Grace Wahba Publications
Grace Wahba Publications

WARNING: Publications through mid1993 ONLY.
click
here for complete list of TR's and MSS since mid 1993
with links to mss since 1993 and some oldies.
 (i)
 In print
 A least squares estimate of satellite attitude, Problems and Solutions
section, SIAM Review, 8, 3, 384 (1966).[Source of the
famous "Wahba's Problem"!]
 On the distribution of some statistics useful in the analysis of jointly
stationary time series, Ann. Math. Statist., 39, 6, 18491862 (1968).
 A family of summation formulae, Problems and Solutions section,
SIAM Review, 11, 3, 409 (1969).
 Estimation of the coefficients in a multidimensional distributed lag
model, Econometrica, 37, 3, 398407 (1969).
 A correspondence between Bayesian estimation of stochastic processes and
smoothing by splines (with George S. Kimeldorf), Ann. Math. Statist.,
41, 2, 495502 (1970).
 Spline functions and stochastic processes (with George S. Kimeldorf),
Sankya, Ser. A, 32, part 2, 173180 (1970).
 Some results on Tchebycheffian spline functions (with George S.
Kimeldorf), J. Math. Anal. Applic., 33, 1, 8295 (1971).
 Some tests of independence for stationary multivariate time series,
J. Roy. Stat. Soc. Series B, 33, 1, 153166 (1971).
 On the regression design problems of Sacks and Ylvisaker, Ann. Math.
Statist., 42, 3, 10351053 (1971).
 A polynomial algorithm for density estimation, Ann. Math. Statist.,
42, 6, 18701886 (1971).
 Convergence rates of certain approximate solutions to first kind integral
equations, J. Approx. Thy., 7, 2, 167185 (1973).
 On the minimization of a quadratic functional subject to a continuous
family of linear inequality constraints, SIAM J. Control, 11, 1, 6479
(1973).
 A class of approximate solutions to linear operator equations, J.
Approx. Thy., 9, 1, 6177 (1973).
 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, 6980 (1974).
 Regression design for some equivalence classes of kernels, Ann.
Statist., 2, 5, 925934 (1974).
 Generalized inverses in reproducing kernel spaces: An approach to
regularization of linear operator equations (with M.Z. Nashed), SIAM J.
Math. Anal., 5, 6, 974987 (1974).
 Regularization and approximation of linear operator equations in
reproducing kernel spaces (with M.Z. Nashed), Bull. Am. Math. Soc., 80,
6, 12131218 (1974).
 Optimal convergence properties of variable knot, kernel, and orthogonal
series methods for density estimation, Ann. Statist., 3, 1, 1529
(1975).
 Interpolating spline methods for density estimation. I. Fixed knots,
Ann. Statist., 3, 1, 3048 (1975).
 A completely automatic French curve: Fitting spline functions by
crossvalidation (with S. Wold), Commun. Statist., 4, 1,
117 (1975).
 Periodic splines for spectral density estimation: The use of
crossvalidation for determining the degree of smoothing (with S. Wold),
Commun. Statist., 4, 2, 125141 (1975).
 Some exponentially decreasing error bounds for a numerical inversion of
the Laplace transform (with M.Z. Nashed), J. Math. Anal. Applic., 52,
3, 660668 (1975).
 Smoothing noisy data by spline functions, Numer. Math., 24, 383393
(1975).
 On the optimal choice of nodes in the collocationprojection method for
solving linear operator equations, J. Approx. Thy., 16, 2, 175186
(1976).
 Histosplines with knots which are order statistics. J. Roy. Stat.
Soc. Series B, 38, 2, 140151 (1976)
 An averaging method for the stiff highly oscillatory problem (with W.L.
Miranker), Math. Comp., 30, 135, 383399 (1976).
 Practical approximate solutions to linear operator equations when the
data are noisy, SIAM J. Num. Anal., 14, 4, 651667 (1977).
 Optimal smoothing of density estimates, in ``Classification and
Clustering'', J. Van Ryzin, ed., 423458, Academic Press (1977).
 A survey of some smoothing problems and the method of generalized
crossvalidation for solving them, in ``Applications of Statistics'', P.R.
Krishnaiah, ed., 507523, North Holland (1977).
 Improper priors, spline smoothing and the problem of guarding against
model errors in regression. J. Roy. Stat. Soc., Ser. B., 40, 3, 364372
(1978).
 Smoothing noisy data with spline functions: estimating the correct
degree of smoothing by the method of generalized crossvalidation (with Peter
Craven). Numer. Math., 31, 377403 (1979).
 Determination of an optimal mesh for a collocationprojection method
for solving twopoint boundary value problems (with Manohar Athavale), J.
Approx. Thy., 28, 1, 3848 (1979).
 Generalized crossvalidation as a method for choosing a good ridge
parameter (with G. Golub and M. Heath). Technometrics, 21, 215223
(1979).
 How to smooth curves and surfaces with splines and crossvalidation, in
``Proceedings of the 24th Conference on the Design of Experiments'', U.S. Army
Research Office, Report 792, 167192 (1979).
 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, 232246 SpringerVerlag
(1979).
 Smoothing and ill posed problems, in ``Solution Methods for Integral
Equations with Applications'', Michael Golberg, ed., 183194, Plenum Press
(1979).
 Automatic smoothing of the log periodogram. J. Am. Stat. Soc., 75,
369, 122132 (1980).
 Parameter estimation in linear dynamic systems. IEEE Transactions
on Automatic Control, AC25, 2, 235238 (1980).
 Some new mathematical methods for variational objective analysis using
splines and crossvalidation (with J. Wendelberger), Monthly Weather
Review 108, 3657 (1980).
 Spline bases, regularization, and generalized cross validation for
solving approximation problems with large quantities of noisy data, in
``Approximation Theory III'', W. Cheney, ed., 905912, Academic Press (1980).
 Databased optimal smoothing of orthogonal series density estimates.
Ann. Statist., 9, 1, 146156 (1981).
 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,
189203, SpringerVerlag (1981).
 Design problems for optimal surface interpolation (with C. Micchelli),
in ``Approximation Theory and Applications'' Z. Ziegler, ed., 329348, Academic
Press (1981).
