Two-Stage Maximum Score Estimator
This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score (TSMS) estimator since our estimator involves a first-stage nonparametric regression when applied to the binary choice model of Manski (1975, 1985). We characterize the asymptotic distribution of the TSMS estimator, which features phase transitions depending on the dimension and thus the convergence rate of the first-stage estimation. Effectively, the first-stage nonparametric estimator serves as an imperfect smoothing function on a non-smooth criterion function, leading to the pivotality of the first-stage estimation error with respect to the second-stage convergence rate and asymptotic distribution
Code (0)
등록된 구현이 없습니다.
Tasks
regressionVocal Bursts Valence PredictionSimilar Papers 제목 키워드 기반
ReLU-Based and DNN-Based Generalized Maximum Score Estimators
We propose a new formulation of the maximum score estimator that uses compositions of rectified linear unit (ReLU) functions, instead of indicator functions as in Manski (1975,1985), to encode the sign alignment restrict…
Kernel Exponential Family Estimation via Doubly Dual Embedding
We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual…
Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likeli…
Is Score Matching Suitable for Estimating Point Processes?
Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum li…
Point ProcessesLow-Complexity Methods for Estimation After Parameter Selection
Statistical inference of multiple parameters often involves a preliminary parameter selection stage. The selection stage has an impact on subsequent estimation, for example by introducing a selection bias. The post-selec…
Selection bias