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Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…

Statistics Theory · Mathematics 2016-09-01 Marco Carone , Alexander R. Luedtke , Mark J. van der Laan

The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…

Probability · Mathematics 2014-02-04 Soummya Kar , Jose Moura

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Statistics Theory · Mathematics 2009-09-29 Lawrence D. Brown , M. Levine

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Machine Learning · Computer Science 2023-06-14 Marc Finzi , Anudhyan Boral , Andrew Gordon Wilson , Fei Sha , Leonardo Zepeda-Núñez

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Statistics Theory · Mathematics 2024-11-07 Arnab Ganguly

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…

It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…

Statistics Theory · Mathematics 2010-06-09 Radhendushka Srivastava , Debasis Sengupta

We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…

Probability · Mathematics 2016-01-20 Robert Azencott , Peng Ren , Ilya Timofeyev

This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…

Methodology · Statistics 2008-12-16 Heng Lian

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…

Statistics Theory · Mathematics 2009-09-29 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Machine Learning · Computer Science 2025-10-07 Carlo Kneissl , Christopher Bülte , Philipp Scholl , Gitta Kutyniok

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Machine Learning · Computer Science 2024-08-06 Gen Li , Yuting Wei , Yuejie Chi , Yuxin Chen

We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…

Statistics Theory · Mathematics 2011-05-12 Markus Reiß

Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…

Methodology · Statistics 2007-12-25 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…

Applications · Statistics 2021-09-10 Ioana Schiopu-Kratina , Hai Yan Liu , Mayer Alvo , Pierre-Jerome Bergeron

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

Statistics Theory · Mathematics 2007-06-13 Cun-Hui Zhang

Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…

Statistics Theory · Mathematics 2026-05-06 Yannick Baraud

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…

Methodology · Statistics 2022-05-27 Jukka Corander , Ulpu Remes , Ida Holopainen , Timo Koski

We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…

Methodology · Statistics 2019-02-04 Frank van der Meulen , Moritz Schauer

This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…

Methodology · Statistics 2016-12-06 Tianqing Liu , Xiaohui Yuan , Zhaohai Li , Aiyi Liu