 Spline interpolation and smoothing on the sphere. SIAM J. Sci. Statist.
Comp., 2, 1, 516 (1981).
Erratum 3, 3, 385386 (1982).
 On the estimation of functions of several variables from aggregated data
(with N. Dyn), SIAM J. Math. Anal., 13, 1, 134152 (1982).
 Numerical experiments with the thin plate histospline. Commun.
Statist. Theor. Meth., A10 (24), 24752514 (1981).
 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., 383418,
Academic Press (1982).
 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., 283296, Academic Press (1982).
 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., 407429,
Birkhauser Verlag (1982).
 Variational methods in simultaneous optimum interpolation and
initialization. In ``The Interaction Between Objective Analysis and
Initialization'', D. Williamson, ed., 178185, Publication in Meteorology 127
Atmospheric Analysis and Prediction Division, National Center for Atmospheric
Research, Boulder, CO (1982).
 Bayesian confidence intervals for the cross validated smoothing spline.
J. Roy. Stat. Soc. B., 45, 1, 133150 (1983).
 Multivariate thin plate spline estimates for the posterior probabilities
in the classification problem (with M. Villalobos). Commun. Statist.
Theor. Meth., 12, 13, 14491480 (1983).
 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, 12611268 (1983).
 Surface fitting with scattered, noisy data on Euclidean dspace and on
the sphere. Rocky Mountain J. Math., 14, 1,
281299 (1984).
 Cross validated spline methods for direct and indirect sensing
experiments. In ``Statistical Signal Processing'', E.J. Wegman and J. Smith,
eds., Marcel Dekker (1984).
 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,
205235 (1984).
 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, 178183 (1984).
 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, 832846 (1984).
 A cross validated Bayesian retrieval algorithm for nonlinear remote
sensing experiments (with F. O'Sullivan). J. Comput. Physics, 59,
441455 (1985).
 Design Criteria and eigensequence plots for satellite computed
tomography. J. Atmos. Ocean Tech., 2, 125132 (1985).
 A comparison of GCV and GML for choosing the smoothing parameter in the
generalized spline smoothing problem. Ann. Statist. 13, 13781402 (1985).
 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. 385408 (1985).
 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).
 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).
 Partial spline modeling of the tropopause and other discontinuities in
Function Estimates, Contemporary Mathematics Volume 59, American
Mathematical Society, Providence, R.I., pp. 125135 (1986).
 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, 125130 (1986).
 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, 714725 (1986).
 Inequalityconstrained multivariate smoothing splines with application
to the estimation of posterior probabilities (with Miguel Villalobos). J.
Amer. Statist. Assoc. 82, 239248 (1987).
 GCVPACKroutines for generalized cross validation (with D. Bates, M.
Lindstrom and B. Yandell). Commun. Statist., Simulation and
Computation, 16, 263297 (1987).
 Three topics in ill posed inverse problems. In
"Inverse and IllPosed Problems", M. Engl and G. Groetsch, eds.,
Academic Press, 3751 (1987).
 Testing the (parametric) null model hypothesis in (semiparametric)
partial and generalized spline models (with D. Cox, E. Koh and B. Yandell),
Ann. Statist. 16, 113119 (1988).
 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 479491 (1988).
 Rates of convergence of some estimators for a semiparametric model (with J.J.
Shiau) Commun. Statist. Comp. 17, 11171133 (1988).
 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., 435441 (1989).
 Spline Functions. Entry in the Encyclopedia of Statistical Sciences, Suppl. Vol., S. Kotz and N.L. Johnson, eds., 148160 (1989).
 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, 347358 (1989).
 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, 457480 (1989)
 ``Spline Models for Observational Data''
Vol. 59 in the CBMSNSF
Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA (1990).
xii + 169 pp.
 Comment on Cressie, Letters to the Editor, American
Statistician, 44, 255256 (1990).
 Regularization and cross validation methods for nonlinear implicit,
illposed inverse problems.
In "Geophysical Data Inversion Methods and Applications",
A. Vogel, C. Ofoegbu, R. Gorenflo and B. Ursin, eds., Vieweg,
WiesbadenBraunschweig, 313 (1990).
 When is the optimal regularization parameter
insensitive to the choice
of the loss function? (with Yonghua Wang).
Commun. Statist., A19, 5 16851700, (1990).
 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, ClermontFerrand, 1990, F. X. LeDimet and O. Talagrand,
eds., WMO, 448453 (1991).
 Minimizing GCV/GML scores with multiple smoothing parameters via the
Newton methods (with C. Gu). SIAM J. Sci. Stat. Comput. 12,
383398 (1991).
 Book Review of "IllPosed Problems in the
Natural Sciences" by A. N. Tikhonov and A. V. Goncharsky, eds., in
American Scientist 79, 282283, MayJune, 1991.
 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, 491504 (1991).
 Eigenvalues of sine and cosine matrices, Solution to
Advanced Problem No. 6591, with D. Callan. Amer. Math. Monthly,
98, 6465 (1991).
 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, AddisonWesley, 95112 (1992).
 A note on generalized cross validation with
replicates (with Chong Gu and Nancy Heckman).
Stat. Prob. Letters. 14, 283287 (1992).
 Smoothing spline ANOVA with componentwise Bayesian "confidence
intervals" (with Chong Gu).
J. Comput. Graph. Statist., 2, 97117 (1993)
 Getting better contour plots with S and GCVPACK
(with Douglas Bates and Fred Reames).
Comp. Stat. Data Anal., 15, 329342 (1993).
 Semiparametric ANOVA with tensor product thin
plate splines (with Chong Gu).
J. Roy. Stat. Soc. B, 55, 353368 (1993).
 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 415422, (1994).

