Related papers: LAMN in a class of parametric models for null recu…
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…
We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and…
We study the local asymptotic normality (LAN) property for the likelihood function associated with discretely observed $d$-dimensional McKean-Vlasov stochastic differential equations over a fixed time interval. The model involves a joint…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…
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…
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…
In this paper, we consider a linear model with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its intensity are unknown parameters. Supposing that the process is…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper,…
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…
Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…
We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…