Grace Wahba Publications

Grace Wahba Publications

In print
  1. A least squares estimate of satellite attitude, Problems and Solutions section, SIAM Review, 8, 3, 384 (1966).[Source of the famous "Wahba's Problem"!]
  2. On the distribution of some statistics useful in the analysis of jointly stationary time series, Ann. Math. Statist., 39, 6, 1849-1862 (1968).
  3. A family of summation formulae, Problems and Solutions section, SIAM Review, 11, 3, 409 (1969).
  4. Estimation of the coefficients in a multi-dimensional distributed lag model, Econometrica, 37, 3, 398-407 (1969).
  5. A correspondence between Bayesian estimation of stochastic processes and smoothing by splines (with George S. Kimeldorf), Ann. Math. Statist., 41, 2, 495-502 (1970).
  6. Spline functions and stochastic processes (with George S. Kimeldorf), Sankya, Ser. A, 32, part 2, 173-180 (1970).
  7. Some results on Tchebycheffian spline functions (with George S. Kimeldorf), J. Math. Anal. Applic., 33, 1, 82-95 (1971).
  8. Some tests of independence for stationary multivariate time series, J. Roy. Stat. Soc. Series B, 33, 1, 153-166 (1971).
  9. On the regression design problems of Sacks and Ylvisaker, Ann. Math. Statist., 42, 3, 1035-1053 (1971).
  10. A polynomial algorithm for density estimation, Ann. Math. Statist., 42, 6, 1870-1886 (1971).
  11. Convergence rates of certain approximate solutions to first kind integral equations, J. Approx. Thy., 7, 2, 167-185 (1973).
  12. On the minimization of a quadratic functional subject to a continuous family of linear inequality constraints, SIAM J. Control, 11, 1, 64-79 (1973).
  13. A class of approximate solutions to linear operator equations, J. Approx. Thy., 9, 1, 61-77 (1973).
  14. Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind (with M.Z. Nashed), Math. Comp., 28, 125, 69-80 (1974).
  15. Regression design for some equivalence classes of kernels, Ann. Statist., 2, 5, 925-934 (1974).
  16. Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations (with M.Z. Nashed), SIAM J. Math. Anal., 5, 6, 974-987 (1974).
  17. Regularization and approximation of linear operator equations in reproducing kernel spaces (with M.Z. Nashed), Bull. Am. Math. Soc., 80, 6, 1213-1218 (1974).
  18. Optimal convergence properties of variable knot, kernel, and orthogonal series methods for density estimation, Ann. Statist., 3, 1, 15-29 (1975).
  19. Interpolating spline methods for density estimation. I. Fixed knots, Ann. Statist., 3, 1, 30-48 (1975).
  20. A completely automatic French curve: Fitting spline functions by cross-validation (with S. Wold), Commun. Statist., 4, 1, 1-17 (1975).
  21. Periodic splines for spectral density estimation: The use of cross-validation for determining the degree of smoothing (with S. Wold), Commun. Statist., 4, 2, 125-141 (1975).
  22. Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform (with M.Z. Nashed), J. Math. Anal. Applic., 52, 3, 660-668 (1975).
  23. Smoothing noisy data by spline functions, Numer. Math., 24, 383-393 (1975).
  24. On the optimal choice of nodes in the collocation-projection method for solving linear operator equations, J. Approx. Thy., 16, 2, 175-186 (1976).
  25. Histosplines with knots which are order statistics. J. Roy. Stat. Soc. Series B, 38, 2, 140-151 (1976)
  26. An averaging method for the stiff highly oscillatory problem (with W.L. Miranker), Math. Comp., 30, 135, 383-399 (1976).
  27. Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Num. Anal., 14, 4, 651-667 (1977).
  28. Optimal smoothing of density estimates, in ``Classification and Clustering'', J. Van Ryzin, ed., 423-458, Academic Press (1977).
  29. A survey of some smoothing problems and the method of generalized cross-validation for solving them, in ``Applications of Statistics'', P.R. Krishnaiah, ed., 507-523, North Holland (1977).
  30. Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Stat. Soc., Ser. B., 40, 3, 364-372 (1978).
  31. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation (with Peter Craven). Numer. Math., 31, 377-403 (1979).
  32. Determination of an optimal mesh for a collocation-projection method for solving two-point boundary value problems (with Manohar Athavale), J. Approx. Thy., 28, 1, 38-48 (1979).
