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We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Large-scale data analysis poses both statistical and computational problems which need to be addressed simultaneously. A solution is often straightforward if the data are homogeneous: one can use classical ideas of subsampling and mean…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…
In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a…
I study partial identification of distributional parameters in triangular systems. This model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity and selection on…
Difficulties may arise when analyzing longitudinal data using mixed-effects models if there are nonparametric functions present in the linear predictor component. This study extends the use of semiparametric mixed-effects modeling in cases…
The degree heterogeneity and homophily are two typical features in network data. In this paper, we formulate a general model for undirected networks with these two features and present the moment estimation for inferring the degree and…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
Statistical inference on histograms and frequency counts plays a central role in categorical data analysis. Moving beyond classical methods that directly analyze labeled frequencies, we introduce a framework that models the multiset of…