This bibliography is an ongoing project. I welcome any suggestions or input (email me).

• Asymptotic Equivalence Background

  • Lucien Le Cam (1964) "Sufficiency and approximate sufficiency." Annals of Mathematical Statististics 35: 1419-1455. JSTOR
  • Lucien Le Cam (1986) Asymptotic Methods in Statistical Decision Theory. Springer.
  • Erik Torgerson (1991) Comparison of Statistical Experiments, volume 36 of Encyclopedia of Mathematics. Cambridge University Press.
  • Lucien Le Cam and Grace Yang (2000) Asymptotics in Statistics, Some Basic Concepts (2nd edition) Springer.
  • Michael Nussbaum (2004) "Equivalence asymptotique des expériences statistiques." (Survey paper in French). Journal de la Société Française de Statistique 145: 31-45.

• Nonparametric Regression

  • Lawrence Brown and Mark Low (1996) "Asymptotic equivalence of nonparametric regression and white noise." Annals of Statistics, 24: 2384-2398. JSTOR
  • Ion Grama and Michael Nussbaum (1998) "Asymptotic equivalence for nonparametric generalized linear models" Probability Theory and Related Fields, 111: 167-214. SpringerLink
  • Lawrence Brown, Tony Cai, Mark Low, and Cun-Hui Zhang (2002) "Asymptotic equivalence theory for nonparametric regression with random design" Annals of Statistics, 30: 688-707. JSTOR
  • Ion Grama and Michael Nussbaum (2002) "Asymptotic equivalence for nonparametric regression" Mathematical Methods of Statistics, 11:1-36. preprint
  • Angelika Rohde (2004) "On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise" Statistics & Decisions, 22:235-243. DeGruyter
  • Andrew Carter (2006) "A continuous Gaussian process approximation to a nonparametric regression in two dimensions."Bernoulli, 12: 143-156. Euclid
  • Andrew Carter (2007) "Asymptotic approximation of nonparametric regression experiments with unknown variances." Annals of Statistics, 35: 1644-1673. JSTOR CDL postprint
  • Markus Reiss (2008) "Asymptotic equivalence for nonparametric regression with multivariate and random design."Annals of Statistics, 36: 1957-1982. JSTOR
  • Andrew Carter (2009) "Asymptotically sufficient statistics in nonparametric regression experiments with correlated noise." Journal of Probability and Statistics 2009:Article ID 275308. Hindawi
  • Alexander Meister (2011) "Asymptotic equivalence of functional linear regression and a white noise inverse problem." Annals of Statistics 39: 1471-1495. Euclid
  • Alexander Meister and Markus Reiss (2013) "Asymptotic equivalence for nonparametric regression with non-regular errors." Probability Theory and Related Fields 155: 201-229. SpringerLink

• Density Estimation

  • Michael Nussbaum (1996) "Asymptotic equivalence of density estimation and Gaussian white noise" Annals of Statistics. 24:2399-2430. JSTOR original preprint
  • Jussi Klemelä and Michael Nussbaum (1998) "Constructive asymptotic equivalence of density estimation and Gaussian white noise" Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes. Discussion paper 53. Humboldt Edocs
  • Andrew Carter (2002) "Deficiency distance between multinomial and multivariate normal experiments" Annals of Statistics. 30: 708-730. JSTOR
  • Michael Jähnisch and Michael Nussbaum (2003) "Asymptotic equivalence for a model of independent non identically distributed observations"Statistics & Decisions. 21:197-218. DeGruyter
  • Lawrence Brown, Andrew Carter, Mark Low, and Cun-Hui Zhang (2004) "Equivalence theory for density estimation, Poisson processes, and Gaussian white noise with drift" Annals of Statistics. 24 2399-2430. JSTOR CDL postprint
  • Friedrich Liese, Alexander Meister, and Johanna Kappus (2016) "Strong Gaussian approximation of the mixture Rasch model" preprint. arXiv

• Time Series

  • Grigori Milstein and Michael Nussbaum. (1998) "Diffusion approximation for nonparametric autoregression" Probability Theory and Related Fields. 112: 535-543. SpringerLink
  • Ion Grama and M. H. Neumann. (2006) "Asymptotic equivalence of nonparametric autoregression and nonparametric regression" Annals of Statistics. 34: 1701-1732. JSTOR
  • Georgi Golubev, Michael Nussbaum, and Harrison H. Zhou (2010) "Asymptotic equivalence of spectral density estimation and Gaussian white noise" Annals of Statistics. 38: 181-214. JSTOR

• Diffusion Processes

  • Valentine Genon-Catalot, Catherine Laredo, and Michael Nussbaum (2002) "Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift." Annals of Statistics 30:731-753. JSTOR
  • S. Delattre. and M. Hoffmann. (2002). "Asymptotic equivalence for a null recurrent diffusion." Bernoulli 8 (2):139-174. Euclid
  • Arnak Dalalyan and Markus Reiss (2006) "Asymptotic statistical equivalence for ergodic diffusions." Probability Theory and Related Fields. 134: 248-282.SpringerLink
  • Arnak Dalalyan and Markus Reiss (2007) "Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case." Probability Theory and Related Fields. 137: 25-47. SpringerLink
  • Markus Reiss (2011) "Asymptotic equivalence for the inference on the volatility from noisy observations." Annals of Statistics, 39: 772-802. JSTOR

• Counterexamples

  • Sam Efromovich and Alex Samarov (1996) "Asymptotic equivalence of nonparametric regression and white noise model has its limits" Statistics & Probability Letters, 28: 143-145. ScienceDirect
  • Lawrence Brown and Cun-Hui Zhang (1998) "Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2" Annals of Statistics, 26:279-287. JSTOR
  • Yazhen Wang (2002) "Asymptotic nonequivalence of GARCH models and diffusions" Annals of Statistics, 30:754-783. JSTOR
    

• Information contained in additional observations

  • Erik Torgersen. (1972) "Comparison of translation experiments" Annals of Mathematical Statistics, 43:1383-1399. JSTOR
  • Enno Mammen. (1986) "The statistical information contained in additional observations" Annals of Statistics, 14: 6650-678. JSTOR
  • Harrison Zhou and Mark Low. (2007) "A complement to Le Cam's theorem" Annals of Statistics, 35:1146-1165. JSTOR