Related papers: Inference on a Distribution Function from Ranked S…
The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…
Let $X$ be an observable random variable with unknown distribution function $F(x) = \mathbb{P}(X \leq x), - \infty < x < \infty$, and let \[\ \theta = \sup\left \{ r \geq 0:~ \mathbb{E}|X|^{r} < \infty \right \}. \] We call $\theta$ the…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
In this paper, some of the properties of non-parametric estimation of the expectation of g(X) (any function of X), by using a Judgment Post-stratification Sample (JPS), are discussed. A class of estimators (including the standard JPS…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
Kagan and Shalaevski 1967 have shown that if the random variables $X_1,\dots,X_n$ are independent and identically distributed and the distribution of $\sum_{i=1}^n(X_i+a_i)^2$ $a_i\in \mathbb{R}$ depends only on $\sum_{i=1}^na_i^2$ , then…
Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…
In a recent paper entitled "Inconsistencies of Recently Proposed Citation Impact Indicators and how to Avoid Them," Schreiber (2012, at arXiv:1202.3861) proposed (i) a method to assess tied ranks consistently and (ii) fractional attribution…
Let $\mathbf{X}=(X_1,X_2,X_3)$ be a spherically symmetric random vector of which only $(X_1,X_2)$ can be observed. We focus attention on estimating F, the distribution function of the squared radius $Z:=X_1^2+X_2^2+X_3^2$, from a random…
What proportion of treated units actually benefited from an experimental intervention? What is the median or the largest individual treatment effect? This paper develops methods for answering such questions about the distribution of…
This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\mathbf{s}_k;t),t\in[0,T]$,…
Consider a continuous random pair $(X,Y)$ whose dependence is characterized by an extreme-value copula with Pickands dependence function $A$. When the marginal distributions of $X$ and $Y$ are known, several consistent estimators of $A$ are…
While rankings are at the heart of social science research, little is known about how to analyze ranking data in experimental studies. This paper introduces a potential-outcomes framework to perform causal inference when outcome data are…
We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable when the event time is subject to interval censoring case 1 and the continuous mark variable is only observed in case the…
The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying…
We consider the problem of estimating functions of distributed data using a distributed algorithm over a network. The extant literature on computing functions in distributed networks such as wired and wireless sensor networks and…