Bootstrap confidence
intervals for smoothing splines and their comparison
to Bayesian confidence intervals, Y. Wang and G.
Wahba, J. Stat.
Comp. Sim.,
51, 263279 (1995).

Behavior near zero
of the distribution of GCV smoothing parameter
estimates, G. Wahba and Y. Wang,
Stat. Prob. Letters, 25, 105111 (1995).

Simulation studies of
smoothing parameter estimates and Bayesian confidence intervals in
Bernoulli SSANOVA models,
Y. Wang, G. Wahba, R. Chappell and C. Gu,
Commun. Stat. Comp. Sim.,
24, 10371059 (1995).

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, 33583369 (1995).
 `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.
AddisonWesley 329360 (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 133162 (1995).
 Generalization and regularization in nonlinear
learning systems, in M. Arbib, ed., `Handbook of Brain Theory and
Neural Networks', MIT Press, pp. 426430 (1995).

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, 18651895 (1995).
 A generalized
approximate cross validation for smoothing
splines with nonGaussian data,
D. Xiang and G. Wahba, Statistica Sinica,
6, 675692 (1996).

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, 579596 (1997).
 Hybrid adaptive splines, Z. Luo and G. Wahba,
J. Amer. Statist. Assoc. 92, 107114 (1997)
 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, 13571376 (1997)
 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, 210231 (1998)
 Spatialtemporal analysis of temperature using
smoothing spline ANOVA, Z. Luo and G. Wahba,
J. Climate 11 1828 (1998)
 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 9498 (1998)
 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,
6988 (1999)

WARNING: Updated only sporadically since 1993,
click
here for complete list of TR's and MSS since mid 1993.
 (ii)
 To appear
 108.

