相关论文: Asymptotic behaviour of penalized robust estimator…

The Wallace--Freeman estimator is a classical invariant point estimator whose large-sample properties have not been fully developed in a modern asymptotic framework. We show that the estimator can be formulated as a penalised M-estimator…

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…

We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…

We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is non differentiable when pairs of columns in the optimization…

We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…

We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory…

This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model as the sizes of the rows, columns, and cells tend to infinity. Under very mild…

We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…

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…

This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…

We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When…

A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as…

Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…

A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

We study reinforcement learning in continuous state and action spaces endowed with a metric. We provide a refined analysis of a variant of the algorithm of Sinclair, Banerjee, and Yu (2019) and show that its regret scales with the…