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We introduce a flexible parametric mixed effects model for correlated binary data, with parameters that can be directly interpreted as marginal odds ratios. This leads to a robust estimation equation with an optimal weighting matrix being…
Non-parametric maximum likelihood estimation encompasses a group of classic methods to estimate distribution-associated functions from potentially censored and truncated data, with extensive applications in survival analysis. These methods,…
This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…
Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…
Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are…
A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…
This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of…
In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate.…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a…
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
The aim of this note is to state a couple of general results about the properties of the penalized maximum likelihood estimators (pMLE) and of the posterior distribution for parametric models in a non-asymptotic setup and for possibly large…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first…
We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard.…
Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…
We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…
We consider the problem of max-min beamforming (MMB) for cell-free massive multi-input multi-output (MIMO) systems, where the objective is to maximize the minimum achievable rate among all users. Existing MMB methods are mainly based on…