The biasvariance 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.
 109.

Adaptive tuning, four dimensional variational data
assimilation and representers in RKHS, Technical Report 1000,
Department of Statistics, University of WisconsinMadison,
to appear
Proceedings ECMWF Workkshop on the Diagnosis of Data Assimilation
Systems, F. Bouttier, Ed. ECMWF, Reading UK.
 (iii)
 Submitted
 110.

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).
 111.
 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).
 (iv)
 Invited discussion to
 Consistent nonparametric regression, C.J. Stone, Ann.
Stat., 5,
4, 636645 (1977).
 Curve fitting and optimal design for prediction, A. O'Hagan,
J. Roy.
Stat. Soc. B, 40, 3536 (1978).
 Density estimation, stochastic processes and prior information,
Tom Leonard, J. Roy. Stat. Soc. B, 40, 2, 140 (1978).
 Smooth pychnophylactic interpolation, W. Tobler (with N. Dyn
and W.H. Wong), J. Amer. Statist. Soc., 74, 367, 530535
(1979).
 Projection pursuit, Peter J. Huber, Ann. Statist.,
13, 2, 518521 (1985).
 Some aspects of the spline smoothing approach to nonparametric
regression curve
fitting, Bernard Silverman, J. Roy. Stat. Soc. B, 46
(1985).
 A statistical perspective on ill posed inverse problems,
Finbarr O'Sullivan,
Statistical Science, 1, 521522 (1987).
 Monotone regression splines in action, by J. O. Ramsey. (with
C. Gu),
Statistical Science, 3, 456458 (1988).
 Linear smoothers and additive models, by Buja, Hastie and
Tibshirani,
(with
Z. Chen and C. Gu), Ann. Statist., 17, 515522 (1989).
 Multivariate Adaptive Regression Splines, by J. Friedman,
(with C. Gu), Ann. Statist., 19, 115122 (1991).
 Maximum entropy and the nearly black object, by Donoho,
Johnstone
and Hoch, J. Roy. Stat. Soc. B, 54,
76 (1992).
 Empirical functionals and efficient smoothing parameter
selection, by Hall and Johnstone,
J. Roy. Stat. Soc. B,
54, 525526 (1992).
 Varyingcoefficient models,
by Hastie and Tibshirani, J. Roy. Stat. Soc. B,
55, 757796 (1993).
 Neural networks and related methods
for classification, by B. D. Ripley, J. Roy. Stat. Soc. B,
56, 409456 (1994).
 Wavelet shrinkage: asymptopia?, by
Donoho, Johnstone, Kerkyacharian and Picard,
J. Roy. Stat. Soc. B 57, 301370 (1995).
 The fast MonteCarlo crossvalidation and C_L procedures:
Comments, new results and application to image recovery problems,
by D. Girard. Comp. Stat., 10, 249250 (1995).
 Model indexing and smoothing parameter selection in
nonparametric function estimation, by Chong Gu. Statistica
Sinica, 8, 632638 (1998).
 Smoothing spline models for the
analysis of nested and crossed samples of curves, by
Babette Brumback and John Rice. (with Y. Wang). JASA, 93,
976980 (1998).
 (vi)
 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 WisconsinMadison, Statistics Department TR
217, October 1969, also Mathematics Research Center TSR 990.

 A note on interpolation over all the integers. University
of WisconsinMadison, Statistics Department TR 231. April 1970.

 Some RadonNikodym derivatives for processes equivalent to Integrated
weighted Wiener processes. University of WisconsinMadison, 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 WisconsinMadison, Mathematics Research Center TSR 1265, August 1972.

 A quick and dirty method for solving the nonlinear implicit
regression problem (with S. Wold), University of WisconsinMadison, Statistics
Department TR 375, May 1974.

 A canonical form for the problem of estimating smooth surfaces,
University of WisconsinMadison, Statistics Department TR 420,
August 1975.

 Interpolating surfaces: High order convergence rates and their
associated designs, with applications to Xray image reconstruction. University
of WisconsinMadison, 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
WisconsinMadison 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
mildlyill posed problems. University of WisconsinMadison, Statistics
Department TR 629, January 1981.
 (vii)
 Other

 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 semiparametric 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