### Table 1. pMSE and Bias of Power Estimates for Two-sample t-Statistic with Parametric Bootstrap Critical Values O = 1000, I = 59

2000

"... In PAGE 12: ... We look at two (O; I) combinations, (O = 1000; I = 59) and (O = 596; I = 99), that have about 59000 computations each. Table1 reports estimates of the root mean squared error (pMSE) and bias 1000 of the various power estimates. The standard errors of the estimates are in the range .... In PAGE 12: ...002 for pMSE and around 2 for the bias 1000. The rst and seventh rows (p1) of Table1 give results for power estimates based on the true known t percentiles appropriate for normal data. They are labeled p1 to re ect the fact that resampling with I approaching 1 would give this result.... In PAGE 12: ... They are labeled p1 to re ect the fact that resampling with I approaching 1 would give this result. These of course are unbiased (the nonzero bias results in Table1 just re ect Monte Carlo variation), and here pMSE could have been calculated simply by ppower(1-power)=O. For a given O, p1 represents the best power estimates possible.... In PAGE 12: ... For these raw estimates the (O = 596; I = 99) situation is more e cient in terms of pMSE than (O = 1000; I = 59) for all but = 0:5 because the bias is a large factor except at = 0:5. The other estimators in Table1 are 1. b plin: the simple linear extrapolation method using (5) for the (O = 1000; I = 59) case and (6) for the (O = 596; I = 99) case.... In PAGE 13: ...a;bb) distribution. From Table1 we see that the the linear extrapolation estimators, b plin and b pgls, perform the best and very similarly. Their similarity is likely due to the fact (not displayed) that the estimated covariance matrix of the b pI used as dependent variables in the regressions has nearly equal diagonal elements and nearly equal o -diagonal elements.... ..."

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### Table 5: Possible Implementations of the NL Filter for the NAS-RIF Method Constraint Nonlinear(NL) Filter

"... In PAGE 17: ... In general, a variety of image constraints may be imposed in the nonlinear lter denoted by NL in Figure 8. Table5 gives a list of possibilities. If the image is assumed to be nonnegative with known support, the NL block of Figure 8 represents the projection of the estimated image onto the set of images that are nonnegative with given nite support.... In PAGE 17: ...mposed in the nonlinear lter denoted by NL in Figure 8. Table 5 gives a list of possibilities. If the image is assumed to be nonnegative with known support, the NL block of Figure 8 represents the projection of the estimated image onto the set of images that are nonnegative with given nite support. This requires replacing the negative pixel values within the region of support to zero, and the pixel values outside the region of support to the background grey-level LB as shown in Table5 . Either the nonnegativity constraint or support constraint or both can be used for restoration.... ..."

### Table 4.2: Transformation of the covariance matrix under transformations on the sample. t is the sample mean and the sample covariance, with spectral decomposition U UT . a 2 R f0g, d 2 RD, D = diag (d1; : : : ; dD) is diagonal, R is orthogonal, ed is the unit vector in the direction of td, the primes denote the new entity after the transformation f and the symbol 6 = is used to indicate that the subsequent transformation is complex (not obviously related to f).

### Table 1. Impulsive noise models; envelope PDFs and LO nonlinear filters.

2002

"... In PAGE 13: ...onparametric filters. These require no explicit knowledge of the noise PDF. An example is the hardlimiter narrowband correlator (HNC) filter ([8, 10]) which is widely used in impulsive environments; y y g 1 ) ( = (4) The parametric version of the processor requires a choice of noise model, and estimation of the model parameters from the received data. The LO filters for several impulsive noise models are given in Table1 . To apply the processor, we read-in a segment of time-series data, estimate the model parameters from that segment of data,9 and then input these parameter estimates into the nonlinear filter to tune the processor.... ..."

### Table 3. MC filters: nonlinear time series

2000

"... In PAGE 10: ... Results In this case, it is not possible to estimate the optimal filter. For the MC filters, the results are displayed in Table3 . The average percentages of SIR steps are presented in Table 4.... ..."

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### Table 3: MC filters: nonlinear time series

2000

"... In PAGE 26: ... Results In this case, it is not possible to estimate the optimal filter. For the MC filters, the results are displayed in Table3 . The average percentages of SIR steps are presented in Table 4.... ..."

Cited by 293

### Table 2. Probability of Attending Weekly Services by Class, Gender, and Individual Work Hours, Controlling for Several Covariates.*

"... In PAGE 13: ... To see this a little better, we reran the regression analysis, replacing our joint work time variable with straightforward counts of how many hours respondents and their spouses worked and running the analyses for husbands and wives separately (see Appendix 2, Table A3). One way to see the results is in Table2 , below. It displays the estimated probability of attending services as a function of work hours, estimated for parents, age 40, who were white, had average income, and... In PAGE 14: ... There were no significant non-linear effects of hours. Table2 shows that, other things being equal, middle-class respondents were likelier to attend than working-class respondents, especially among men, and that women were likelier to attend than men, especially in the working class. But what interests us most here are the effects of work hours.... In PAGE 30: ... Table2 : Ordinary Least Squares Regression, Dependent Variable = Probability of Attending Religious Services Any Given Week. R squared = .... ..."

