Related papers: Large deviations for weighted empirical mean with …
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…
We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
This paper is concerned with detecting the presence of out of sample predictability in linear predictive regressions with a potentially large set of candidate predictors. We propose a procedure based on out of sample MSE comparisons that is…
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…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
A popular approach for comparing gene expression levels between (replicated) conditions of RNA sequencing data relies on counting reads that map to features of interest. Within such count-based methods, many flexible and advanced…
Weighting methods are used in observational studies to adjust for covariate imbalances between treatment and control groups. Entropy balancing (EB) is an alternative to inverse probability weighting with an estimated propensity score. The…
It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…
Recent work used importance sampling ideas for better variational bounds on likelihoods. We clarify the applicability of these ideas to pure probabilistic inference, by showing the resulting Importance Weighted Variational Inference (IWVI)…
We find the perhaps surprising inequality that the weighted average of independent and identically distributed Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
Drawdowns are essential aspects of risk assessment in investment management. They offer a more natural measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) distributions of returns.…
We establish large deviation type estimates for i.i.d. products of two dimensional random matrices with finitely supported probability distribution. The estimates are stable under perturbations and require no irreducibility assumptions. In…
We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in…
The median absolute deviation (MAD) is a robust measure of scale that is simple to implement and easy to interpret. Motivated by this, we introduce interval estimators of the MAD to make reliable inferences for dispersion for a single…
In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative extropy are…
The detection of influential observations for the standard least squares regression model is a question that has been extensively studied. LAD regression diagnostics offers alternative approaches whose main feature is the robustness. In…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…