Related papers: A criterion for hypothesis testing for stationary …
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
The concept of homology, originally developed as a useful tool in algebraic topology, has by now become pervasive in quite different branches of mathematics. The notion particularly appears quite naturally in ergodic theory in the study of…
In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…
For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients, we find necessary and…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
We define a notion of entropy for an infinite family $\mathcal{C}$ of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}$ under every ergodic transformation if and only if…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way.…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
We show homogenization for a family of $\mathbb{R}^d$-valued stable-like processes $(X_t^{\epsilon;\theta})_{t\ge 0}$, $\epsilon\in(0,1]$, whose (random) Fourier symbols equal…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…
Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null…
We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…