  33. Generalized cross-validation as a method for choosing a good ridge parameter (with G. Golub and M. Heath). Technometrics, 21, 215-223 (1979).
  34. How to smooth curves and surfaces with splines and cross-validation, in ``Proceedings of the 24th Conference on the Design of Experiments'', U.S. Army Research Office, Report 79-2, 167-192 (1979).
  35. Convergence rates of ``Thin Plate'' smoothing splines when the data are noisy, in ``Smoothing Techniques for Curve Estimation'', T. Gasser and M. Rosenblatt, eds. Lecture Notes in Mathematics No. 757, 232-246 Springer-Verlag (1979).
  36. Smoothing and ill posed problems, in ``Solution Methods for Integral Equations with Applications'', Michael Golberg, ed., 183-194, Plenum Press (1979).
  37. Automatic smoothing of the log periodogram. J. Am. Stat. Soc., 75, 369, 122-132 (1980).
  38. Parameter estimation in linear dynamic systems. IEEE Transactions on Automatic Control, AC-25, 2, 235-238 (1980).
  39. Some new mathematical methods for variational objective analysis using splines and cross-validation (with J. Wendelberger), Monthly Weather Review 108, 36-57 (1980).
  40. Spline bases, regularization, and generalized cross validation for solving approximation problems with large quantities of noisy data, in ``Approximation Theory III'', W. Cheney, ed., 905-912, Academic Press (1980).
  41. Data-based optimal smoothing of orthogonal series density estimates. Ann. Statist., 9, 1, 146-156 (1981).
  42. A new approach to the numerical inversion of the Radon transform with discrete, noisy data, in ``Mathematical Aspects of Computerized Tomography'', G.T. Herman and F. Natterer, eds. Lecture Notes in Medical Informatics, 189-203, Springer-Verlag (1981).
  43. Design problems for optimal surface interpolation (with C. Micchelli), in ``Approximation Theory and Applications'' Z. Ziegler, ed., 329-348, Academic Press (1981).
  44. Spline interpolation and smoothing on the sphere. SIAM J. Sci. Statist. Comp., 2, 1, 5-16 (1981). Erratum 3, 3, 385-386 (1982).
  45. On the estimation of functions of several variables from aggregated data (with N. Dyn), SIAM J. Math. Anal., 13, 1, 134-152 (1982).
  46. Numerical experiments with the thin plate histospline. Commun. Statist. Theor. Meth., A10 (24), 2475-2514 (1981).
  47. Constrained regularization for ill posed linear operator equations, with applications in meteorology and medicine, in ``Statistical Decision Theory and Related Topics III'', Vol. 2, S.S. Gupta and J.O. Berger, eds., 383-418, Academic Press (1982).
  48. Computational methods for generalized cross validation with large data sets (with D.M. Bates). In ``Treatment of Integral Equations by Numerical Methods'', C.T.H. Baker and G.F. Miller, eds., 283-296, Academic Press (1982).
  49. Vector splines on the sphere, with application to the estimation of vorticity and divergence from discrete, noisy data. In ``Multivariate Approximation Theory'', Vol. 2, W. Schempp and K. Zeller, eds., 407-429, Birkhauser Verlag (1982).
  50. Variational methods in simultaneous optimum interpolation and initialization. In ``The Interaction Between Objective Analysis and Initialization'', D. Williamson, ed., 178-185, Publication in Meteorology 127 Atmospheric Analysis and Prediction Division, National Center for Atmospheric Research, Boulder, CO (1982).
  51. Bayesian confidence intervals for the cross validated smoothing spline. J. Roy. Stat. Soc. B., 45, 1, 133-150 (1983).
  52. Multivariate thin plate spline estimates for the posterior probabilities in the classification problem (with M. Villalobos). Commun. Statist. Theor. Meth., 12, 13, 1449-1480 (1983).
  53. Reliable mathematical stereologic method for estimating the number of hepatocellular foci from their transections. (With T.D. Pugh, J.H. King, H. Koen, D. Nychka, and J. Chover). Cancer Research 43, 1261-1268 (1983).
  54. Surface fitting with scattered, noisy data on Euclidean d-space and on the sphere. Rocky Mountain J. Math., 14, 1, 281-299 (1984).
