Related papers: Asymptotics for minimisers of convex processes

This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…

Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic…

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…

We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…

Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semi-parametric Cox model is widely used to study different types of data arising…

Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…

We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…

We study regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We provide a detailed proof of asymptotic normality of the covariate-adjusted estimator under minimal…

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…

Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide…

Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…

We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…

We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…

This paper introduces and investigates a regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. Under this regularity condition, the normalization argument in asymptotic analysis…