Related papers: Power comparison of sequential testing by betting …
Martingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and its extensions for various counting processes. We first consider a…
This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…
Anytime valid sequential tests permit us to stop testing based on the current data, without invalidating the inference. Given a maximum number of observations $N$, one may believe this must come at the cost of power when compared to a…
We propose a nonparametric procedure to test for changes in correlation matrices at an unknown point in time. The new test requires only mild assumptions on the serial dependence structure and has considerable power in finite samples. We…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
Consider an observation of a multivariate temporal point process $N$ with law $\mathcal P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathcal P$ belongs to a given parametric family, we construct a convergent…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
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…
In this paper, we consider testing the homogeneity of risk differences in independent binomial distributions especially when data are sparse. We point out some drawback of existing tests in either controlling a nominal size or obtaining…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
We consider a $d$-dimensional continuous martingale $X(t)$ with quadratic variation matrix $\langle X\rangle_t=\int_0^t \Sigma(s)\,ds$ and develop tests for the rank of its spot covariance matrix $\Sigma(t)$, $t\in[0,1]$. The process $X$ is…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering…
Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Forecast evaluations aim to choose an accurate forecast for making decisions by using loss functions. However, different loss functions often generate different ranking results for forecasts, which complicates the task of comparisons. In…
In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…