Estimating

"... In PAGE 5: ...uemoud et al., 2000; Jacquemoud amp; Baret, 1990). In the real world, the statistical distribution of these variables over a range of leaves may follow a Gaussian or some other non- Gaussian probability density function. Therefore, a key feature of the experimental design was that the Prospect model input parameters were defined for two different probability density functions, Gaussian and uniform, and for ranges that represented global variability in leaf bio- physical properties ( Table1 ). A uniform distribution may be used in the absence of any other information about the statistical distribution of a given variable and assumes that all values of the input variable are within a range defined by the maximum and minimum and have an equal probability of selection.... ..."

### TABLE I HYPOTHESESAND PULSE SHAPESCORRESPONDINGTO FIG.2. The attenuation of the signal can be modeled by another multiplicative parameter AC, which is a function of AB and AR for Gaussian pulses; and AB and AS for exponential pulses. Once AR, AB, and AC are known, or adaptively estimated, they can be used in conjunction with receiver operating character- istic (ROC) curves to adaptively select the optimum signal de- tection threshold, AL, for minimizing the total error probability.

in An Adaptive Threshold Detector and Channel Parameter Estimator for Deep Space Optical Communications

### Table 1. Selection probabilities

in Empirical Likelihood-Based Model Selection Criteria for Moment Condition Models,” Econometric Theory

2003

"... In PAGE 13: ...estimator resulting from the use of M2 giving the ideal benchmark+ The re- sults are based on 500 repetitions for four sample sizes, N 5 50, 250, 500, and 1,000+ Table1 details the probabilities of selecting the true, other consistent, and inconsistent models under assumption of a homoskedastic error structure ~a50!+ For each estimation method, results are collected by each of the four proposed penalty functions ~BIC, AIC, HQIC, and RNIC!+ Considering the BIC and MN criteria, it is clear that the MSCJ outperforms both the MSCEL and MSCET for the smaller sample sizes+ The probability of selecting the true model is higher by 5% and the probability of selecting a misspecified model lower by up to 10%+ As the sample size increases the discrepancy between the MSCJ and MSCET vanishes, whereas the MSCEL has slightly higher probability of selecting an inconsistent model+ Under the AIC criterion, the MSCET outperforms both MSCJ and MSCEL at all sample sizes+ The gains are of the order of 10%, though they are somewhat smaller when compared to MSCEL at larger sample sizes+ The Table 1. Selection probabilities... In PAGE 15: ...the sample sizes N 5 500 and 1,000+ Consistent with the results of Table1 , as N increases from 250 to 1,000 the bias is essentially eliminated for GMM- and ET-based models and the RMSEs fall at a rate consistent with the increase in sample size+ For both larger sample sizes the ET-based results are marginally better than the GMM-based results, whereas the EL-based results are some- what worse+ For ET and GMM the BIC, HQIC, and RNIC MSC nearly always Table 2. Postselection results 1 N 5 50 N 5 250 Bias RMSE Rej+ Rate Bias RMSE Rej+ Rate GMM M1 20+006 0+115 0+078 0+000 0+046 0+056 M2 0+011 0+091 0+148 0+004 0+036 0+068 M3 0+139 0+152 0+674 0+137 0+139 0+998 M4 0+128 0+143 0+620 0+119 0+119 0+982 M5 0+130 0+146 0+616 0+122 0+122 0+990 BIC 0+032 0+110 0+256 0+005 0+039 0+084 AIC 0+021 0+111 0+224 0+003 0+041 0+080 HQIC 0+027 0+111 0+224 0+004 0+039 0+084 RNIC 0+031 0+111 0+256 0+005 0+038 0+084 Empirical likelihood M1 20+006 0+115 0+078 0+000 0+046 0+056 M2 20+006 0+099 0+152 0+001 0+036 0+072 M3 0+128 0+144 0+626 0+125 0+128 0+992 M4 0+097 0+124 0+470 0+098 0+102 0+932 M5 0+116 0+137 0+536 0+107 0+111 0+958 BIC 0+028 0+109 0+226 0+006 0+042 0+108 AIC 0+020 0+108 0+236 0+008 0+045 0+124 HQIC 0+022 0+110 0+240 0+007 0+044 0+116 RNIC 0+025 0+111 0+252 0+005 0+042 0+108 Exponential tilting M1 20+006 0+115 0+078 0+000 0+046 0+056 M2 20+004 0+113 0+150 0+001 0+036 0+062 M3 0+132 0+148 0+644 0+131 0+133 0+996 M4 0+104 0+135 0+514 0+096 0+100 0+910 M5 0+117 0+138 0+536 0+113 0+116 0+976 BIC 0+029 0+118 0+300 0+003 0+039 0+080 AIC 0+020 0+113 0+254 0+025 0+039 0+082 HQIC 0+024 0+115 0+270 0+003 0+039 0+082 RNIC 0+027 0+117 0+284 0+003 0+039 0+080 6 6 ECT196-2 15021 07021003 5:10 pm Page:937 V V V EMPIRICAL LIKELIHOOD MODEL SELECTION... ..."

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### TABLE 1. Parametrizations of the covariance matrix 6k in the Gaussian model and their geometric interpretation. The models shown here are those discussed in Banfield and Raftery [2].

1998

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### Table 6: Predicting Successful Adjustments - A Few Simple Specifications

"... In PAGE 18: ... The main variable of interest is Exchange Rate (t-1, t-2), the growth in the exchange rate in the two years preceding the adjustment.27 In Table6 we present results for the sub- sample of fiscal adjustments, whereas Tables 7 and 8 will present results for the whole sample, including year and country dummies. The control variables are: - Level of Public Debt (t-1), that is, Government Net Financial Liabilities as percent of GDP in the year preceding adjustment; - Change in Primary Deficit (t-2, t-1), the change in the primary deficit in the two years preceding adjustment; - GDP growth (t-1), the rate of growth in real GDP the year before the adjustment; - Change in Spending (t), the contemporaneous change in primary public spending, corrected for the business cycle.... In PAGE 20: ... Nevertheless, the small size of the coefficient in this and the other specifications confirms that money supply is not a key variable in determining success. In Table6 we follow the same procedure and specification to examine the impact of exchange rates on success, examining both nominal and real exchange rates, different lags of the exchange rate (one year and two year),29 different definitions of success (two and three years following the adjustment), with and without additional controls.30 For each variable we present the percentage point change in the density function of a 1 percent change in the right-hand side variable.... In PAGE 20: ... However, throughout the specifications, the coefficient on the exchange rate variable is negative and close to significance. 30 The coefficient and its significance for the control variables is not presented in Table6 for lack of space.... ..."