相关论文: Optimal Linear Discriminators For The Discrete Cho…
This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish…
We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to…
This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we…
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…
In this paper we study the applicability of the bootstrap to do inference on Manski's maximum score estimator under the full generality of the model. We propose three new, model-based bootstrap procedures for this problem and show their…
The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a…
Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are…
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…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing…