### Table 1. Quadratic spline for GBCW function; Uniform knots. Median Reg Mean Reg

"... In PAGE 11: ...nd Gu et al. (1989). We take 1000 samples of size 150 in the experiment. The estimated LE and NE are given in Table1 . Also included are the average number of knots (Mi) used for each variable ti and the dimensionality of the tted model (d.... ..."

### Table 1: The squared bias and mean squared error for the simulation. The regression functions are m(x) = sin ( x=2) =[1 + 2x2fsign(x) + 1g] (Cases 1, 2, 3 and 6), m(x) = 1000x3 +(1 ? x)3 + (Case 4) and m(x) = 10sin(4 x) (Case 5). Case 7 is same as Case 1 above except that X is a normalized chi- square(4) random variable, and is generated as a Laplace random variable. Case 8 is same as Case 1 except that m(x) = H(100x) + Hf?100(x ? :5)g, where H(x) = f1 + exp(?x)g?1. This function is poorly t by a regression P{spline with 35 knots. \Naive quot; is the naive smoothing spline, \ICM quot; is the fully iterated ICM method, \Bayes quot; is the fully Bayesian method, and \Structural(m) quot; is the Structural regression P{spline of Carroll, et al. (1999) with m knots. In each column, the smallest MSE values is in boldface. The Cases 1{8 are discussed in the text, see Section 4.

2002

"... In PAGE 17: ... Structural method (Carroll, et al., 1999), 5 knots. Structural method, 15 knots. Table1 presents summary results for mean squared bias and mean squared error. The SIMEX method discussed by Carroll et al.... In PAGE 17: ... Here we focus on Case 1 in the simulation, with the priors modi ed as follows: 2 IG(3; 1), 2 u IG(3; 1), Gamma(2; 2000), x N(0; 1002), and 2 x IG(3; 1). Comparing with Table1 , when we ran the simulation using... In PAGE 18: ... In case 8, it is the spline representation of the function m(x) that fails. Since all the methods in Table1 are based on splines, it was di cult to guess a priori what would happen in the simulation, although one perhaps would have expected that all the methods would be equally bad, although as it turns out the Bayes method had the smallest bias and mean squared error.... ..."

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### Table 2. Spline Approximation Measures

"... In PAGE 16: ... In each case, knots were equally spaced between = ?10:0 and = 0:1. Table2 shows the slope of log error versus log np, Table 2 where np is the number of knots, and the L1 norm of interpolation error at a reference point of 5051 spline knots. The slope of log error versus log np represents the order of the approximation for each of the respective interpolants.... ..."

### Table 4. Free knot monotone cubic spline approximation of arctan noisy data.

"... In PAGE 15: ...oise uniformly distributed in [-0.075,0.075]. Unconstrained splines, even when the data contains no noise, produce undesirable oscillations, and to enforce monotonicity of the approximant monotonicity constraints have been imposed [6]. However, using monotone splines in this example requires an unacceptably large number of equidistant knots to achieve the accuracy consistent with the noise level ( Table4 ). The same accuracy was achieved using only 4 free internal knots.... ..."

### Table 2: Returns to Education, Spline Specification

"... In PAGE 15: ...reported in the upper panel of the table, while results without these dummies are reported in the lower panel. A number of things are worth noting about the results in Table2 . First, a joint F- test shows that the more flexible spline function is a significant improvement in fit over the prototypical Mincerian equation in all of the specifications.... In PAGE 15: ...ear of primary school (.062) and a year of university (.171), and greatly reduces the sheepskin effects at the primary and secondary levels (but not university). The results based on the semi-parametric regressions in equation (2), presented in Table 3 and Figure 4, are quite consistent with those reported in Table2... In PAGE 32: ...57*** 11.35*** Number of observations 2,355 2,355 2,851 2,851 Note: See note at foot of Table2 for explanation of coefficients, standard errors, test statistics, and levels of significance. Specifications 1 and 2 are limited to men whose relationship to the household head is son in households in which both the household head and his spouse are members and report their education levels.... ..."

### Table 1: Multiplicity of Breakpoints in Product Knot Vector

in Splines

"... In PAGE 3: ...1 Product B-spline Represented in Multisubsets of Multisets Because each internal breakpoint comes from one of the factors, its multiplicity must be increased by d or hatwide d (cf. Table1 ) to preserve the correct order of continuity. Hence, it has multiplicity greater than 1 (cf.... In PAGE 3: ... Hence, it has multiplicity greater than 1 (cf. Table1 ). Therefore, Eq.... ..."

### Table 2 QID Variables

2007

"... In PAGE 37: ... We use the CES-D score transformed into a spline with knots placed at the terciles of the distribution of CES-D scores in the sample. These are defined in Table2 . In the analysis of the QID data, we estimate the variance components.... ..."

### 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. Work Trip Mode Choice Model, Estimated Pre-BART Mode Description Number Percent 1 Auto Alone 429 55.6% 2 Bus with Walk Access 134 17.4%

2000

"... In PAGE 7: ... TDFP used the introduction of BART as a natural experiment to test the ability of 2 disaggregate travel demand models to forecast a new transportation mode. Table3 below, taken from McFadden (1978), gives the work mode choice model that we estimated using data collected in 1972, before BART began operation, and subsequently used to predict BART patronage. The family annual income variable in this model enters as a linear spline with knots at $7.... ..."

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### Table 1. Work Trip Mode Choice Model, Estimated Pre-BART

2000

"... In PAGE 5: ... TDFP used the introduction of BART as a natural experiment to test 2 the ability of disaggregate travel demand models to forecast a new transportation mode. Table1 below, taken from McFadden (1978), gives the work mode choice model that we estimated using data collected in 1972, before BART began operation, and subsequently used to predict BART patronage. The family annual income variable in this model enters as a linear spline with knots at $7.... ..."

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