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Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
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…
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…
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…
This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
An adaptive design adjusts dynamically as information is accrued and a consequence of applying an adaptive design is the potential for inducing small-sample bias in estimates. In psychometrics and psychophysics, a common class of studies…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…
The adaptive quasi-likelihood analysis is developed for a degenerate diffusion process. Asymptotic normality and moment convergence are proved for the quasi-maximum likelihood estimators and quasi-Bayesian estimators, in the adaptive…
We study the nonparametric estimators of the infinitesimal coefficients of the second-order jump-diffusion models. Under the mild conditions, we obtain the weak consistency and the asymptotic normalities of the estimators.
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
The paper proposes a specification test based on two estimates of distribution function. One is the traditional kernel distribution function estimate and the other is a newly proposed convolution-type distribution function estimate.…
We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…