  55. Cross validated spline methods for direct and indirect sensing experiments. In ``Statistical Signal Processing'', E.J. Wegman and J. Smith, eds., Marcel Dekker (1984).
  56. Cross validated spline methods for the estimation of multivariate functions from data on functionals. In ``Statistics, an Appraisal, Proceedings of the Iowa State University Statistical Laboratory 50th Anniversary Conference'' H.A. David and H.T. David, eds. The Iowa State University Press, 205-235 (1984).
  57. Optimal use of sampled tissue sections for estimating the number of hepatocellular foci. (With D. Nychka, T.D. Pugh, J.H. King, H. Koen, J. Chover and S. Goldfarb). Cancer Research, Vol. 44, 178-183 (1984).
  58. Cross validated spline methods for the estimation of three dimensional tumor size distributions from observations on two dimensional cross sections. (With D. Nychka, S. Goldfarb and T. Pugh). J. Amer. Statist. Assoc., 79, 832-846 (1984).
  59. A cross validated Bayesian retrieval algorithm for non-linear remote sensing experiments (with F. O'Sullivan). J. Comput. Physics, 59, 441-455 (1985).
  60. Design Criteria and eigensequence plots for satellite computed tomography. J. Atmos. Ocean Tech., 2, 125-132 (1985).
  61. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Ann. Statist. 13, 1378-1402 (1985).
  62. Variational methods for multidimensional inverse problems, in ``Remote Sensing Retrieval Methods'', A. Deepak, H.E. Fleming and M.T. Chahine, eds., A. Deepak Publishing Co., pp. 385-408 (1985).
  63. Multivariate thin plate spline smoothing with positivity and other linear inequality constraints, in ``Statistical Image Processing and Graphics'', E. Wegman and E.J. dePriest, eds., Marcel Dekker (1985).
  64. Partial and interaction spline models for the semiparametric estimation of functions of several variables. In Proceedings of Computer Science and Statistics: 18th Symposium on the Interface, T.J. Boardman, Ed., American Statistical Association, Washington, D.C. (1986).
  65. Partial spline modeling of the tropopause and other discontinuities in Function Estimates, Contemporary Mathematics Volume 59, American Mathematical Society, Providence, R.I., pp. 125-135 (1986).
  66. Partial spline models for the estimation of three dimensional atmospheric temperature distribution from satellite radiance data and tropopause height information. In ``Variational Methods in Geosciences'', Y.K. Sasaki, ed. Elsevier, 125-130 (1986).
  67. Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two and three dimensional objective analysis (with J.-J. Shiau and D.R. Johnson). J. Atmos. Ocen Tech., 3, 714-725 (1986).
  68. Inequality-constrained multivariate smoothing splines with application to the estimation of posterior probabilities (with Miguel Villalobos). J. Amer. Statist. Assoc. 82, 239-248 (1987).
  69. GCVPACK-routines for generalized cross validation (with D. Bates, M. Lindstrom and B. Yandell). Commun. Statist., Simulation and Computation, 16, 263-297 (1987).
  70. Three topics in ill posed inverse problems. In "Inverse and Ill-Posed Problems", M. Engl and G. Groetsch, eds., Academic Press, 37-51 (1987).
  71. Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models (with D. Cox, E. Koh and B. Yandell), Ann. Statist. 16, 113-119 (1988).
  72. Partial and interaction spline models, in ``Bayesian Statistics 3, J.M. Bernardo, M.M. deGroot, D.V. Lindley and A.F.M. Smith, eds, Oxford University Press 479-491 (1988).
  73. Rates of convergence of some estimators for a semiparametric model (with J.-J. Shiau) Commun. Statist. Comp. 17, 1117-1133 (1988).
  74. Multiple smoothing parameters in semiparametric multivariate model building. In "Computing Science and Statistics", Proceedings of the 20th Symposium on the Interface, E.J. Wegman, ed., American Statistical Association, Washington, D.C., 435-441 (1989).
  75. Spline Functions. Entry in the Encyclopedia of Statistical Sciences, Suppl. Vol., S. Kotz and N.L. Johnson, eds., 148-160 (1989).
  76. On the dynamic estimation of relative weights for observation and forecast in numerical weather prediction, in ``RSRM '87: Advances in Remote Sensing Retrieval Methods'', A. Deepak, H.E. Fleming and J.S. Theon, eds., A. Deepak Publishing Co., Hampton, VA, 347-358 (1989).
