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We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop…
Data augmentation is essential when applying Machine Learning in small-data regimes. It generates new samples following the observed data distribution while increasing their diversity and variability to help researchers and practitioners…
Randomized A/B tests within online learning platforms represent an exciting direction in learning sciences. With minimal assumptions, they allow causal effect estimation without confounding bias and exact statistical inference even in small…
P-hacking poses challenges to traditional hypothesis testing. In this paper, we propose a robust method for the one-sample significance test that can protect against p-hacking from sample manipulation. Precisely, assuming a sequential…
We consider finite-sample inference for a single regression coefficient in the fixed-design linear model $Y = Z\beta + bX + \varepsilon$, where $\varepsilon\in\mathbb{R}^n$ may exhibit complex dependence or heterogeneity. We develop a group…
Pearson's correlation is among the mostly widely reported measures of association. The strength of the statistical evidence for linear association is determined by the p-value of a hypothesis test. If the true distribution of a dataset is…
The literature on hypothesis testing with data-dependent and post-hoc significance levels relies on a particular extension of the Type-I error to data-dependent levels. Existing arguments for this extension are heuristic, and primarily…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Many real-world classification problems are significantly class-imbalanced to detriment of the class of interest. The standard set of proper evaluation metrics is well-known but the usual assumption is that the test dataset imbalance equals…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
Importance sampling is a common technique for Monte Carlo approximation, including Monte Carlo approximation of p-values. Here it is shown that a simple correction of the usual importance sampling p-values creates valid p-values, meaning…
We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make…
Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of…
Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices.…
The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…
Sample overlap is a common issue in evidence synthesis in the field of medical research, particularly when integrating findings from observational studies utilizing existing databases such as registries. Due to the general inaccessibility…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…