Papers available
in electronic format
- Nussbaum,
M., Spline smoothing in regression models and asymptotic efficiency in L 2. Ann. Statist. 13
984-997 (1985) .
pdf
- Golubev, G. and
Nussbaum, M., A risk bound in Sobolev class
regression. Ann. Statist. 18 758-778 (1990). pdf
- Golubev, G. and
Nussbaum, M., Adaptive spline estimates in a nonparametric regression
model. (Russian) Teor. Veroyatnost. i Primenen. 37 (1992),
no. 3, 554-561; translation in Theory Probab.
Appl. 37 (1992), no. 3, 521-529 pdf
- Nussbaum,
M., Asymptotic equivalence of density estimation and Gaussian white noise.
Ann. Statist. 24, 2399-2430 (1996 ).
pdf The corresponding preprint contains one more section than the published
paper, on application to asymptotics of
estimation risk
- Hall, P., Nussbaum, M., Stern, S. E. : On the estimation
of a support curve of indeterminate sharpness. J. Multivariate
Analysis, 62 (2), 204-232 (1997). pdf Contains one more section than the
published paper, with detailed discussions.
- Grama, I and Nussbaum, M: Asymptotic equivalence for
nonparametric generalized linear models. Prob. Theor. Rel.
Fields, 111 (1998), 167-214 pdf
- Milstein,
G. and Nussbaum, M., Diffusion approximation for nonparametric autoregression. Prob. Theor. Rel. Fields 112 (1998),
535-543. pdf
- Korostelev, A. and
Nussbaum, M., The asymptotic minimax constant for sup-norm loss in
nonparametric density estimation. Bernoulli 5 (1999)
1099-1118 pdf
- Nussbaum,
M., Minimax risk: Pinsker bound. In:
Encyclopedia of Statistical Sciences, Update Volume 3, 451-460 (S. Kotz, Ed.)
1999. Wiley, New York. Survey paper written as an
Encyclopedia entry. pdf
- Milstein.
G. and Nussbaum, M., Maximum likelihood estimation of a
nonparametric signal in white noise by optimal control. Statistics
and Probability Letters, 55 (2) 193-203 (2001) pdf
- Genon-Catalot, V,
Laredo, C. and Nussbaum, M., Asymptotic equivalence of estimating a
Poisson intensity and a positive diffusion drift. Ann.
Statist. 30 731-753
(2002) pdf
- Grama, I and Nussbaum, M., Asymptotic equivalence for
nonparametric regression. Mathematical
Methods of Statistics 11 (1) 1-36 (2002) pdf
- Grama, I and Nussbaum, M., A functional Hungarian
construction for sums of independent random variables. Annales de l'Institut Henri
Poincaré, Probabilités et Statistiques, 38
(6) pp. 923-957 (2002) pdf Based on the preprint A
nonstandard Hungarian construction for partial sums. WIAS-preprint No.
324, 1997, Weierstrass Institute, Berlin
- Jaehnisch,
M. and Nussbaum, M., Asymptotic equivalence for a model of
independent non identically distributed observations. Statistics
& Decisions 21 197-218 (2003) pdf
- Nussbaum,
M., Equivalence asymptotique des expériences
statistiques. (Survey paper in
French). Journal de la Société francaise de Statistique 145
(1) 31-45 (2004) pdf, English
translation: Asymptotic equivalence of statistical experiments, pdf
- Jaehnisch,
M. and Nussbaum, M., A functional Hungarian construction for
the sequential empirical process, C.R. Acad. Sci. Paris, Ser. I 341
761-763 (2005) pdf
- Audenaert, K. M.
R., Nussbaum, M., Szkola, A. and Verstraete, F.,
Asymptotic error rates in quantum hypothesis testing. Commun.
Math. Phys. 279 (1) 251-283 (2008) pdf
- Nussbaum,
M. and Szkola, A., The Chernoff
lower bound for symmetric quantum hypothesis testing. Ann. Statist. 37
(2) 1040-1057 (2009) pdf
- Golubev, G. K., Nussbaum, M. and Zhou, H. H.,
Asymptotic equivalence of spectral density estimation and Gaussian white
noise, Ann. Statist. 38 (1) 181-214 (2010) pdf The corresponding preprint contains more detailed proofs
- Nussbaum,
M. and Szkola, A., Exponential error
rates in multiple state discrimination on a quantum spin chain, J.
Math. Phys. 51 072203 (2010) pdf
- Nussbaum,
M. and Szkola, A., Asymptotically
optimal discrimination between multiple pure quantum states. In: Theory
of Quantum Computation, Communication and Cryptography. 5th Conference,
TQC 2010, Leeds, UK. Revised Selected Papers. Lecture Notes in Computer
Science, Vol 6519, van Dam, Wim; Kendon,
Vivien M.; Severini, Simone (Eds.), pp.
1-8, Springer (2011) pdf
- Nussbaum,
M. and Szkola, A., An asymptotic
error bound for testing multiple quantum hypotheses. Ann. Statist.
39 (6) 3211 3233 (2011) pdf
- Tecuapetla-Gomez,
I. and Nussbaum, M., On large deviations in testing simple
hypotheses for locally stationary Gaussian processes. Statistical Inference
for Stochastic Processes, 15 (3) 225-239 (2012) pdf
- Nussbaum,
M., Attainment of the multiple quantum Chernoff
bound for certain ensembles of mixed states. In: Proceedings of the
First International Workshop on Entangled Coherent States and Its
Application to Quantum Information Science, (Usuda, T.S., Kato, K., Eds.), Tamagawa University Quantum ICT
Research Institute, Tokyo, Japan, 77-81 (2013). pdf Also at arXiv:1308.6563 [quant-ph]
- Nussbaum,
M., Sharp
adaptive nonparametric testing for Sobolev
ellipsoids. In: Low M, Munk A, Tsybakov A. (Eds.), Adaptive Statistical Inference. Oberwolfach Report 11
(2014), 721-779, European Mathematical Society Publishing House,
Zurich pdf
- Ji, P.,
Nussbaum, M., Sharp minimax adaptation over Sobolev
ellipsoids in nonparametric testing, Electron. J. Stat. 11 (2)
4515-4562 (2017) pdf
- Butucea, C, Guţă,
M. and Nussbaum, M., Local asymptotic equivalence of pure quantum states
ensembles and quantum Gaussian white noise. Ann. Statist.
46
3676-3706 (2018) pdf
- Butucea, C, Guţă,
M. and Nussbaum, M., Supplement to “Local asymptotic equivalence of pure
quantum states ensembles and quantum Gaussian white noise”, DOI: 10.1214/17-AOS1672SUPP
pdf
- Lahiry, S., Nussbaum, M., Minimax nonparametric
estimation of pure quantum states. Ann. Statist. 50
(1) 430–459
(2022) pdf
- Lahiry, S.; Nussbaum, M., Local asymptotic normality and optimal estimation of low-rank quantum
systems and their linear functionals. Bernoulli 30 (1),
610–635 (2024) pdf
- Lahiry, S.; Nussbaum, M., Supplement to “Minimax
estimation of low-rank quantum states and their linear functionals”. DOI: 10.3150/23BEJ1610SUPP pdf
- Mishra, H.
K., Nussbaum, M. and Wilde. M. M., On the optimal
error exponents for classical and quantum antidistinguishability. arXiv:2309.03723 (2024) pdf