  77. The computation of GCV functions through Householder tridiagonalization with application to the fitting of interaction spline models (with C. Gu, D. Bates, and Z. Chen), SIAM J. Matrix Anal., 10, 457-480 (1989)
  78. ``Spline Models for Observational Data'' Vol. 59 in the CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA (1990). xii + 169 pp.
  79. Comment on Cressie, Letters to the Editor, American Statistician, 44, 255-256 (1990).
  80. Regularization and cross validation methods for nonlinear implicit, ill-posed inverse problems. In "Geophysical Data Inversion Methods and Applications", A. Vogel, C. Ofoegbu, R. Gorenflo and B. Ursin, eds., Vieweg, Wiesbaden-Braunschweig, 3-13 (1990).
  81. When is the optimal regularization parameter insensitive to the choice of the loss function? (with Yonghua Wang). Commun. Statist., A19, 5 1685-1700, (1990).
  82. Multiple smoothing and weighting parameters in direct variational methods for objective analysis of meteorological information (with F. Reames and D. R. Johnson). In "Assimilation of Observations in Meteorology and Oceanography", Proceedings of the WMO International Symposium, Clermont-Ferrand, 1990, F.- X. LeDimet and O. Talagrand, eds., WMO, 448-453 (1991).
  83. Minimizing GCV/GML scores with multiple smoothing parameters via the Newton methods (with C. Gu). SIAM J. Sci. Stat. Comput. 12, 383-398 (1991).
  84. Book Review of "Ill-Posed Problems in the Natural Sciences" by A. N. Tikhonov and A. V. Goncharsky, eds., in American Scientist 79, 282-283, May-June, 1991.
  85. Multivariate model building with additive, interaction, and tensor product thin plate splines. In "Curves and Surfaces" , P.-J. Laurent, A. Le Mehaute and L. L. Schumaker, eds., Academic Press, 491-504 (1991).
  86. Eigenvalues of sine and cosine matrices, Solution to Advanced Problem No. 6591, with D. Callan. Amer. Math. Monthly, 98, 64-65 (1991).
  87. Multivariate function and operator estimation, based on smoothing splines and reproducing kernels, in ``Nonlinear Modeling and Forecasting, SFI Studies in the Sciences of Complexity'', Proc. Vol. XII, Eds. M. Casdagli and S. Eubank, Addison-Wesley, 95-112 (1992).
  88. A note on generalized cross validation with replicates (with Chong Gu and Nancy Heckman). Stat. Prob. Letters. 14, 283-287 (1992).
  89. Smoothing spline ANOVA with component-wise Bayesian "confidence intervals" (with Chong Gu). J. Comput. Graph. Statist., 2, 97-117 (1993)
  90. Getting better contour plots with S and GCVPACK (with Douglas Bates and Fred Reames). Comp. Stat. Data Anal., 15, 329-342 (1993).
  91. Semiparametric ANOVA with tensor product thin plate splines (with Chong Gu). J. Roy. Stat. Soc. B, 55, 353-368 (1993).
  92. Structured Machine Learning for `Soft' Classification with Smoothing Spline ANOVA and Stacked Tuning, Testing and Evaluation, (G. Wahba, C. Gu, Y. Wang, R. Klein and B. Klein), in ``Advances in Neural Information Processing Systems 6'', J. Cowan, G. Tesauro, and J. Alspector, eds., Morgan Kauffman 415-422, (1994).
  93. Bootstrap confidence intervals for smoothing splines and their comparison to Bayesian confidence intervals, Y. Wang and G. Wahba, J. Stat. Comp. Sim., 51, 263-279 (1995).
  94. Behavior near zero of the distribution of GCV smoothing parameter estimates, G. Wahba and Y. Wang, Stat. Prob. Letters, 25, 105-111 (1995).
  95. Simulation studies of smoothing parameter estimates and Bayesian confidence intervals in Bernoulli SS-ANOVA models, Y. Wang, G. Wahba, R. Chappell and C. Gu, Commun. Stat. Comp. Sim., 24, 1037-1059 (1995).
  96. Adaptive tuning of numerical weather prediction models: randomized GCV in three and four dimensional data assimilation, G. Wahba, D. R. Johnson, F. Gao and J. Gong, Monthly Weather Review, 123, 3358-3369 (1995).
