Related papers: Optimal bounds for aggregation of affine estimator…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little…
It has been recently shown that nonparametric estimators of the additive regression function could be obtained in the presence of right censoring by coupling the marginal integration method with initial kernel-type Inverse Probability of…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
We discuss estimation and inference of conditional treatment effects in regression discontinuity (RD) designs with multiple scores. In addition to local linear regressions and the minimax-optimal estimator more recently proposed by Imbens…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
We develop an estimator for applications where the variable of interest is endogenous and researchers have access to aggregate instruments. Our method addresses the critical identification challenge -- unobserved confounding, which renders…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
Random samples are lossy summaries which allow queries posed over the data to be approximated by applying an appropriate estimator to the sample. The effectiveness of sampling, however, hinges on estimator selection. The choice of…
We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {\em simple observation schemes} and where set…
We derive formulas for the efficiency correction of cumulants with many efficiency bins. The derivation of the formulas is simpler than the previously suggested method, but the numerical cost is drastically reduced from the naive method.…