Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations

A general spline representation for nonparametric and semiparametric density estimates using diffeomorphisms

A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that density estimation can be recast in terms of transformations. In particular, one can fix any absolutely continuous probability measure, call it P, and then reparameterize the whole class of absolutely continuous probability measures as monotone transformations from P. In this paper we utilize this reparameterization of densities, as monotone transformations…

大语言模型评估作为张量补全：低秩结构与半参数效率

LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency

本文将大语言模型评估视为低秩潜在评分张量的半参数推断问题，通过成对比较数据进行张量补全，提出了一种基于信息算子和影响函数的偏差修正估计器，解决了异质信息算子带来的挑战。

Functional stable limit theorems for quasi-efficient spectral covolatility estimators

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. …

Semiparametric modeling of autonomous nonlinear dynamical systems with applications

In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear semi-parametric mixed effects model. We also propose a computationally efficient model selection procedure. We prove consistency of the proposed estimator under suitable regularity conditions. We show by simulation studies that the proposed estimation as well as model selection procedures can efficiently handle sparse and noisy measurements. Finally, we apply the propo…

High-dimensional estimation with geometric constraints

Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i, where e_i is a noise term. However, in practice the precise relationship between the signal x and the observations y_i may not follow the linear model, and in some cases it may not even be known. To address this challenge, in this paper we propose a general model where it is only assumed that each observation y_i may depend on a_i only through <a_i, x>. We do n…

Estimation of a noisy subordinated Brownian Motion via two-scales power variations

High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed by Zhang et. al. (2005) for the estimation of the integrated variance of a continuous Ito process. The proposed estimators are shown to be robust against the noise and, surprisingly, to attain better rates of convergence than their precursors, method of moment estimators, even in the absence of microstructure noise. Our main results give approximate optimal …