### Table 7. Simulation results with t-distributions.

"... In PAGE 42: ...The last two columns in Table7 show that both mixture of normal distributions and normal distribution perform better in estimating percentiles when data is generated from t-distribution with higher degrees of freedom. This is not surprising, because the higher the degree of freedom the more, the distribution resembles normal distribution.... ..."

### Table 1: Asymptotic e ciencies of the SCM eigenvector estimates relative to those based on the sample covariance matrix at t-distribution for several values of the dimension and degrees of freedom. Table B lists the asymptotic e ciencies relative to the MLE.

2003

"... In PAGE 16: ...2. Table1 A lists the asymptotic relative e ciencies calculated for multivariate t-distributions for several dimensions and degrees of freedom. E cien- cies for multinormal distributions, which correspond to the limiting case of the degrees of freedom ( = 1), are also given.... In PAGE 16: ... E cien- cies for multinormal distributions, which correspond to the limiting case of the degrees of freedom ( = 1), are also given. As we can see from Table1 A, the e ciencies are very high in the normal case, and they get larger with increasing dimension. At the multivariate t-distributions, the estimates based on SCM outperform the classical esti- mators, especially at the heavier tailed distributions.... In PAGE 16: ... At the multivariate t-distributions, the estimates based on SCM outperform the classical esti- mators, especially at the heavier tailed distributions. Table1 B list the same asymptotic e ciencies, but now relative to maximum likelihood estimates (MLE) for the respective multivariate t-distributions, the latter being the most e cient estimates at the model distribution. Recall that the sample covariance matrix is the MLE at the normal model.... In PAGE 19: ... Similar pictures have been depicted by Croux and Haesbroeck (1999), who also com- puted asymptotic e ciencies for several estimators of the o - and on-diagonal elements of . For the on-diagonal elements, there is no work to do, since one readily can check that ARE(d Cov12; b C12; F0) = ASV(d Cov12; F0) (k2=c4 F0)ASV( b D12; F0) = ARE(b vCov;j; b vD;j; F ) corresponding to the numbers in Table1 . For the o -diagonal elements there are some extra computations to be done.... In PAGE 21: ...9 1 S25 SCM S50 MCD25 MCD50 Figure 5: E ciencies of the standardized eigenvalues in function of the dimension at the normal model for the SCM estimator and 25/50 percent breakdown MCD estimator and biweight S-estimator. Next, write b Cov;j, j = 1; : : : ; k for the standardized eigenvalue estimates based on the sample covariance matrix d Cov: The asymptotic e ciency of the standardized eigenvalue estimates b D;j relative to b Cov;j for elliptical F is again given by ARE(b Cov;j; b D;j; F ) = ASV(ln b Cov;j; F ) ASV(ln b D;j; F ) = ASV(d Cov12; F0) ASV(b C12; F0) ; (11) which also equals the asymptotic relative e ciencies ARE(b vCov;j; b vD;j; F ) of the eigen- vector estimates, and which have already been reported in Table1 . These e ciencies also equal the e ciencies of the SCM regression slope coe cient estimates relative to corresponding estimates based on the LS regression (see Ollila et al.... ..."

Cited by 1

### Table VII Power of Maximum Likelihood Ratio and GMM Specification Tests Under the Beta and the SDF Methods when Residuals and Factors are Jointly t-Distributed The table presents the probabilities of rejection for maximum likelihood ratio and GMM specification tests under the beta and the SDF methods when the level of significance is 5% and 10%, and the acceptance/rejection decision is based on the empirical distribution under the null hypothesis. The returns and factors are generated under the alternative hypothesis by a one-factor model with parameters given in Table I, and with the factors and the residuals sampled from a multivariate Student-t distribution with five degrees of freedom. For the GMM estimations, we present three specification tests. The first two tests are from the second and third stage GMM when the identity matrix is used as the initial weighting matrix. The third test is from the second stage GMM when the sample estimate of the optimal weighting matrix is used as the initial weighting matrix. Results are presented for different lengths of time series observations (T), and they are based on 10,000 simulations.