### Table 2 Nonlinear models.

1998

"... In PAGE 16: ... Much of the emphasis will be on the choice of bandwidth and the new aspects brought in by using local polynomial approximation. A power experiment on a wide class of nonlinear models listed in Table2 has been conducted in Section 6.3.... In PAGE 18: ...Table2 , however, where M1(x) is approximately quadratic (see Figure 1), as can be expected the best result is achieved with T = 2 and h = 1. For the ^ L(V1)-tests the size tends to be too low.... In PAGE 18: ... If no corrections are made for this e ect, it will lead to conservative tests. Figure 5 shows the power of the ^ L(V )-tests for model la) of Table2 , and we see the same general trend as for the ^ L(M)-tests; the optimal h increases with T and the derivative. Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis.... In PAGE 18: ... Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis. ^ L0(V1) is much more robust than ^ L0(M1), and this is the case for the other models listed in Table2 as well. 6.... In PAGE 18: ... In particular when we have a nonlinear model, we do of course not want h = 1 to be chosen when T = 0 or T = 1, but with a small autocorrelation, this may well happen for T = 0. In fact h = 1 was chosen in 136 of 500 realizations of model lc) of Table2 which is clearly nonlinear (cf. Figure 1).... In PAGE 19: ... 6.3 A power experiment for a wide set of models We have performed a power experiment for the models listed in Table2 , where t N(0; 0:62) in model ld) - lf), t N(0; 0:72) in lg) - lj) and t N(0; 1) in the other models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... In PAGE 36: ...Figure 1-2: Plots of ^ M1(x) (Figure 1) and ^ V1(e) (Figure 2) for the models listed in Table2 with n = 100 000. The kernel estimator with bandwidth h = 0:2 is used and each plot consists of two realizations.... In PAGE 36: ... The possible values for h is given at the vertical axes. Figure 7: The gure is based on 500 realizations of the models in Table2 . It shows the power of ^ LT (M1) with h cross-validated and n = 100, 250 and 204 for models la) - li), aa) - ag) and Aa) - Ag), respectively.... In PAGE 36: ...ower achieved in Hjellvik and Tj stheim (1995). The nominal size is 0.05. Figure 8: The gure is based on 500 realizations of the models in Table2 and shows the power of ^ LT (V1) with h cross-validated and n = 100, 250 and 204 for models la), aa) - ag) and Aa) - Ag), respectively.... In PAGE 37: ....05 for the standard normal distribution has been used. The model is Xt = t, the bandwidth is h = n?1=9 and the number of realizations are 500. Table2 : Various nonlinear models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... ..."

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### Table 5: Possible Implementations of the NL Filter for the NAS-RIF Method

"... In PAGE 17: ... In general, a variety of image constraints maybe imposed in the nonlinear lter denoted by NL in Figure 8. Table5 gives a list of possibilities. If the image is assumed to be nonnegative with known support, the NL blockofFigure8 represents the projection of the estimated image onto the set of images that are nonnegative with given nite support.... In PAGE 17: ...mposed in the nonlinear lter denoted by NL in Figure 8. Table 5 gives a list of possibilities. If the image is assumed to be nonnegative with known support, the NL blockofFigure8 represents the projection of the estimated image onto the set of images that are nonnegative with given nite support. This requires replacing the negative pixel values within the region of support to zero, and the pixel values outside the region of support to the background grey-level L B as shown in Table5 . Either the nonnegativity constraint or support constraint or both can be used for restoration.... ..."

### Table 5: Nonlinear Least Scruares Results

"... In PAGE 1: ... In addition, an F-test indicated that the hypothesis that the two rates are the same could not be rejected at conventional significance levels. The 1,775 observations in Table5 represent all 1981 through 1987 vintage passenger cars owned by RTECS respondents in July of 1988 for which complete data were available. Model year 1988 new cars are considered separately from the older vehicles in the household stock because an F-test indicated that the two samples could not be pooled.... In PAGE 8: ... If however, there is no relationship between life cycle fuel expenditures and vehicle price, the capitalization rate would be zero. Based on the regression estimates in Table5 for the sample of pre-1988 vehicles in household holdings, the estimated mean willingness-to-pay for a one dollar change in life cycle operating costs, is $ 0.39.... In PAGE 11: ...8 million--l6 percent higher-- indicating that excluding a separate measurement for nonfatal injuries causes the fatality valuation to reflect the value of nonfatal injuries. The third regression result in Table5 demonstrates the importance of including controls for the driver characteristics in fatal accidents. The mortality risk measure used in the model does not represent a pure measure of automobile-specific risk because driver characteristics are not excised from the rates.... In PAGE 11: ... As defined in section II, these controls measure the proportion of fatal accidents occurring in each make/model/year vehicle that reflect the characteristic in question. The first column in Table5 indicates that the proportion of drivers who are young, those who are older, and those wearing seat belts were all statistically significant at the 0.05 level, and alcohol involvement was significant at the 0.... ..."