  97. `Soft' classification, a.k.a. penalized log likelihood risk estimation with smoothing spline analysis of variance, G. Wahba, C. Gu, Y. Wang and R. Chappell. in ``The Mathematics of Generalization'', Santa Fe Institute Studies in the Sciences of Complexity, D. Wolpert, ed. Addison-Wesley 329-360 (1995). By agreement with both editors, this paper also appears in the collection `` Computational Learning Theory and Natural Learning Systems'' T. Petsche, ed., MIT Press 133-162 (1995).
  98. Generalization and regularization in nonlinear learning systems, in M. Arbib, ed., `Handbook of Brain Theory and Neural Networks', MIT Press, pp. 426-430 (1995).
  99. Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy, G. Wahba, Y. Wang, C. Gu, R. Klein, and B. Klein, Ann. Statist., 23, 1865-1895 (1995).
  100. A generalized approximate cross validation for smoothing splines with non-Gaussian data, D. Xiang and G. Wahba, Statistica Sinica, 6, 675-692 (1996).
  101. Smoothing spline ANOVA fits for very large, nearly regular data sets, with application to historical global climate data, G. Wahba and Z. Luo, Ann. Numer. Math. 4, 579-596 (1997).
  102. Hybrid adaptive splines, Z. Luo and G. Wahba, J. Amer. Statist. Assoc. 92, 107-114 (1997)
  103. Using Smoothing spline ANOVA to examine the relation of risk factors to the incidence and progression of diabetic retinopathy, Y. Wang, G. Wahba, C. Gu, R. Klein, and B. Klein, Statistics in Medicine 16, 1357-1376 (1997)
  104. Adaptive tuning of numerical weather prediction models: Simultaneous estimation of weighting, smoothing and physical parameters, J. Gong, G. Wahba, D. R. Johnson and J. Tribbia, Monthly Weather Reveiw 126, 210-231 (1998)
  105. Spatial-temporal analysis of temperature using smoothing spline ANOVA, Z. Luo and G. Wahba, J. Climate 11 18-28 (1998)
  106. Approximate smoothing spline methods for large data sets in the binary case, D. Xiang and G. Wahba Proceedings of the 1997 ASA Joint Statistical Meetings, Biometrics Section 94-98 (1998)
  107. Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV, in B. Schoelkopf, C. Burges & A. Smola, eds, `Advances in Kernel Methods Support Vector Learning', MIT Press, 69-88 (1999)

To appear
The bias-variance tradeoff and the randomized GACV, G. Wahba, X. Lin, F. Gao, D. Xiang, R. Klein and B. Klein, Technical Report 997, Department of Statistics, University of Wisconsin, Madison WI. To appear, Advances in Information Processing Systems 11: M. Kearns, S. Solla and D. Cohn, eds. MIT Press 1998.
Adaptive tuning, four dimensional variational data assimilation and representers in RKHS, Technical Report 1000, Department of Statistics, University of Wisconsin-Madison, to appear Proceedings ECMWF Workkshop on the Diagnosis of Data Assimilation Systems, F. Bouttier, Ed. ECMWF, Reading UK.

Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV, X. Lin, G. Wahba, D. Xiang, F. Gao, R. Klein and B. Klein, Technical Report 998, Department of Statistics, University of Wisconsin, Madison WI (1998).
Testing the generalized linear model null hypothesis vs. `smooth' alternatives, D. Xiang and G. Wahba, TR 953, Department of Statistics, University of Wisconsin, Madison WI (1995).

Invited discussion to
  1. Consistent nonparametric regression, C.J. Stone, Ann. Stat., 5, 4, 636-645 (1977).
  2. Curve fitting and optimal design for prediction, A. O'Hagan, J. Roy. Stat. Soc. B, 40, 35-36 (1978).
  3. Density estimation, stochastic processes and prior information, Tom Leonard, J. Roy. Stat. Soc. B, 40, 2, 140 (1978).
  4. Smooth pychnophylactic interpolation, W. Tobler (with N. Dyn and W.H. Wong), J. Amer. Statist. Soc., 74, 367, 530-535 (1979).
