Holdings: Maximum penalized likelihood estimation

Maximum penalized likelihood estimation: 1 Density estimation

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Bibliographic Details
Main Authors:	Eggermont, Paulus P. B. (Author), La Riccia, Vincent N. (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 2001
Series:	Springer series in statistics
Online Access:	Inhaltsverzeichnis
Physical Description:	XVII, 510 S. graph. Darst.
ISBN:	0387952683

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MARC


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adam_text	P.P.B. EGGERMONT V.N. LARICCIA MAXIMUM PENALIZED LIKELIHOOD ESTIMATION VOLUME I: DENSITY ESTIMATION WITH 30 FIGURES SPRINGER CONTENTS PREFACE VII NOTATIONS, ACRONYMS, AND CONVENTIONS XV 1. PARAMETRIC AND NONPARAMETRIC ESTIMATION 1 1. INTRODUCTION 1 2. INDIRECT PROBLEMS, EM ALGORITHMS, KERNEL DENSITY ESTIMATION, AND ROUGHNESS PENALIZATION 8 3. CONSISTENCY OF NONPARAMETRIC ESTIMATORS 13 4. THE USUAL NONPARAMETRIC ASSUMPTIONS 18 5. PARAMETRIC VS NONPARAMETRIC RATES 20 6. SIEVES AND CONVEXITY 22 7. ADDITIONAL NOTES AND COMMENTS 26 PART I: PARAMETRIC ESTIMATION 2. PARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION 29 1. INTRODUCTION 29 2. OPTIMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS 37 3. COMPUTING MAXIMUM LIKELIHOOD ESTIMATORS 49 4. THE EM ALGORITHM 53 5. SENSITIVITY TO ERRORS: M-ESTIMATORS 63 6. RIDGE REGRESSION 75 7. RIGHT-SKEWED DISTRIBUTIONS WITH HEAVY TAILS 80 8. ADDITIONAL COMMENTS 88 3. PARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION IN ACTION 91 1. INTRODUCTION 91 2. BEST ASYMPTOTICALLY NORMAL ESTIMATORS 92 AND SMALL SAMPLE BEHAVIOR 3. MIXTURES OF NORMALS 96 4. COMPUTING WITH THE LOG-NORMAL DISTRIBUTION 101 5. ON CHOOSING PARAMETRIC FAMILIES OF DISTRIBUTIONS 104 6. TOWARD NONPARAMETRICS: MIXTURES REVISITED 113 CONTENTS PART II: NONPARAMETRIC ESTIMATION 4. KERNEL DENSITY ESTIMATION 119 1. INTRODUCTION 119 2. THE EXPECTED L 1 ERROR IN KERNEL DENSITY ESTIMATION 130 3. INTEGRATION BY PARTS TRICKS 136 4. SUBMARTINGALES, EXPONENTIAL INEQUALITIES, 139 AND ALMOST SURE BOUNDS FOR THE L 1 ERROR 5. ALMOST SURE BOUNDS FOR EVERYTHING ELSE 151 6. NONPARAMETRIC ESTIMATION OF ENTROPY 159 7. OPTIMAL KERNELS 167 8. ASYMPTOTIC NORMALITY OF THE L 1 ERROR 173 9. ADDITIONAL COMMENTS 186 5. NONPARAMETRIC MAXIMUM PENALIZED LIKELIHOOD ESTIMATION 187 1. INTRODUCTION 187 2. GOOD S ROUGHNESS PENALIZATION OF ROOT-DENSITIES 189 3. ROUGHNESS PENALIZATION OF LOG-DENSITIES 202 4. ROUGHNESS PENALIZATION OF BOUNDED LOG-DENSITIES 207 5. ESTIMATION UNDER CONSTRAINTS 213 6. ADDITIONAL NOTES AND COMMENTS 218 6. MONOTONE AND UNIMODAL DENSITIES 221 1. INTRODUCTION 221 2. MONOTONE DENSITY ESTIMATION 225 3. ESTIMATING SMOOTH MONOTONE DENSITIES 232 4. ALGORITHMS AND CONTRACTIVITY 234 5. CONTRACTIVITY: THE GENERAL CASE 244 6. ESTIMATING SMOOTH UNIMODAL DENSITIES 250 7. OTHER UNIMODAL DENSITY ESTIMATORS 262 8. AFTERTHOUGHTS: CONVEX DENSITIES 265 9. ADDITIONAL NOTES AND COMMENTS 267 7. CHOOSING THE SMOOTHING PARAMETER 271 1. INTRODUCTION 271 2. LEAST-SQUARES CROSS-VALIDATION AND PLUG-IN METHODS 276 3. THE DOUBLE KERNEL METHOD 283 4. ASYMPTOTIC PLUG-IN METHODS 295 5. AWAY WITH PILOT ESTIMATORS!? 