Related papers: Time-uniform, nonparametric, nonasymptotic confide…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
We analyse the asymptotic behaviour of the probability of observing the expected number of successes at each stage of a sequence of nested Bernoulli trials. Our motivation is the attempt to give a genuinely frequentist interpretation to the…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-armed bandits, off-policy evaluation, election auditing,…
We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs.…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
This paper considers the problem of constructing a confidence sequence, which is a sequence of confidence intervals that hold uniformly over time, for estimating the mean of bounded real-valued random processes. This paper revisits the…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
When assessing risks on a finite-time horizon, the problem can often be reduced to the study of a random sequence $C(N)=(C_1,\ldots,C_N)$ of random length $N$, where $C(N)$ comes from the product of a matrix $A(N)$ of random size $N \times…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We demonstrate and discuss nonasymptotic bounds in probability for the cost of a regression scheme with a general loss function from the perspective of the Rademacher theory, and for the optimality with respect to the average…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…