Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties

Introduction.- Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator.- Asymptotic properties of M, ML and maximum a posteriori estimators.- Local optimality criteria based on asymptotic normality.- Criteria based on the small-sample precision of the LS estimator.- Identifiability, estimability and extended optimality criteria.- Nonlocal optimum design.- Algorithms-a survey.- Subdifferentials and subgradients.- Computation of derivatives through sensitivity functions.- Proofs.- Symbols and notation.- List of labeled assumptions.- References.

[1]  H. Cramér.  Mathematical methods of statistics , 1947 .

[2]  A. Wald.  Note on the Consistency of the Maximum Likelihood Estimate , 1949 .

[3]  T. Koopmans,et al.  The Identification of Structural Characteristics , 1950 .

[4]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[5]  G. Elfving.  Optimum Allocation in Linear Regression Theory , 1952 .

[6]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[7]  Le Cam,et al.  On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates , 1953 .

[8]  A. D. L. Garza,et al.  Spacing of Information in Polynomial Regression , 1954 .

[9]  C. Stein.  Efficient Nonparametric Testing and Estimation , 1956 .

[10]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[11]  D. Lindley.  On a Measure of the Information Provided by an Experiment , 1956 .

[12]  J. E. Kelley,et al.  The Cutting-Plane Method for Solving Convex Programs , 1960 .

[13]  J. Kiefer,et al.  The Equivalence of Two Extremum Problems , 1960, Canadian Journal of Mathematics.

[14]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[15]  J. Kiefer,et al.  Two More Criteria Equivalent to D-Optimality of Designs , 1962 .

[16]  Max Halperin,et al.  Confidence Interval Estimation in Non‐Linear Regression , 1963 .

[17]  E. Nadaraya.  On Estimating Regression , 1964 .

[18]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[19]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[20]  H. O. Hartley,et al.  Exact confidence regions for the parameters in non-linear regression laws , 1964 .

[21]  W. J. Studden,et al.  Optimal Experimental Designs , 1966 .

[22]  Arthur F. Veinott,et al.  The Supporting Hyperplane Method for Unimodal Programming , 1967, Oper. Res..

[23]  Andrej Pázman,et al.  Design of Physical Experiments (Statistical Methods) , 1968, 1968.

[24]  Corwin L. Atwood,et al.  Optimal and Efficient Designs of Experiments , 1969 .

[25]  R. Jennrich.  Asymptotic Properties of Non-Linear Least Squares Estimators , 1969 .

[26]  H. Wynn.  The Sequential Generation of $D$-Optimum Experimental Designs , 1970 .

[27]  V. V. Fedorov,et al.  The Design of Experiments in the Multiresponse Case , 1971 .

[28]  W. J. Studden.  Elfving's Theorem and Optimal Designs for Quadratic Loss , 1971 .

[29]  M. J. Box.  Bias in Nonlinear Estimation , 1971 .

[30]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[31]  H. Wynn.  Results in the Theory and Construction of D‐Optimum Experimental Designs , 1972 .

[32]  G. McCormick,et al.  The Gradient Projection Method under Mild Differentiability Conditions , 1972 .

[33]  E. Schlossmacher.  An Iterative Technique for Absolute Deviations Curve Fitting , 1973 .

[34]  Second-order approximation of the autocorrelation matrix function , 1973 .

[35]  C. Atwood.  Sequences Converging to $D$-Optimal Designs of Experiments , 1973 .

[36]  S. Silvey,et al.  A geometric approach to optimal design theory , 1973 .

[37]  D. Cox,et al.  Planning Experiments for Discriminating between Models , 1974 .

[38]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[39]  R. C. St. John,et al.  D-Optimality for Regression Designs: A Review , 1975 .

[40]  D. Titterington.  Optimal design: Some geometrical aspects of D-optimality , 1975 .

[41]  A. Atkinson,et al.  Optimal design : Experiments for discriminating between several models , 1975 .

[42]  Geoffrey S. Watson,et al.  The inefficiency of least squares , 1975 .

[43]  A. Atkinson,et al.  The design of experiments for discriminating between two rival models , 1975 .

[44]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[45]  Mordecai Avriel,et al.  Nonlinear programming , 1976 .

