Related papers: Optimum thresholding using mean and conditional me…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…
The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function…
The inefficiency of using an unbiased estimator in a Monte Carlo procedure can be quantified using an inefficiency constant, equal to the product of the variance of the estimator and its mean computational cost. We develop methods for…
This paper addresses the following simple question about sparsity. For the estimation of an $n$-dimensional mean vector $\boldsymbol{\theta}$ in the Gaussian sequence model, is it possible to find an adaptive optimal threshold estimator in…
Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random…
Individualized treatment rules (ITRs) are considered a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate the average treatment effect conditional on a subject's…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
We develop a projected least squares estimator for the change point parameter in a high dimensional time series model with a potential change point. Importantly we work under the setup where the jump size may be near the boundary of the…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…