### Table 4: Results for the simulated datasets: variance of the martingale residuals.

2007

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### Table 8: Results for the real-life datasets: variance of the martingale residuals.

2007

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### Table 4 reports the RMSE for the LWR forecasts divided by the RMSE of

1993

"... In PAGE 10: ...Table 5 reports the MAE of the LWR forecasts divided by the MAE of the martingale model. The results are similar to those in Table4 . The martingale model typically has a lower MAE than the LWR models.... ..."

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### Table 1. Video anni ugs outdoor indoor

"... In PAGE 6: ... Table1 : Experimental Results. Based on the F1 measure, the multiple-martingale test performed the best three out of the four video sequences.... ..."

### Table 2 Summary of maximum likelihood estimates of 160 rms apos; default risk processes implied by corporate bond term structures

1999

"... In PAGE 12: ...3. Results assuming no measurement error in the long bond The summary of rms apos; ^ j apos;s in Panel A of Table2 indicates that for most rms, their instantaneous default probability is a martingale. Therefore for these rms, j is an irrel- evant parameter.... In PAGE 13: ...9 percent. (This is not reported in Table2 .) Although lower than the median of 8.... In PAGE 18: ...5. Results assuming no measurement error in the ve-year bond As in Panel A of Table2 , the parameter estimates associated with the equivalent martingale measure in Panel B of Table 2 are striking, but they are striking only in the sense that they are dramatically di erent from those in Panel A. The estimate of j j is positive for most rms (all but 13 rms have positive estimates).... In PAGE 18: ...5. Results assuming no measurement error in the ve-year bond As in Panel A of Table 2, the parameter estimates associated with the equivalent martingale measure in Panel B of Table2 are striking, but they are striking only in the sense that they are dramatically di erent from those in Panel A. The estimate of j j is positive for most rms (all but 13 rms have positive estimates).... In PAGE 18: ... I use the outer product of rst derivatives of the log-likelihood function and do not adjust them for the fact that the default-free parameters are estimated instead of known with certainty. Summary statistics for the standard errors are not reported in Table2 , but are available on request. Here I summarize a couple of features of these standard errors.... In PAGE 26: ... For now, we can think of these two rms as independent rms in the same industry, so that their prospects are closely related. I assume that for each rm, their instantaneous default process under the equivalent martingale measure is described by dhi;t = ?0:075hi;tdt + p0:0092hi;tdZt (16) This process has the median drift given in Panel A in Table2 and a volatility given by the third quartile in the same panel. I assume the initial instantaneous default probability is 0.... ..."

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### Table 4: Forecasting evaluation, 1981:10-1991:12a

1998

"... In PAGE 11: ... For our second forecast period these gures are 158 and 111 respectively. - Table4 here - Table 4 displays the results for evaluations in the forecast period 1981:10 - 1991:12. Up to the two-year horizon none of the monetary versions of model (5) out-performs the martingale-based no-change forecasts over the four exchange rates.... In PAGE 11: ... For our second forecast period these gures are 158 and 111 respectively. - Table 4 here - Table4 displays the results for evaluations in the forecast period 1981:10 - 1991:12. Up to the two-year horizon none of the monetary versions of model (5) out-performs the martingale-based no-change forecasts over the four exchange rates.... ..."

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### Table 3 The 16 17 term-document matrix corresponding to the book titles in Table 2.

1995

"... In PAGE 7: ... Underlined keywords appear in more than one book title. Label Titles B1 ACourseonIntegral Equations B2 Attractors for Semigroups and Evolution Equations B3 Automatic Di erentiation of Algorithms: Theory, Implementation, and Application B4 Geometrical Aspects of Partial Di erential Equations B5 Ideals, Varieties, and Algorithms {AnIntroduction to Computational Algebraic Geometry and Commutative Algebra B6 Introduction to Hamiltonian Dynamical Systems and the N-Body Problem B7 Knapsack Problems: Algorithms and Computer Implementations B8 Methods of Solving Singular Systems of Ordinary Di erential Equations B9 Nonlinear Systems B10 Ordinary Di erential Equations B11 Oscillation Theory for Neutral Di erential Equations with Delay B12 Oscillation Theory of Delay Di erential Equations B13 Pseudodi erential Operators and Nonlinear Partial Di erential Equations B14 Sinc Methods for Quadrature and Di erential Equations B15 StabilityofStochastic Di erential Equations with Respect to Semi-Martingales B16 The Boundary Integral Approach to Static and Dynamic Contact Problems B17 The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory Corresponding to the text in Table 2 is the 16 17 term-document matrix shown in Table3 . The elements of this matrix are the frequencies in which a term occurs in a document or book title (see Section 4).... In PAGE 11: ... That is, one can discuss ordinary algorithms and ordinary di erential equations in di erentcontexts. Folding-in the 3 new book titles based on the existing rank-2 approximation to A (de ned by Table3 ) may not accurately reproduce the true LSI representation of the new (or updated) database. In practice, the di erence between folding-in and SVD-updating is likely to depend on the number of new documents and terms relativetothenumber in the original SVD of A.... ..."

