相关论文: U-max-Statistics

This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…

This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP)…

This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its…

A simple characterization of uniformly minimum variance unbiased estimators (UMVUEs) is provided (in the case when the sample space is finite) in terms of a linear independence condition on the likelihood functions corresponding to the…

We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three…

Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample…

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…

Estimating properties of unknown unitary operations is a fundamental task in quantum information science. While full unitary tomography requires a number of samples to the unknown unitary scaling linearly with the dimension (implying…

In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable. A class of estimators is defined which includes [1], [2] and [3]…

Euclidean functions with values in an arbitrary well-ordered set were first considered in a 1949 work of Motzkin and studied in more detail in work of Fletcher, Samuel and Nagata in the 1970's and 1980's. Here these results are revisited,…

In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…

We show a deviation inequality for U-statistics of independent data taking values in a separable Banach space which satisfies some smoothness assumptions. We then provide applications to rates in the law of large numbers for U-statistics, a…

The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…

Effect modification means the size of a treatment effect varies with an observed covariate. Generally speaking, a larger treatment effect with more stable error terms is less sensitive to bias. Thus, we might be able to conclude that a…

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…

In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution in the absence of a location parameter, including powers of the rate parameter, the $q$th quantile, the…

Hotelling's T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the…

Feature selection is important for high-dimensional data analysis and is non-trivial in unsupervised learning problems such as dimensionality reduction and clustering. The goal of unsupervised feature selection is finding a subset of…

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by \cite{hdcp} and the $L_q$-norm based…

A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…