Related papers: Testing equality of functions under monotonicity c…
In this paper we develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time…
The interaction between points in a spatial point process can be measured by its empty space function F, its nearest-neighbour distance distribution function G, and by combinations such as the J-function $J = (1-G)/(1-F)$. The estimation of…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…
We consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n)$ such that, conditional on the $X_i$, the $Y_i$ are independent random variables with distribution functions $F_{X_i}$, where $(F_x)_x$ is an unknown family of distribution…
In the context of functional data analysis, we propose new two sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
For $m,n\in \mathbb{N}$, let $0 < \alpha_i,\beta_j,\lambda_{ij} \leq 1$ be such that $\sum_{j=1}^n \lambda_{ij} = \alpha_i$, $\sum_{i=1}^m \lambda_{ij} = \beta_j$, and $\sum_{i=1}^m \alpha_i = \sum_{j=1}^n \beta_j \leq 1$. We prove that the…
Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…
This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the…