  5. Projection pursuit, Peter J. Huber, Ann. Statist., 13, 2, 518-521 (1985).
  6. Some aspects of the spline smoothing approach to nonparametric regression curve fitting, Bernard Silverman, J. Roy. Stat. Soc. B, 46 (1985).
  7. A statistical perspective on ill posed inverse problems, Finbarr O'Sullivan, Statistical Science, 1, 521-522 (1987).
  8. Monotone regression splines in action, by J. O. Ramsey. (with C. Gu), Statistical Science, 3, 456-458 (1988).
  9. Linear smoothers and additive models, by Buja, Hastie and Tibshirani, (with Z. Chen and C. Gu), Ann. Statist., 17, 515-522 (1989).
  10. Multivariate Adaptive Regression Splines, by J. Friedman, (with C. Gu), Ann. Statist., 19, 115-122 (1991).
  11. Maximum entropy and the nearly black object, by Donoho, Johnstone and Hoch, J. Roy. Stat. Soc. B, 54, 76 (1992).
  12. Empirical functionals and efficient smoothing parameter selection, by Hall and Johnstone, J. Roy. Stat. Soc. B, 54, 525-526 (1992).
  13. Varying-coefficient models, by Hastie and Tibshirani, J. Roy. Stat. Soc. B, 55, 757-796 (1993).
  14. Neural networks and related methods for classification, by B. D. Ripley, J. Roy. Stat. Soc. B, 56, 409-456 (1994).
  15. Wavelet shrinkage: asymptopia?, by Donoho, Johnstone, Kerkyacharian and Picard, J. Roy. Stat. Soc. B 57, 301-370 (1995).
  16. The fast Monte-Carlo cross-validation and C_L procedures: Comments, new results and application to image recovery problems, by D. Girard. Comp. Stat., 10, 249-250 (1995).
  17. Model indexing and smoothing parameter selection in nonparametric function estimation, by Chong Gu. Statistica Sinica, 8, 632-638 (1998).
  18. Smoothing spline models for the analysis of nested and crossed samples of curves, by Babette Brumback and John Rice. (with Y. Wang). JASA, 93, 976-980 (1998).

Unpublished technical reports
Estimating derivatives from outer space. Mathematics Research Center TSR 989, May 1969.
On the approximate solution of Fredholm integral equations of the first kind. University of Wisconsin-Madison, Statistics Department TR 217, October 1969, also Mathematics Research Center TSR 990.
A note on interpolation over all the integers. University of Wisconsin-Madison, Statistics Department TR 231. April 1970.
Some Radon-Nikodym derivatives for processes equivalent to Integrated weighted Wiener processes. University of Wisconsin-Madison, Statistics Department TR 262, February 1971.
Approximate regularized solutions to linear operator equations when the data are not in the range of the operator (with M.Z. Nashed), University of Wisconsin-Madison, Mathematics Research Center TSR 1265, August 1972.
A quick and dirty method for solving the non-linear implicit regression problem (with S. Wold), University of Wisconsin-Madison, Statistics Department TR 375, May 1974.
A canonical form for the problem of estimating smooth surfaces, University of Wisconsin-Madison, Statistics Department TR 420, August 1975.
Interpolating surfaces: High order convergence rates and their associated designs, with applications to X-ray image reconstruction. University of Wisconsin-Madison, Statistics Department TR 523, May 1978.
Ill posed problems: Numerical and statistical methods for mildly, moderately, and severely ill posed problems with noisy data. University of Wisconsin-Madison Statistics Department TR 595, February 1980. Prepared for the Proceedings of the International Conference on Ill Posed Problems, M.Z. Nashed, ed.
A New Approach to the Numerical Evaluation of the Inverse Radon Transform with Discrete, Noisy Data. University of Wisconsin- Madison Statistics Department TR612, June, 1980.
Cross validation and constrained regularization methods for mildly-ill posed problems. University of Wisconsin-Madison, Statistics Department TR 629, January 1981.

Some new techniques for variational objective analysis on the sphere using splines, Hough functions, and sample spectral data. Preprints of the Seventh Conference on Probability and Statistics in the Atmospheric Sciences, American Meteorological Society, November 1981.
Partial spline models for the semi-parametric estimation of functions of several variables. In ``Statistical Analysis of Time Series'', publication of the Institute of Statistical Mathematics, Tokyo, September 1984.

Grace Wahba
Tue Feb 16 20:14:25 CST 1999