Free Access
Issue
ESAIM: PS
Volume 23, 2019
Page(s) 524 - 551
DOI https://doi.org/10.1051/ps/2018027
Published online 09 August 2019
  1. P.J. Bickel and Y. Ritov, Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhyā Ser. A 50 (1988) 381–393. [Google Scholar]
  2. N. Bissantz, G. Claeskens, H. Holzmann and A. Munk, Testing for lack of fit in inverse regression—with applications to biophotonic imaging. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 (2009) 25–48. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Butucea, Goodness-of-fit testing and quadratic functional estimation from indirect observations. Ann. Stat. 35 (2007) 1907–1930. [CrossRef] [Google Scholar]
  4. C. Butucea, C. Matias and C. Pouet, Adaptive goodness-of-fit testing from indirect observations. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009) 352–372. [CrossRef] [Google Scholar]
  5. C. Butucea and K. Meziani, Quadratic functional estimation in inverse problems. Stat. Methodol. 8 (2011) 31–41. [CrossRef] [Google Scholar]
  6. T.T. Cai and M.G. Low, Nonquadratic estimators of a quadratic functional. Ann. Stat. 33 (2005) 2930–2956. [CrossRef] [Google Scholar]
  7. T.T. Cai and M.G. Low, Optimal adaptive estimation of a quadratic functional. Ann. Stat. 34 (2006) 2298–2325. [CrossRef] [Google Scholar]
  8. L. Cavalier, Inverse problems in statistics. In Inverse problems and high-dimensional estimation, Vol. 203 of Lect. Notes Stat. Proc. Springer, Heidelberg (2011) 3–96. [CrossRef] [Google Scholar]
  9. L. Cavalier and N.W. Hengartner, Adaptive estimation for inverse problems with noisy operators. Inverse Probl. 21 (2005) 1345–1361. [CrossRef] [Google Scholar]
  10. C. Chesneau, On adaptive wavelet estimation of a quadratic functional from a deconvolution problem. Ann. Inst. Stat. Math. 63 (2011) 405–429. [Google Scholar]
  11. O. Collier, L. Comminges and A.B. Tsybakov, Minimax estimation of linear and quadratic functionals on sparsity classes. Ann. Stat. 45 (2017) 923–958. [Google Scholar]
  12. F. Comte and C. Lacour, Data-driven density estimation in the presence of additive noise with unknown distribution. J. R. Stat. Soc. Ser. B Stat. Methodol. 73 (2011) 601–627. [CrossRef] [Google Scholar]
  13. D.L. Donoho, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101–126. [Google Scholar]
  14. D.L. Donoho and M. Nussbaum, Minimax quadratic estimation of a quadratic functional. J. Complex. 6 (1990) 290–323. [Google Scholar]
  15. S. Efromovich and V. Koltchinskii, On inverse problems with unknown operators. IEEE Trans. Inf. Theory 47 (2001) 2876–2894. [Google Scholar]
  16. M.S. Ermakov, Minimax detection of a signal in Gaussian white noise. Teor. Veroyatnost. i Primenen. 35 (1990) 704–715. [Google Scholar]
  17. J. Fan, On the estimation of quadratic functionals. Ann. Stat. 19 (1991) 1273–1294. [Google Scholar]
  18. J. Fan and I. Gijbels, Minimax estimation of a bounded squared mean. Stat. Probab. Lett. 13 (1992) 383–390. [Google Scholar]
  19. G. Gayraud and K. Tribouley, Wavelet methods to estimate an integrated quadratic functional: adaptivity and asymptotic law. Stat. Probab. Lett. 44 (1999) 109–122. [Google Scholar]
  20. E. Giné and R. Nickl, A simple adaptive estimator of the integrated square of a density. Bernoulli 14 (2008) 47–61. [CrossRef] [Google Scholar]
  21. M. Hoffmann and M. Reiss, Nonlinear estimation for linear inverse problems with error in the operator. Ann. Stat. 36 (2008) 310–336. [Google Scholar]
  22. Y.I. Ingster and I.A. Suslina, Nonparametric goodness-of-fit testing under Gaussian models. In Vol. 169 of Lecture Notes in Statistics. Springer-Verlag, New York (2003). [CrossRef] [Google Scholar]
  23. Y.I. Ingster, Asymptotically minimax hypothesis testing for nonparametric alternatives (i–iii). Math. Methods Stat. 2 (1993) 85–114, 171–189, 249–268. [Google Scholar]
  24. Y.I. Ingster, T. Sapatinas and I.A. Suslina. Minimax signal detection in ill-posed inverse problems. Ann. Stat. 40 (2012) 1524–1549. [Google Scholar]
  25. J. Johannes, Deconvolution with unknown error distribution. Ann. Stat. 37 (2009) 2301–2323. [Google Scholar]
  26. J. Johannes and M. Schwarz, Adaptive Gaussian inverse regression with partially unknown operator. Commun. Stat. Theory Methods 42 (2013) 1343–1362. [Google Scholar]
  27. I. Johnstone, Thresholding for weighted χ2. Stat. Sinica 11 (2001) 691–704. [Google Scholar]
  28. I.M. Johnstone, Chi-square oracle inequalities. In State of the art in probability and statistics (Leiden, 1999). In Vol. 36 of IMS Lecture Notes Monogr. Ser. Inst. Math. Stat., Beachwood, OH (2001) 399–418. [CrossRef] [Google Scholar]
  29. J. Klemelä, Sharp adaptive estimation of quadratic functionals. Probab. Theory Related Fields 134 (2006) 539–564. [CrossRef] [Google Scholar]
  30. C. Lacour and T.M. Pham Ngoc, Goodness-of-fit test for noisy directional data. Bernoulli 20 (2014) 2131–2168. [CrossRef] [Google Scholar]
  31. B. Laurent, J.-M. Loubes and C. Marteau, Testing inverse problems: a direct or an indirect problem? J. Stat. Plann. Infer. 141 (2011) 1849–1861. [CrossRef] [Google Scholar]
  32. B. Laurent and P. Massart, Adaptive estimation of a quadratic functional by model selection. Ann. Stat. 28 (2000) 1302–1338. [Google Scholar]
  33. B. Laurent, Adaptive estimation of a quadratic functional of a density by model selection. ESAIM: PS 9 (2005) 1–18. [CrossRef] [EDP Sciences] [Google Scholar]
  34. C. Marteau and T. Sapatinas, A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection. Stat. Surv. 9 (2015) 253–297. [Google Scholar]
  35. C. Marteau and T. Sapatinas, Minimax goodness-of-fit testing in ill-posed inverse problems with partially unknown operators. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 1675–1718. [CrossRef] [Google Scholar]
  36. M.H. Neumann, On the effect of estimating the error density in nonparametric deconvolution. J. Nonparametr. Stat. 7 (1997) 307–330. [Google Scholar]
  37. V. Rivoirard and K. Tribouley, The maxiset point of view for estimating integrated quadratic functionals. Stat. Sinica 18 (2008) 255–279. [Google Scholar]
  38. A.B. Tsybakov, Introduction to nonparametric estimation. In Springer Series in Statistics. Revised and extended fromthe 2004 French original, Translated by Vladimir Zaiats. Springer, New York (2009). [Google Scholar]
  39. A.B. Tsybakov, Aggregation and minimax optimality in high-dimensional estimation. In Proc. of the International Congress of Mathematicians—Seoul 2014. Vol. IV. Kyung Moon Sa, Seoul (2014) 225–246. [Google Scholar]

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