Related papers: U-Quantile-Statistics
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different…
We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function $h(u)$ as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributions…
This article proposes a co-variance operator for Banach valued random elements using the concept of $U$-statistic. We then study the asymptotic distribution of the proposed co-variance operator along with related large sample properties.…
Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…
Kemeny (1959) introduced a topologically complete metric space to study ordinal random variables, particularly in the context of Condorcet's paradox and the measurability of ties. Building on this, Emond & Mason (2002) reformulated Kemeny's…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
In this paper, we establish an exponential inequality for U-statistics of i.i.d. data, varying kernel and taking values in a separable Hilbert space. The bound are expressed as a sum of an exponential term plus an other one involving the…
A classifier for two or more samples is proposed when the data are high-dimensional and the underlying distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable…
For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$,…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific…
We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on the two-sample U-quantile processes, in the case of short…
This paper establishes the functional average as an important estimand for causal inference. The significance of the estimand lies in its robustness against traditional issues of confounding. We prove that this robustness holds even when…
Even though dyadic regressions are widely used in empirical applications, the (asymptotic) properties of estimation methods only began to be studied recently in the literature. This paper aims to provide in a step-by-step manner how…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…