Related papers: Asymptotically uniformly most powerful tests for d…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
This paper outlines a new nonparametric estimation procedure for unobserved phi-mixing processes. It is assumed that the only information on the stationary hidden states (Xk) is given by the process (Yk), where Yk is a noisy observation of…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample…
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…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
This work is devoted to the development of a distributionally robust active fault diagnosis approach for a class of nonlinear systems, which takes into account any ambiguity in distribution information of the uncertain model parameters.…
We study sufficient conditions for local asymptotic mixed normality. We weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhya Ser. A 1982) so that they can be applied to a wider class of statistical models including a…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
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…
We study the simple hypothesis testing problem for the drift coefficient for stochastic fractional heat equation driven by additive noise. We introduce the notion of asymptotically the most powerful test, and find explicit forms of such…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…