299 6. A DISCREPANCY PRINCIPLE 306 7. THE GOOD ESTIMATOR 309 8. ADDITIONAL NOTES AND COMMENTS 316 8. NONPARAMETRIC DENSITY ESTIMATION IN ACTION 319 1. INTRODUCTION 319 2. FINITE-DIMENSIONAL APPROXIMATIONS 320 3. SMOOTHING PARAMETER SELECTION 323 4. TWO DATA SETS 329 CONTENTS XIII 5. KERNEL SELECTION 333 6. UNIMODAL DENSITY ESTIMATION 338 PART III: CONVEXITY 9. CONVEX OPTIMIZATION IN FINITE- 347 DIMENSIONAL SPACES 1. CONVEX SETS AND CONVEX FUNCTIONS 347 2. CONVEX MINIMIZATION PROBLEMS 357 3. LAGRANGE MULTIPLIERS 361 4. STRICT AND STRONG CONVEXITY 370 5. COMPACTNESS ARGUMENTS 373 6. ADDITIONAL NOTES AND COMMENTS 375 10. CONVEX OPTIMIZATION IN INFINITE- 377 DIMENSIONAL SPACES 1. CONVEX FUNCTIONS 377 2. CONVEX INTEGRALS 383 3. STRONG CONVEXITY 387 4. COMPACTNESS ARGUMENTS 390 5. EULER EQUATIONS 395 6. FINITELY MANY CONSTRAINTS 398 7. ADDITIONAL NOTES AND COMMENTS 402 11. CONVEXITY IN ACTION 405 1. INTRODUCTION 405 2. OPTIMAL KERNELS 405 3. DIRECT NONPARAMETRIC MAXIMUM ROUGHNESS 412 PENALIZED LIKELIHOOD DENSITY ESTIMATION 4. EXISTENCE OF ROUGHNESS PENALIZED LOG-DENSITIES 417 5. EXISTENCE OF LOG-CONCAVE ESTIMATORS 423 6. CONSTRAINED MINIMUM DISTANCE ESTIMATION 425 APPENDICES 1. SOME DATA SETS 433 1. INTRODUCTION 433 2. THE OLD FAITHFUL GEYSER DATA 433 3. THE BUFFALO SNOW FALL DATA 434 4. THE RUBBER ABBRASION DATA 434 5. CLOUD SEEDING DATA 434 6. TEXO OIL FIELD DATA 435 2. THE FOURIER TRANSFORM 437 1. INTRODUCTION 437 2. SMOOTH FUNCTIONS 437 3. INTEGRABLE FUNCTIONS 441 4. SQUARE INTEGRABLE FUNCTIONS 443 5. SOME EXAMPLES 446 6. THE WIENER THEOREM FOR ***.) 456 XIV CONTENTS 3. BANACH SPACES, DUAL SPACES, AND COMPACTNESS 459 1. BANACH SPACES 459 2. BOUNDED LINEAR OPERATORS 462 3. COMPACT OPERATORS 463 4. DUAL SPACES 469 5. HILBERT SPACES 472 6. COMPACT HERMITIAN OPERATORS 478 7. REPRODUCING KERNEL HILBERT SPACES 484 8. CLOSING COMMENTS 485 REFERENCES 487 AUTHOR INDEX 499 SUBJECT INDEX 505
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author	Eggermont, Paulus P. B. La Riccia, Vincent N.
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spelling	Eggermont, Paulus P. B. Verfasser aut Maximum penalized likelihood estimation 1 Density estimation P. P. B. Eggermont ; V. N. LaRiccia New York [u.a.] Springer 2001 XVII, 510 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics La Riccia, Vincent N. Verfasser aut (DE-604)BV013902900 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Eggermont, Paulus P. B. La Riccia, Vincent N. Maximum penalized likelihood estimation
title	Maximum penalized likelihood estimation
title_auth	Maximum penalized likelihood estimation
title_exact_search	Maximum penalized likelihood estimation
title_full	Maximum penalized likelihood estimation 1 Density estimation P. P. B. Eggermont ; V. N. LaRiccia
title_fullStr	Maximum penalized likelihood estimation 1 Density estimation P. P. B. Eggermont ; V. N. LaRiccia
title_full_unstemmed	Maximum penalized likelihood estimation 1 Density estimation P. P. B. Eggermont ; V. N. LaRiccia
title_short	Maximum penalized likelihood estimation
title_sort	maximum penalized likelihood estimation density estimation
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