Related papers: Sequential Nonparametric Testing with the Law of t…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
We propose a new class of metrics, called the survival independence divergence (SID), to test dependence between a right-censored outcome and covariates. A key technique for deriving the SIDs is to use a counting process strategy, which…
This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the…
We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…
A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric…
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying parameters. This result complements recent annealed (averaged)…
A non parametric method based on the empirical likelihood is proposed for detecting the change in the coefficients of high-dimensional linear model where the number of model variables may increase as the sample size increases. This amounts…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…
We propose a general framework of sequential testing procedures based on $U$-statistics which contains as an example a sequential CUSUM test based on differences in mean but also includes a robust sequential Wilcoxon change point procedure.…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…