### TABLE I PRIMARY FUNCTIONS AND OPERATORS FOR SMOOTHING SPLINE ESTIMATION AND THE MODELING OF FRACTAL PROCESSES

2007

Cited by 1

### TABLE I PRIMARY FUNCTIONS AND OPERATORS FOR SMOOTHING SPLINE ESTIMATION AND THE MODELING OF FRACTAL PROCESSES

2007

Cited by 1

### TABLE C1. The nonnegative definite functions in the representation (C1) of a smoothing spline estimate.

### Table 2 B-splines estimation of the Archimedean copula generator: posterior means and 90% credible intervals for the B-splines parameters associated to K = 20 equidistant knots on (0,1)

"... In PAGE 12: ...haracterized by the copula in the continuous case. Our expectations were confirmed in our example. Note that this would not be the case anymore if we were dealing with discrete data, see Denuit and Lambert (2005), Vandenhende and Lambert (2002a) and the references therein for motivating arguments. Summary measures of the posterior distributions can be found in Table 1 for the marginal skewed-Student regression models for log(SBP) and log(DBP), and in Table2 for the B-splines parameters describing the fitted Archimedean copula generator. Table 1 reveals a positive marginal association between the cholesterol level and blood pressures (see afii98261), the positive skewness of the distributions of log(DBP) and log(SBP), as well as very moderate kurtosis.... In PAGE 12: ... Note that the quality of the fits provided by the marginal parametric models was assessed and found to be excellent. The results in Table2 are summarized graphically in Fig. 5.... ..."

### Table 3: NLLS Coe cient EstimatesExp-Spline Full-Spline

"... In PAGE 13: ... We will call this model Exp-Spline. The parameter estimates for Exp-Spline are given in Table3 , where we have used the same variables as in the model Spline as a starting point. The Spline model is calculated by OLS, and hence trivial to compute.... In PAGE 15: ...Wooldridge (1994), for example. Getting back to the empirical results, the coe cient estimates of (12) are provided in Table3 under the model called Full-Spline, and the conditional expectations are given in Figure 5. Like before, we used the variables found to be signi cant in (11) as a starting point for estimating the Full-Spline.... ..."

### Table 4: NLLS Coe cient EstimatesQexp-Spline Full-Spline

"... In PAGE 13: ... Consistency and asymptotic normality results can be found in Wooldridge (1992). The parameter estimates for Qexp-Spline are given in Table4 , where we have used the same variables as in the model Spline as a starting point.13 The Spline model is calculated by OLS, and hence trivial to compute.... In PAGE 15: ...and 2, consistency, asymptotic normality, and consistent estimates of the asymptotic variance matrix are obtained by the standard additional assumptions that can be found in Wooldridge (1994b), for example. Getting back to the empirical results, the coe cient estimates of (10) are provided in Table4 under the model called Full-Spline, partial e ects are outlined in Table 5, and plots of the conditional expectations are given in Figure 5. Like before, we used the variables found to be signi cant in (9) as a starting point for estimating the Full-Spline.... ..."

### Table 2: OLS Coe cient Estimates Log Spline Log-Spline S amp;S

"... In PAGE 10: ... This variable is a relative measure of the number of non-licensed drivers to size of household, and in all models estimated, higher powers of this variable, [(F-D)/F]l; l gt; 1, where not signi cant. We ran four versions of (1), and the results are given in Table2 . The rst model, Log, is the basic model in which all non-indicator regressors are transformed by the logarithmic function, hj(xj) = j log(xj).... ..."

### Table 2: OLS Coe cient Estimates Log Spline Log-Spline S amp;S

"... In PAGE 10: ... This variable is a relative measure of the number of non- licensed drivers to size of household, and in all models estimated, higher powers of this variable, [(F-D)/F]l; l gt; 1, where not signi cant. We ran four versions of (1), and the results are given in Table2 . The rst model, Log, is the basic model in which all non-indicator regressors are transformed by the logarithmic function, hj(xj) = j log(xj).... ..."

### Table 3. Estimation errors for histograms, splinegrams, KernelSpline, and Optimal- Splines, for (a) worldnet, (b) thyroid, and (c) cloud data sets.

1999

"... In PAGE 6: ...1 Estimation Accuracy We averaged the estimation errors of the histogram and spline methods over 1000 queries. Table3 summarizes the results for the worldnet, thyroid, and cloud data sets. For brevity, we present only the results of range queries where the selectivity is uniformly chosen between 0-100% and omit high (80-100%) and low (0-20%) selec- tivity queries, as their relative results were similar.... In PAGE 6: ... For brevity, we present only the results of range queries where the selectivity is uniformly chosen between 0-100% and omit high (80-100%) and low (0-20%) selec- tivity queries, as their relative results were similar. As Table3 (a) shows, the eb-continuous (end-biased) knot (bin) placement did not increase the accuracy much in the worldnet data set and even significantly performed worse in the case of the OptimalSpline. This suggests that the goal of minimizing within-bucket frequency variances is implicitly better suited for discrete data than for contin- uous data.... ..."

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### Table 6: Estimates of Earnings Function in terms of Spline of Years of Schooling Completed. (Ages 15-64 years)

"... In PAGE 14: ...33 This suggests that the 3-segment spline specification is a better empirical approximation of the earnings function. Table6 shows that among the wage earners, return to schooling at the primary school level is 2.... In PAGE 15: ...36 Schultz (2001) also observed this pattern with Ghanaian data37, which according to Schultz (1988) is attributable to the fact that in many low-income countries, serious bottleneck to education occurs at the secondary and post-secondary school level. We observe, from Table6 that estimated private returns to post-secondary education are about 3 percentage points higher for self-employed workers than they are for wage earners. The differences were less than 1 percentage point in the primary and secondary school levels.... ..."