2001

Cited by 1

### Table 1 Models for the weekly returns from 519 weeks. Three models: the normal-polynomial quantile mixture (NP3), the Cauchy-polynomial quantile mixture (CP3) and the skew-t distribution are fitted to four datasets of stock index returns. Estimated pa- rameters and their standard errors (SE) are reported together with the Kolmogorov- Smirnov statistics (K-S). Index NP3 CP3 skew-t

"... In PAGE 13: ...ig. 5. L-moments of the stock index returns. and the value of the Kolmogorov-Smirnov goodness-of-fit statistics (Conover, 1971). It can be seen from Table1 that all models provided good fit to the 519 weeks data in terms of the Kolmogorov-Smirnov statistics. The parameter b indicates the contribution of the normal component (NP3) or Cauchy com- ponent (CP3) in the quantile mixture.... ..."

### Table 1 Models for the weekly returns from 519 weeks. Three models: the normal-polynomial quantile mixture (NP3), the Cauchy-polynomial quantile mixture (CP3) and the skew-t distribution are fitted to four datasets of stock index returns. Estimated pa- rameters and their standard errors (SE) are reported together with the Kolmogorov- Smirnov statistics (K-S). Index NP3 CP3 skew-t

"... In PAGE 13: ...ig. 5. L-moments of the stock index returns. and the value of the Kolmogorov-Smirnov goodness-of-fit statistics (Conover, 1971). It can be seen from Table1 that all models provided good fit to the 519 weeks data in terms of the Kolmogorov-Smirnov statistics. The parameter b indicates the contribution of the normal component (NP3) or Cauchy com- ponent (CP3) in the quantile mixture.... ..."

### Table 6. Parameter estimates for generated t-distribution data samples. T-distribution Technique p

### Table 2 Studies of TAM extension incorporating social influence factors

2006

"... In PAGE 6: ... Thus, based on the above dis- cussion, it seems reasonable to incorporate not only intrinsic motivation factors but also factors of social influence into the TAM model and investigate their direct effect and moderating effect on per- ceived usefulness and behavior intention regarding using a KM program. Table2 provides a list of recent literature that incorporates social influence factors into the TAM. 3.... ..."

### Table 2 Models for the weekly returns from 52 weeks. Three models: the normal-polynomial quantile mixture (NP3), the Cauchy-polynomial quantile mixture (CP3) and the skew-t distribution are fitted to four datasets of stock index returns. Estimated pa- rameters and their standard errors (SE) are reported together with the Kolmogorov- Smirnov statistics (K-S). The applied maximum likelihood procedure did not return standard errors for the skew-t parameters with AORD index. Index NP3 CP3 skew-t

"... In PAGE 2: ... Unfortunately, it is impossible to derive closed form L-estimators for many well-known distributions. For instance, Table2 in (Hosking, 1990) gives only approximate estimators for log-normal, gamma and generalized ex- treme value (GEV) distributions. Another example is the generalized lambda distribution (GLD) (Dudewicz and Karian, 2000) for which the L-moment es-... In PAGE 14: ...Table2 summarizes the fitted models estimated from the 52 weeks data. The results reveal a drawback of skew-t distribution.... In PAGE 14: ...1226. Two of these indexes, Nikkei225 and DAX are included also in the Table2 . For both of them the estimated degree of freedom (df) is high indicating that in practice the model reduced to the skew-normal distribution.... ..."

### Table 2 Models for the weekly returns from 52 weeks. Three models: the normal-polynomial quantile mixture (NP3), the Cauchy-polynomial quantile mixture (CP3) and the skew-t distribution are fitted to four datasets of stock index returns. Estimated pa- rameters and their standard errors (SE) are reported together with the Kolmogorov- Smirnov statistics (K-S). The applied maximum likelihood procedure did not return standard errors for the skew-t parameters with AORD index. Index NP3 CP3 skew-t

"... In PAGE 2: ... Unfortunately, it is impossible to derive closed form L-estimators for many well-known distributions. For instance, Table2 in (Hosking, 1990) gives only approximate estimators for log-normal, gamma and generalized ex- treme value (GEV) distributions. Another example is the generalized lambda distribution (GLD) (Dudewicz and Karian, 2000) for which the L-moment es- timators were derived in (Karvanen et al.... In PAGE 14: ...Table2 summarizes the fitted models estimated from the 52 weeks data. The results reveal a drawback of skew-t distribution.... In PAGE 14: ...1226. Two of these indexes, Nikkei225 and DAX are included also in the Table2 . For both of them the estimated degree of freedom (df) is high indicating that in practice the model reduced to the skew-normal distribution.... ..."