Related papers: Admissible anytime-valid sequential inference must…
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework…
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…
In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar…
In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…
We argue for supplementing the process of training a prediction algorithm by setting up a scheme for detecting the moment when the distribution of the data changes and the algorithm needs to be retrained. Our proposed schemes are based on…
A/B tests are typically analyzed via frequentist p-values and confidence intervals; but these inferences are wholly unreliable if users endogenously choose samples sizes by *continuously monitoring* their tests. We define *always valid*…
Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…
A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…
This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
We propose a new algorithmic framework for sequential hypothesis testing with i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and independence testing as special cases. It is novel in several ways: (a) it takes…
A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference…
We propose a sequential test for detecting arbitrary distribution shifts that allows conformal test martingales (CTMs) to work under a fixed, reference-conditional setting. Existing CTM detectors construct test martingales by continually…
Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshadowed by Robbins,…
Supermartingales are here defined on a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators one of them providing a…
We introduce a general methodology for quantitative model checking and control synthesis with supermartingale certificates. We show that every specification that is invariant to time shifts admits a stochastic invariant that bounds its…
The family of log-concave density functions contains various kinds of common probability distributions. Due to the shape restriction, it is possible to find the nonparametric estimate of the density, for example, the nonparametric maximum…