Related papers: Asymptotics of resampling without replacement in r…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional…
We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…
Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the…
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…
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized…
We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make…
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…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
This paper studies phase transitions for the existence of unregularized M-estimators under proportional asymptotics where the sample size $n$ and feature dimension $p$ grow proportionally with $n/p \to \delta \in (1, \infty)$. We study the…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…