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We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process with a small noise based on high frequency spatio-temporal data. We…

Statistics Theory · Mathematics 2024-08-06 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

Statistics Theory · Mathematics 2024-07-26 Randolf Altmeyer , Anton Tiepner , Martin Wahl

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation…

Statistics Theory · Mathematics 2014-02-05 Guang Cheng , Lan Zhou , Jianhua Z. Huang

We develop an asymptotic limit theory for nonparametric estimation of the noise covariance kernel in linear parabolic stochastic partial differential equations (SPDEs) with additive colored noise, using space-time infill asymptotics. The…

Statistics Theory · Mathematics 2025-08-29 Andreas Petersson , Dennis Schroers

We consider the estimation of a non-linear reaction term in the stochastic heat or more generally in a semi-linear stochastic partial differential equation (SPDE). Consistent inference is achieved by studying a small diffusivity level,…

Statistics Theory · Mathematics 2022-03-22 Sascha Gaudlitz , Markus Reiß

We establish well-posedness and maximal regularity estimates for linear parabolic SPDE in divergence form involving random coefficients that are merely bounded and measurable in the time, space, and probability variables. To reach this…

Analysis of PDEs · Mathematics 2023-10-17 Pascal Auscher , Pierre Portal

This paper investigates the nonparametric estimation of the functional coefficients of the FBSDEs with random terminal time, including the local constant and local linear estimators. We provide complete two-dimensional asymptotics in both…

Statistics Theory · Mathematics 2024-05-24 Shaolin Ji , Chenyao Yu , Linlin Zhu

In this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and \sqrtn-normality property of the estimator of the finite-dimensional parameters of…

Statistics Theory · Mathematics 2007-06-13 Ibrahim Ahmad , Sittisak Leelahanon , Qi Li

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Methodology · Statistics 2017-04-03 Nina Munkholt Jakobsen , Michael Sørensen

Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…

Numerical Analysis · Mathematics 2026-01-09 Jan Bouwe van den Berg , Maxime Breden

This paper discusses the non-parametric estimation of a non-linear reaction term in a semi-linear parabolic stochastic partial differential equation (SPDE). The estimator's consistency is due to the spatial ergodicity of the SPDE while the…

Probability · Mathematics 2025-01-09 Sascha Gaudlitz

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…

Statistics Theory · Mathematics 2008-12-18 Oliver Linton , Stefan Sperlich , Ingrid Van Keilegom

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

Methodology · Statistics 2019-05-28 Arun Kumar Kuchibhotla , Rohit Kumar Patra

Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological…

Quantitative Methods · Quantitative Biology 2024-10-08 Yosef Berman , Joshua Forrest , Matthew Grote , Alexey Ovchinnikov , Sonia Rueda

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

Methodology · Statistics 2019-12-30 Minggen Lu , Yan Liu , Chin-Shang Li , Jianguo Sun

A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…

Probability · Mathematics 2009-06-25 W. Liu , S. V. Lototsky

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…

Statistics Theory · Mathematics 2013-04-03 Yanyuan Ma , Liping Zhu

We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient…

Methodology · Statistics 2024-02-09 Changyu Liu , Wen Su , Kin-Yat Liu , Guosheng Yin , Xingqiu Zhao

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

Statistics Theory · Mathematics 2021-09-20 Teppei Ogihara , Mitja Stadje

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

Statistics Theory · Mathematics 2017-10-16 Jana Jankova , Sara van de Geer