Department of Statistics
University of California, Santa Barbara
ANDREW V. CARTER







Asymptotic Equivalence of Nonparametric Experiments
Bibliography

Home
Research
Publications
Classes
Contact Info


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

Asymptotic Equivalence Background

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

Nonparametric Regression

  1. Lawrence Brown and Mark  Low (1996)  "Asymptotic equivalence of nonparametric regression and white noise " Annals of Statistics. 24: 2384-2398. [JSTOR]
  2. Ion Grama and Michael Nussbaum (1998) "Asymptotic equivalence for nonparametric generalized linear models" Probability Theory and Related Fields. 111: 167–214. [SpringerLink]
  3. 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]
  4. Ion Grama and Michael Nussbaum  (2002) "Asymptotic equivalence for nonparametric regression" Mathematical  Methods of Statistics. 11: 1–36. [preprint]
  5. Angelika Rohde (2004) "On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise" Statistics & Decisions. 22: 235-243. [Extenza]
  6. Andrew Carter (2006) "A continuous Gaussian process approximation to a nonparametric regression in two dimensions."  Bernoulli. 12: 143-156. [Euclid]
  7. Andrew Carter (2007) "Asymptotic approximation of nonparametric regression experiments with unknown variances." Annals of  Statistics. 35: 1644-1673. [Euclid] [CDL postprint]
  8. Markus Reiss (2007) "Asymptotic equivalence for nonparametric regression with multivariate and random design."  Annals of Statistics [preprint]

Density Estimation

  1. Michael Nussbaum (1996) "Asymptotic equivalence of density estimation and Gaussian white noise" Annals of Statistics. 24: 2399-2430. [JSTOR] [original preprint]
  2. Jussi Klemelä and Michael Nussbaum. (1998) "Constructive asymptotic equivalence of density estimation and Gaussian white noise" Discussion paper 53, Sonderforschungsbereich 373, Humboldt Univeristy, Berlin, 1998.
  3. Andrew Carter (2002) "Deficiency distance between  multinomial and multivariate normal experiments" Annals of Statistics. 30: 708-730.  [JSTOR]
  4. Michael Jähnisch and Michael Nussbaum (2003) "Asymptotic equivalence for a model of independent non identically distributed observations"  Statistics & Decisions. 21: 197–218. [Extenza]
  5. 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. [Euclid] [CDL postprint]

Time Series

  1. Grigori Milstein and Michael Nussbaum. (1998) "Diffusion approximation for nonparametric autoregression" Probability Theory and Related Fields. 112: 535–543. [SpringerLink]
  2. Ion Grama and M. H. Neumann. (2006) "Asymptotic equivalence of nonparametric autoregression and nonparametric regression." Annals of Statistics. 34: 1701-1732. [Euclid]
  3. Georgi Golubev,  Michael Nussbaum, and Harrison Huibin Zhou (2007) "Asymptotic equivalence of spectral density estimation and Gaussian white noise" Annals of Statistics. [preprint]

Diffusion Processes

  1. 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]
  2. S. Delattre. and M. Hoffmann. (2002). "Asymptotic equivalence for a null recurrent diffusion." Bernoulli 8 (2):139-174. [Euclid]
  3. Arnak Dalalyan and Markus Reiss (2006) "Asymptotic statistical equivalence for ergodic diffusions." Probability Theory and Related Fields. 134: 248–282. [SpringerLink]
  4. Arnak Dalalyan and Markus Reiss (2007) "Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case." Probability Theory and Related Fields. 137: 25–47. [SpringerLink]

Counterexamples

  1. 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]
  2. 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]
  3. Yazhen Wang (2002) "Asymptotic nonequivalence of GARCH models and diffusions" Annals of Statistics 30:754–783. [JSTOR]

Information contained in additional observations

  1. Erik Torgersen. (1972) "Comparison of translation experiments" Annals of Mathematical Statistics, 43: 1383–1399. [JSTOR]
  2. Enno Mammen. (1986) "The statistical information contained in additional observations" Annals of Statistics 14: 665–678. [JSTOR]
  3. Harrison Zhou and Mark Low. (2007) "A complement to Le Cam's theorem" Annals of Statistics 35:3. [preprint]
 



[ Home ] [ Research ] [ Publications ] [ Classes ] [Contact Info ]



Any questions about this page should be directed to Prof.Carter.
Last updated on 8/30/2007