Related papers: Uniform Estimation and Inference for Nonparametric…
The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…
In this paper, we establish a uniform error rate of a Bahadur representation for local polynomial estimators of quantile regression functions. The error rate is uniform over a range of quantiles, a range of evaluation points in the…
The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…
We study how the divide and conquer principle --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- works in non-standard problems where…
Existing identification and estimation methods for semiparametric sample selection models rely heavily on exclusion restrictions. However, it is difficult in practice to find a credible excluded variable that has a correlation with…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
For a class of martingales, this paper provides a framework on the uniform consistency with broad applicability. The main condition imposed is only related to the conditional variance of the martingale, which holds true for stationary…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular…