Related papers: Ridge-penalised spectral least-squares estimation …

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…

Randomized algorithms can be used to speed up the analysis of large datasets. In this paper, we develop a unified methodology for statistical inference via randomized sketching or projections in two of the most fundamental problems in…

We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…

We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…

A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method…

Here we propose a novel searching scheme for a tuning parameter in high-dimensional penalized regression methods to address variable selection and modeling when sample sizes are limited compared to the data dimensions. Our method is…

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for…

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

This paper is concerned with the detection of multiple change-points in the joint distribution of independent categorical variables. The procedures introduced rely on model selection and are based on a penalized least-squares criterion.…

We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…

We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent samples. Our procedures are based on model selection by minimization of a…

Projected kernel calibration is a newly proposed frequentist calibration method, which is asymptotic normal and semi-parametric. Its loss function is usually referred to as the PK loss function. In this work, we prove the uniform…

Spectroscopic measurements can show distorted spectral shapes arising from a mixture of absorbing and scattering contributions. These distortions (or baselines) often manifest themselves as non-constant offsets or low-frequency…

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…

We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourself to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and…