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Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for…
This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (Value-at-Risk, Expected Shortfall) or reinsurance premiums and related quantities (Large Claim Index,…
Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters…
We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear function of a given…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear…
We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
This paper proposes a novel and simple linear model to capture line losses for use in linearized DC models, such as optimal power flow (DC-OPF) and security-constrained economic dispatch (SCED). The \textit{Line Loss Outer Approximation}…
Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…
Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is…