[46]  Corwin L. Atwood,et al.  Convergent Design Sequences, for Sufficiently Regular Optimality Criteria , 1976 .

[47]  H. Wynn.  OPTIMUM DESIGNS FOR FINITE POPULATIONS SAMPLING , 1977 .

[48]  N. Z. Shor.  Cut-off method with space extension in convex programming problems , 1977, Cybernetics.

[49]  Z. Galil,et al.  Comparison of Simplex Designs for Quadratic Mixture Models , 1977 .

[50]  Martin B. Zarrop,et al.  Optimal experiment design for dynamic system identification , 1977 .

[51]  Changbao Wu,et al.  Some iterative procedures for generating nonsingular optimal designs , 1978 .

[52]  H. Robbins,et al.  Strong consistency of least squares estimates in multiple regression , 1978 .

[53]  Changbao Wu,et al.  Some Algorithmic Aspects of the Theory of Optimal Designs , 1978 .

[54]  D. Titterington.  Estimation of Correlation Coefficients by Ellipsoidal Trimming , 1978 .

[55]  H. Robbins,et al.  Strong consistency of least squares estimates in multiple regression. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[56]  S. Silvey,et al.  An algorithm for optimal designs on a design space , 1978 .

[57]  N. Sundaraij.  A METHOD FOR CONFIDENCE REGIONS FOR NONLINEAR MODELS , 1978 .

[58]  H. Wynn,et al.  The Convergence of General Step-Length Algorithms for Regular Optimum Design Criteria , 1978 .

[59]  Peter D. H. Hill,et al.  A Review of Experimental Design Procedures for Regression Model Discrimination , 1978 .

[60]  E. Parzen.  Nonparametric Statistical Data Modeling , 1979 .

[61]  L. G. H. Cijan.  A polynomial algorithm in linear programming , 1979 .

[62]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

[63]  E. Aiyoshi,et al.  Necessary conditions for min-max problems and algorithms by a relaxation procedure , 1980 .

[64]  J. Kiefer,et al.  Time- and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs , 1980 .

[65]  S. Silvey,et al.  A sequentially constructed design for estimating a nonlinear parametric function , 1980 .

[66]  M. Todd,et al.  The Ellipsoid Method: A Survey , 1980 .

[67]  Wayne A. Fuller,et al.  Least Squares Estimation When the Covariance Matrix and Parameter Vector are Functionally Related , 1980 .

[68]  Andrej Pázman,et al.  Singular experimental designs (standard and HILBEKT-space approaches) , 1980 .

[69]  G. Pflug.  Stochastic Approximation Methods for Constrained and Unconstrained Systems - Kushner, HJ.; Clark, D.S. , 1980 .

[70]  D. G. Watts,et al.  Relative Curvature Measures of Nonlinearity , 1980 .

[71]  V. Fedorov,et al.  Convex design theory 1 , 1980 .

[72]  Characterizing the Consistent Directions of Least Squares Estimates , 1980 .

[73]  Corwin L. Atwood.  Convergent Design Sequences, for Sufficiently Regular Optimality Criteria, II: Singular Case , 1980 .

[74]  Changbao Wu,et al.  Asymptotic Theory of Nonlinear Least Squares Estimation , 1981 .

[75]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[76]  Petre Stoica,et al.  Comparison of some instrumental variable methods - Consistency and accuracy aspects , 1981, Autom..

[77]  T. Lai,et al.  Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems , 1982 .

[78]  P. Bickel.  On Adaptive Estimation , 1982 .

[79]  H. P. Wynn,et al.  OPTIMUM SUBMEASURES WITH APPLICATION TO FINITE POPULATION SAMPLING , 1982 .

[80]  Michael J. Todd.  On Minimum Volume Ellipsoids Containing Part of a Given Ellipsoid , 1982, Math. Oper. Res..

[81]  Eric Walter,et al.  Identifiability of State Space Models , 1982 .

[82]  W. Welch.  Branch-and-Bound Search for Experimental Designs Based on D Optimality and Other Criteria , 1982 .

[83]  D. G. Watts,et al.  Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions , 1982 .

[84]  Jaroslava Mikulecká.  On a hybrid experimental design , 1983, Kybernetika.