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### Table 3 The 16 17 term-document matrix corresponding to the book titles in Table 2.

1995

"... In PAGE 7: ... Underlined keywords appear in more than one book title. Label Titles B1 ACourseonIntegral Equations B2 Attractors for Semigroups and Evolution Equations B3 Automatic Di erentiation of Algorithms: Theory, Implementation, and Application B4 Geometrical Aspects of Partial Di erential Equations B5 Ideals, Varieties, and Algorithms {AnIntroduction to Computational Algebraic Geometry and Commutative Algebra B6 Introduction to Hamiltonian Dynamical Systems and the N-Body Problem B7 Knapsack Problems: Algorithms and Computer Implementations B8 Methods of Solving Singular Systems of Ordinary Di erential Equations B9 Nonlinear Systems B10 Ordinary Di erential Equations B11 Oscillation Theory for Neutral Di erential Equations with Delay B12 Oscillation Theory of Delay Di erential Equations B13 Pseudodi erential Operators and Nonlinear Partial Di erential Equations B14 Sinc Methods for Quadrature and Di erential Equations B15 StabilityofStochastic Di erential Equations with Respect to Semi-Martingales B16 The Boundary Integral Approach to Static and Dynamic Contact Problems B17 The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory Corresponding to the text in Table 2 is the 16 17 term-document matrix shown in Table3 . The elements of this matrix are the frequencies in which a term occurs in a document or book title (see Section 4).... In PAGE 11: ... That is, one can discuss ordinary algorithms and ordinary di erential equations in di erentcontexts. Folding-in the 3 new book titles based on the existing rank-2 approximation to A (de ned by Table3 ) may not accurately reproduce the true LSI representation of the new (or updated) database. In practice, the di erence between folding-in and SVD-updating is likely to depend on the number of new documents and terms relativetothenumber in the original SVD of A.... ..."

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### Table 2 Database of titles from books reviewedinSIAM Review. Underlined keywords appear in more

1995

"... In PAGE 5: ...3 are applied to a small database of book titles. In Table2 , 17 book titles from book reviews published in the December 1993 issue (volume 54, number 4) of SIAM Review are listed. All the underlined words in Table 2 denote keywords which... In PAGE 5: ... In Table 2, 17 book titles from book reviews published in the December 1993 issue (volume 54, number 4) of SIAM Review are listed. All the underlined words in Table2 denote keywords which... In PAGE 7: ...Computational Algebraic Geometry and Commutative Algebra B6 Introduction to Hamiltonian Dynamical Systems and the N-Body Problem B7 Knapsack Problems: Algorithms and Computer Implementations B8 Methods of Solving Singular Systems of Ordinary Di erential Equations B9 Nonlinear Systems B10 Ordinary Di erential Equations B11 Oscillation Theory for Neutral Di erential Equations with Delay B12 Oscillation Theory of Delay Di erential Equations B13 Pseudodi erential Operators and Nonlinear Partial Di erential Equations B14 Sinc Methods for Quadrature and Di erential Equations B15 StabilityofStochastic Di erential Equations with Respect to Semi-Martingales B16 The Boundary Integral Approach to Static and Dynamic Contact Problems B17 The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory Corresponding to the text in Table2 is the 16 17 term-document matrix shown in Table 3. The elements of this matrix are the frequencies in which a term occurs in a document or book title (see Section 4).... In PAGE 10: ....3. Folding-In. Suppose the ctitious titles listed in Table 5 are to be added to the original set of titles in Table2 . While some titles in Table 5 use terms related to nonlinear systems or di erential equations, notice the di erent meaning of the speci c term ordinary in book titles B19 and B20 as opposed to book titles B8 and B10.... In PAGE 10: ... While some titles in Table 5 use terms related to nonlinear systems or di erential equations, notice the di erent meaning of the speci c term ordinary in book titles B19 and B20 as opposed to book titles B8 and B10.Aswith Table2 , all underlined words in Table 5 are considered signi cant since they appear in more than one title (across all 20 titles from Tables 2 and 5). Folding- in (see Section 2.... In PAGE 11: ... As discussed in [23], the the accuracy of SVD-updating approaches can be easily compared to that obtained when the SVD of ~ A is explicitly computed. Suppose the titles from Table 5 are combined with those of Table2 in order to create a new 16 20 term-document matrix ~ A.Following Figure 1, we then construct the best rank-2 approximation to ~ A, ~ A 2 = ~ U 2 ~ 2 ~ V T 2 : (9) Figure 8 is a two-dimensional plot of the 16 terms and 20 documents (book titles) using the elements of ~ U 2 and ~ V 2 for term and document coordinates, respectively.... ..."

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