Related papers: Bahadur representations for the bootstrap median a…

For more than $50$ years the {\it Mean Measure of Divergence} (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology…

We investigate a Bahadur-Kiefer type representation for the p-th empirical quantile corresponding to a sample of n i.i.d. random variables, when 0<p<1 is a sequence which, in particular, may tend to 0 or 1, i.e. we consider the case of…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

We consider a high quantile homogeneity test to determine whether a certain set of explanatory variables has homogeneous effects on different high quantiles of the response variable in the tail. To accommodate for situations under both the…

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

Entropy estimation plays a crucial role in various fields, such as information theory, statistical data science, and machine learning. However, traditional entropy estimation methods often struggle with complex data distributions.…

We introduce a new one-parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive…

The posterior in probabilistic programs with stochastic support decomposes as a weighted sum of the local posterior distributions associated with each possible program path. We show that making predictions with this full posterior…

In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve…

Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been…

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…

Mean-field Variational Bayes (MFVB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when MFVB provides accurate posterior means for…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…

In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…

The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes…