Related papers: A note on critical dimensions in profile semiparam…
We study the role of probe dimension in determining the bounds of precision and the level of incompatibility in multi-parameter quantum estimation problems. In particular, we focus on the paradigmatic case of unitary encoding generated by…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher…
The critical indices \alpha', \beta, \gamma' and \delta of the Quark Gluon Bags with Surface Tension Model with the tricritical endpoint are calculated as functions of the usual parameters of this model and two newly introduces parameters…
The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain…
We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both the cross-sectional dimension, $n$, and the sample size, $T$,…
The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation…
Estimating the dimensionality of the latent representation needed for prediction -- the task-relevant dimension -- is a difficult, largely unsolved problem with broad scientific applications. We cast it as an Information Bottleneck…
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…
Popularly used eigendecomposition-based criteria such as BIC type, ratio estimation and principal component-based criterion often underdetermine model dimensionality for regressions or the number of factors for factor models. This…
It is widely admitted that structured nonparametric modeling that circumvents the curse of dimensionality is important in nonparametric estimation. In this paper we show that the same holds for semi-parametric estimation. We argue that…
Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension d_c. However, it has long been known that numerical…
We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…
Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…
In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is…
In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile…
This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…
The notion of relative universality with respect to a {\sigma}-field was introduced to establish the unbiasedness and Fisher consistency of an estimator in nonlinear sufficient dimension reduction. However, there is a gap in the proof of…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…