Related papers: Asymptotic Statistical Theory for the Samples Prob…
This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $\psi$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
A general notion of bootstrapped $\phi$-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped $\phi$-divergence estimates are obtained, by mean of the…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
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…
The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Gaussian limit is established under metric entropy…
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…
This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…
We aim to develop simultaneous inference tools for the mean function of functional data from sparse to dense. First, we derive a unified Gaussian approximation to construct simultaneous confidence bands of mean functions based on the…
A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
This paper proposes asymptotically distribution-free inference methods for comparing a broad range of welfare indices across dependent samples, including those employed in inequality, poverty, and risk analysis. Two distinct situations are…
A joint limit theorem for the point process of the off-diagonal entries of a sample covariance matrix $\mathbf{S}$, constructed from $n$ observations of a $p$-dimensional random vector with iid components, and the Frobenius norm of…
In this paper, we derive the joint asymptotic distributions of functions of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile estimator) with functions of measure of dispersion estimators…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
In this paper, we seek to establish asymptotic results for selective inference procedures removing the assumption of Gaussianity. The class of selection procedures we consider are determined by affine inequalities, which we refer to as…