[85]  B. Torsney.  A Moment Inequality and Monotonicity of an Algorithm , 1983 .

[86]  T. Söderström,et al.  Instrumental variable methods for system identification , 1983 .

[87]  Further Results on the Consistent Directions of Least Squares Estimators , 1983 .

[88]  M. E. Johnson,et al.  Some Guidelines for Constructing Exact D-Optimal Designs on Convex Design Spaces , 1983 .

[89]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[90]  Sandor Vajda,et al.  An extended ode solver for sensitivity calculations , 1984, Comput. Chem..

[91]  P. Green.  Iteratively reweighted least squares for maximum likelihood estimation , 1984 .

[92]  Andrej Pázman.  Probability distribution of the multivariate nonlinear least squares estimates , 1984, Kybernetika.

[93]  H. Müller.  Optimal designs for nonparametric kernel regression , 1984 .

[94]  A. Pázman.  Nonlinear least squares - uniqueness versus ambiguity , 1984 .

[95]  Changbao Wu,et al.  Asymptotic inference from sequential design in a nonlinear situation , 1985 .

[96]  D. G. Watts,et al.  A Quadratic Design Criterion for Precise Estimation in Nonlinear Regression Models , 1985 .

[97]  Shie-Shien Yang.  A Smooth Nonparametric Estimator of a Quantile Function , 1985 .

[98]  Philip Hougaard.  Saddlepoint approximations for curved exponential families , 1985 .

[99]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[100]  D. Titterington,et al.  Inference and sequential design , 1985 .

[101]  Andrej Pázman,et al.  Foundations of Optimum Experimental Design , 1986 .

[102]  B. Torsney.  Moment inequalities via optimal design theory , 1986 .

[103]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[104]  B. Jørgensen.  Exponential Dispersion Models , 1987 .

[105]  D. Andrews.  CONSISTENCY IN NONLINEAR ECONOMETRIC MODELS: A GENERIC UNIFORM LAW OF LARGE NUMBERS , 1987 .

[106]  Eric Walter,et al.  Identifiability of parametric models , 1987 .

[107]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[108]  A. Gallant,et al.  Nonlinear Statistical Models , 1988 .

[109]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[110]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[111]  S. Schwartz,et al.  An accelerated sequential algorithm for producing D -optimal designs , 1989 .

[112]  Johan Fellman,et al.  An empirical study of a class of iterative searches for optimal designs , 1989 .

[113]  Donald W. Hearn,et al.  Lagrangian dual ascent by generalized linear programming , 1989 .

[114]  Guido del Pino,et al.  The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms , 1989 .

[115]  Werner G. Müller,et al.  batch sequential design for a nonlinear estimation problem , 1989 .

[116]  Valerii V. Fedorov,et al.  Optimal design with bounded density: optimization algorithms of the exchange type , 1989 .

[117]  D. Pollard,et al.  Cube Root Asymptotics , 1990 .

[118]  Alfred O. Hero,et al.  Lower bounds for parametric estimation with constraints , 1990, IEEE Trans. Inf. Theory.

[119]  J. P. Vila,et al.  Exact Experimental Designs Via Stochastic Optimization for Nonlinear Regression Models , 1990 .

[120]  R. Kass.  Nonlinear Regression Analysis and its Applications , 1990 .

[121]  W. Newey,et al.  Uniform Convergence in Probability and Stochastic Equicontinuity , 1991 .

[122]  Emo Welzl,et al.  Smallest enclosing disks (balls and ellipsoids) , 1991, New Results and New Trends in Computer Science.

[123]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[124]  Guy Chavent.  New size×curvature conditions for strict quasiconvexity of sets , 1991 .

[125]  D. Andrews.  Generic Uniform Convergence , 1992, Econometric Theory.

[126]  V. Spokoinyi,et al.  On asymptotically optimal sequential experimental design , 1992 .

[127]  GEOMETRY OF THE NONLINEAR REGRESSION WITH PRIOR , 1992 .

[128]  N. Shor,et al.  New algorithms for constructing optimal circumscribed and inscribed ellipsoids , 1992 .

