Related papers: Test Martingales for bounded random variables
A strict local martingale is a local martingale that is not a martingale. We investigate how such a process might arise from a true martingale as a result of an enlargement of the filtration. We study and implement a particular type of…
Recent advances in reasoning techniques have substantially improved the performance of large language models (LLMs), raising expectations for their ability to provide accurate, truthful, and reliable information. However, emerging evidence…
We address the problem of testing conditional mean and conditional variance for non-stationary data. We build e-values and p-values for four types of non-parametric composite hypotheses with specified mean and variance as well as other…
In this paper in which we address the evaluation of measurement process quality, we mainly focus on the evaluation procedure, as far as it is based on the numerical measurement outcomes. We challenge the approach where the "exact" value of…
In this article we relate the set of structure preserving equivalent martingale measures $(\mathcal{M})$ for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
Let $(S_0,S_1,...)$ be a supermartingale relative to a nondecreasing sequence of $\sigma$-algebras $H_{\le0},H_{\le1},...$, with $S_0\le0$ almost surely (a.s.) and differences $X_i:=S_i-S_{i-1}$. Suppose that $X_i\le d$ and $\mathsf…
Suppose we observe an infinite series of coin flips $X_1,X_2,\ldots$, and wish to sequentially test the null that these binary random variables are exchangeable. Nonnegative supermartingales (NSMs) are a workhorse of sequential inference,…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…
Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical function $T(r)$ with its simulated counterparts from the null model. However, the type I…
We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
Let $\mathbb{\hat{E}}$ be the upper expectation of a weakly compact but non-dominated family $\mathcal{P}$ of probability measures. Assume that $Y$ is a $d$-dimensional $\mathcal{P}$-semimartingale under $\mathbb{\hat{E}}$. Given an open…
We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…
We give a bare-hands approach to the martingale representation theorem for integer valued random measures, which allows for a wide class of infinite activity jump processes, as well as all processes with well-ordered jumps.
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…