Efficiency of estimators for locally asymptotically normal quantum statistical models
نویسندگان
چکیده
We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This enables us to study the efficiency of estimators, such as regular estimators and minimax leading a universal tight lower bound beyond i.i.d. assumption. formulation complements theory contiguity developed in previous paper [Fujiwara Yamagata, Bernoulli 26 (2020) 2105–2141], providing solid foundation weak local normality.
منابع مشابه
Consistent and asymptotically normal PLS estimators for linear structural equations
A vital extension to partial least squares (PLS) path modeling is introduced: consistency. While maintaining all the strengths of PLS, the consistent version provides two key improvements. Path coefficients, parameters of simultaneous equations, construct correlations, and indicator loadings are estimated consistently. The global goodness-of-fit of the structural model can also now be assessed,...
متن کاملAsymptotically efficient estimators for nonparametric heteroscedastic regression models
This paper concerns the estimation of a function at a point in nonparametric heteroscedastic regression models with Gaussian noise or noise having unknown distribution. In those cases an asymptotically efficient kernel estimator is constructed for the minimax absolute error risk.
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Bayesian prediction and model selection for locally asymptotically mixed normal models
The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and c...
متن کاملLocally asymptotically optimal tests for nonlinear time-series models
Based on the local asymptotic normality (LAN) of the log-likelihood ratio statistic, we proposed some distribution-free tests for examining simultaneously hypotheses about the conditional mean and the conditional variance functions in time series models. Our results are established under stationarity and ergodicity conditions with unspecified "innovation" densities under the null hypothesis as ...
متن کاملLocally efficient semiparametric estimators for functional measurement error models
A class of semiparametric estimators are proposed in the general setting of functional measurement error models. The estimators follow from estimating equations that are based on the semiparametric efficient score derived under a possibly incorrect distributional assumption for the unobserved ‘measured with error’ covariates. It is shown that such estimators are consistent and asymptotically no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Statistics
سال: 2023
ISSN: ['0090-5364', '2168-8966']
DOI: https://doi.org/10.1214/23-aos2285