[129]  Andrej Pázman.  A classification of nonlinear regression models and parameter confidence regions , 1992, Kybernetika.

[130]  Andrej Pázman,et al.  Nonlinear experimental design based on the distribution of estimators , 1992 .

[131]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[132]  Leonid Khachiyan,et al.  On the complexity of approximating the maximal inscribed ellipsoid for a polytope , 1993, Math. Program..

[133]  H. Kushner,et al.  Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for , 1993 .

[134]  K. Chaloner,et al.  Optimum experimental designs for properties of a compartmental model. , 1993, Biometrics.

[135]  Xavier Joulia,et al.  A general strategy for parameter estimation in differential—algebraic systems , 1993 .

[136]  Higher Dimensional Nonlinear Regression-A Statistical Use of the Riemannian Curvature Tensor , 1993 .

[137]  D. Firth.  Bias reduction of maximum likelihood estimates , 1993 .

[138]  Tze Leung Lai,et al.  Asymptotic Properties of Nonlinear Least Squares Estimates in Stochastic Regression Models , 1994 .

[139]  Herman J. Bierens,et al.  Topics in advanced econometrics , 1997 .

[140]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[141]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[142]  Yurii Nesterov,et al.  Complexity estimates of some cutting plane methods based on the analytic barrier , 1995, Math. Program..

[143]  Scott L. Zeger,et al.  [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Rejoinder , 1995 .

[144]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[145]  Rainer Schwabe,et al.  Designing Experiments for Additive Nonlinear Models , 1995 .

[146]  L. Pronzato,et al.  Identifiabilities and nonlinearities , 1995 .

[147]  Yurii Nesterov,et al.  New variants of bundle methods , 1995, Math. Program..

[148]  A. Ivanov.  Asymptotic Theory of Nonlinear Regression , 1996 .

[149]  Rainer Schwabe,et al.  Optimum Designs for Multi-Factor Models , 1996 .

[150]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[151]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[152]  J. Simonoff.  Multivariate Density Estimation , 1996 .

[153]  P. Spreij.  Probability and Measure , 1996 .

[154]  Andrej Pázman,et al.  A Dirac-function method for densities of nonlinear statistics and for marginal densities in nonlinear regression , 1996 .

[155]  Leonid Khachiyan,et al.  Rounding of Polytopes in the Real Number Model of Computation , 1996, Math. Oper. Res..

[156]  H. Neudecker,et al.  Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models , 1997 .

[157]  B. Lindsay,et al.  On second-order optimality of the observed Fisher information , 1997 .

[158]  Shu-Cherng Fang,et al.  On the entropic regularization method for solving min-max problems with applications , 1997, Math. Methods Oper. Res..

[159]  Harold J. Kushner,et al.  Stochastic Approximation Algorithms and Applications , 1997, Applications of Mathematics.

[160]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[161]  C. Heyde,et al.  Quasi-likelihood and its application , 1997 .

[162]  A. Atkinson,et al.  Designing for a Response Transformation Parameter , 1997 .

[163]  R. Schwabe.  Maximin efficient designs another view at D-optimality , 1997 .

[164]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[165]  B. Torsney,et al.  MV-Optimization in Weighted Linear Regression , 1998 .

[166]  Luc Pronzato,et al.  Sequential Design and Active Control , 1998 .

[167]  Approximate Densities of Two Bias-Corrected Nonlinear LS Estimators , 1998 .

[168]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[169]  Yinyu Ye,et al.  Interior point algorithms: theory and analysis , 1997 .

[170]  Andrej Pázman,et al.  Applications of necessary and sufficient conditions for maximin efficient designs , 1998 .

[171]  Stephen P. Boyd,et al.  Determinant Maximization with Linear Matrix Inequality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[172]  Margaret H. Wright,et al.  The interior-point revolution in constrained optimization , 1998 .

[173]  B. C. Ng,et al.  On the Cramer-Rao bound under parametric constraints , 1998, IEEE Signal Processing Letters.

[174]  Inchi Hu,et al.  On sequential designs in nonlinear problems , 1998 .

[175]  A. V. D. Vaart.  Asymptotic Statistics: Delta Method , 1998 .

[176]  Jean-Louis Goffin,et al.  Convergence of a simple subgradient level method , 1999, Math. Program..

[177]  Steven E. Rigdon,et al.  Model-Oriented Design of Experiments , 1997, Technometrics.

[178]  Efficiency Bounds for Product Designs in Linear Models , 1999 .

[179]  Luc Pronzato,et al.  Adaptive control for sequential design , 2000 .

[180]  John E. Mitchell,et al.  An ellipsoid algorithm for equality-constrained nonlinear programs , 2001, Comput. Oper. Res..

[181]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[182]  S. Geer.  Empirical Processes in M-Estimation , 2000 .

[183]  Toby J. Mitchell,et al.  An Algorithm for the Construction of “D-Optimal” Experimental Designs , 2000, Technometrics.

[184]  José Mario Martínez,et al.  Nonmonotone Spectral Projected Gradient Methods on Convex Sets , 1999, SIAM J. Optim..

[185]  Eugene Demidenko,et al.  Is this the least squares estimate , 2000 .

[186]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[187]  Ilya Molchanov,et al.  Variational Calculus in the Space of Measures and Optimal Design , 2001 .

[188]  Thomas L. Marzetta,et al.  Parameter estimation problems with singular information matrices , 2001, IEEE Trans. Signal Process..

[189]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[190]  Andrej Pázman,et al.  Optimal design of experiments subject to correlated errors , 2001 .

[191]  A. Pázman.  CONCENTRATION SETS, ELFVING SETS AND NORMS IN OPTIMUM DESIGN , 2001 .

[192]  Felipe Cucker,et al.  On the mathematical foundations of learning , 2001 .

[193]  Rainer Schwabe,et al.  A Note on Optimal Bounded Designs , 2001 .

[194]  Andrej Pázman,et al.  Using densities of estimators to compare pharmacokinetic experiments , 2001, Comput. Biol. Medicine.

[195]  Holger Dette,et al.  Minimax Optimal Designs for Nonparametric Regression — A Further Optimality Property of the Uniform Distribution , 2001 .

[196]  A. Vaart.  The statistical work of Lucien Le Cam , 2002 .

[197]  Ilya S. Molchanov,et al.  Steepest descent algorithms in a space of measures , 2002, Stat. Comput..

[198]  A. Pázman.  Results on nonlinear least squares estimators under nonlinear equality constraints , 2002 .

[199]  Sarah E. Gergel,et al.  Collecting Spatial Data at Broad Scales , 2002 .

[200]  Robert F. Phillips,et al.  Least absolute deviations estimation via the EM algorithm , 2002, Stat. Comput..

[201]  A. Pázman.  Optimal design of nonlinear experiments with parameter constraints , 2002 .

[202]  Yin Zhang,et al.  On Numerical Solution of the Maximum Volume Ellipsoid Problem , 2003, SIAM J. Optim..

[203]  A. Tsybakov,et al.  Introduction à l'estimation non-paramétrique , 2003 .

[204]  Andrej Pázman,et al.  Measures for designs in experiments with correlated errors , 2003 .

[205]  Peter L. Bartlett,et al.  Prediction Algorithms: Complexity, Concentration and Convexity , 2003 .

[206]  R. Schaback.  Mathematical Results Concerning Kernel Techniques , 2003 .

[207]  E. Walter,et al.  Interval Analysis for Guaranteed Nonlinear Parameter Estimation , 2003 .

[208]  E. Walter,et al.  Multi-Output Suppport Vector Regression , 2003 .

[209]  Henry P. Wynn,et al.  Maximum Entropy Sampling and General Equivalence Theory , 2004 .

[210]  Andrej Pázman,et al.  Simultaneous Choice of Design and Estimator in Nonlinear Regression with Parameterized Variance , 2004 .

[211]  A. C. Atkinson,et al.  Some Bayesian Optimum Designs for Response Transformation in Nonlinear Models with Nonconstant Variance , 2004 .

[213]  A. Berlinet,et al.  Reproducing kernel Hilbert spaces in probability and statistics , 2004 .

[214]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[215]  Peng Sun,et al.  Computation of Minimum Volume Covering Ellipsoids , 2002, Oper. Res..

[216]  Radoslav Harman.  Minimal efficiency of designs under the class of orthogonally invariant information criteria , 2004 .

[217]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[218]  B. Anderson,et al.  ROBUST IDENTIFICATION OF , 2005 .

[219]  Emmanuel Vazquez,et al.  Modélisation comportementale de systèmes non-linéaires multivariables par méthodes à noyaux et applications , 2005 .

[220]  Andrej Pázman,et al.  On the irregular behavior of LS estimators for asymptotically singular designs , 2006 .

[221]  Andrej Pázman,et al.  Designs in nonlinear regression by stochastic minimization of functionals of the mean square error matrix , 2006 .

[222]  Asymptotic criteria for designs in nonlinear regression with model errors , 2006 .

[223]  Zhengyuan Zhu,et al.  Spatial sampling design under the infill asymptotic framework , 2006 .

[224]  Shaohua Pan,et al.  Smoothing method for minimizing the sum of the r largest functions , 2007, Optim. Methods Softw..

[225]  J. Vila,et al.  Optimal designs based on exact confidence regions for parameter estimation of a nonlinear regression model , 2007 .

[226]  Luc Pronzato,et al.  Improvements on removing nonoptimal support points in D-optimum design algorithms , 2007, 0706.4394.

[227]  Edgar den Boef,et al.  Efficient Line Search Methods for Convex Functions , 2007, SIAM J. Optim..

[228]  Maciej Patan,et al.  D-optimal design of a monitoring network for parameter estimation of distributed systems , 2007, J. Glob. Optim..

[229]  Holger Dette,et al.  On the number of support points of maximin and Bayesian optimal designs , 2007, 0708.1901.

[230]  Michael J. Todd,et al.  On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids , 2007, Discret. Appl. Math..

[231]  Michel Minoux,et al.  Programmation Mathématique. Théorie et Algorithmes , 2008 .

[232]  Peng Sun,et al.  Linear convergence of a modified Frank–Wolfe algorithm for computing minimum-volume enclosing ellipsoids , 2008, Optim. Methods Softw..

[233]  Radoslav Harman,et al.  Computing c-optimal experimental designs using the simplex method of linear programming , 2008, Comput. Stat. Data Anal..

[234]  Radoslav Harman,et al.  Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices , 2009 .

[235]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[236]  Drew Seils,et al.  Optimal design , 2007 .

[237]  Andrej Pázman,et al.  Asymptotic Normality of Nonlinear Least Squares under Singular Experimental Designs , 2009 .

[238]  John Stufken,et al.  SUPPORT POINTS OF LOCALLY OPTIMAL DESIGNS FOR NONLINEAR MODELS WITH TWO PARAMETERS , 2009, 0903.0728.

[239]  Ben Torsney,et al.  W-Iterations and Ripples Therefrom , 2009 .

[240]  Min Yang,et al.  On the de la Garza phenomenon , 2009, 0912.3861.

[241]  Yaming Yu.  Monotonic convergence of a general algorithm for computing optimal designs , 2009, 0905.2646.

[242]  Andrej Pázman,et al.  A Note on the Relationship between Two Approaches to Optimal Design under Correlation , 2010 .

[243]  Yaming Yu,et al.  Strict monotonicity and convergence rate of Titterington's algorithm for computing D-optimal designs , 2010, Comput. Stat. Data Anal..

[244]  Anthony C. Atkinson.  Optimum Experimental Design , 2011, International Encyclopedia of Statistical Science.

[245]  Yaming Yu,et al.  D-optimal designs via a cocktail algorithm , 2009, Stat. Comput..

[246]  Holger Dette,et al.  A note on the de la Garza phenomenon for locally optimal designs , 2011, 1105.3575.

[247]  Luc Pronzato,et al.  Design of computer experiments: space filling and beyond , 2011, Statistics and Computing.

[248]  Jane Ruth Temple.  Adaptive designs for dose-finding trials , 2012 .

[249]  Steven G. Gilmour,et al.  Optimum design of experiments for statistical inference , 2012 .

[250]  O. Barndorff-Nielsen.  Information and Exponential Families in Statistical Theory , 1980 .

[251]  Roland Gautier,et al.  Some results on optimal allocation in two { stepsequential designBy , 2022 .