# Distributed Estimation and Inference for Semi-parametric Binary Response Models

arXiv: https://arxiv.org/abs/2210.08393 · HTML: https://mlsanity.com/paper/2210.08393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 62 references that are in the map.
- First posted on arXiv 15 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Distributed linear regression by averaging](https://mlsanity.com/paper/1810.00412/) (2018)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [First-order Newton-type Estimator for Distributed Estimation and Inference](https://mlsanity.com/paper/1811.11368/) (2018)
- [Smoothing quantile regressions](https://mlsanity.com/paper/1905.08535/) (2019)
- [Heterogeneity-aware and communication-efficient distributed statistical inference](https://mlsanity.com/paper/1912.09623/) (2019)
- [High-Dimensional Quantile Regression: Convolution Smoothing and Concave Regularization](https://mlsanity.com/paper/2109.05640/) (2021)
- [Distributed Inference for Linear Support Vector Machine](https://mlsanity.com/paper/1811.11922/) (2018)
- [A Distributed One-Step Estimator](https://mlsanity.com/paper/1511.01443/) (2015)
- [Distributed inference for quantile regression processes](https://mlsanity.com/paper/1701.06088/) (2017)
- [Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference](https://mlsanity.com/paper/2103.02860/) (2021)
- [Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guarantees](https://mlsanity.com/paper/2110.13113/) (2021)
- [Divide and Conquer in Non-standard Problems and the Super-efficiency Phenomenon](https://mlsanity.com/paper/1605.04446/) (2016)
- [Simultaneous Inference for Massive Data: Distributed Bootstrap](https://mlsanity.com/paper/2002.08443/) (2020)
- [Distributed Bootstrap for Simultaneous Inference Under High Dimensionality](https://mlsanity.com/paper/2102.10080/) (2021)
- [Distributed Adaptive Huber Regression](https://mlsanity.com/paper/2107.02726/) (2021)
- [Nonregular and Minimax Estimation of Individualized Thresholds in High Dimension with Binary Responses](https://mlsanity.com/paper/1905.10888/) (2019)
- [ReBoot: Distributed statistical learning via refitting bootstrap samples](https://mlsanity.com/paper/2207.09098/) (2022)

## Abstract (arXiv)

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 binary choice model under a distributed computing environment without pre-specifying the noise distribution. An intuitive divide-and-conquer estimator is computationally expensive and restricted by a non-regular constraint on the number of machines, due to the highly non-smooth nature of the objective function. We propose (1) a one-shot divide-and-conquer estimator after smoothing the objective to relax the constraint, and (2) a multi-round estimator to completely remove the constraint via iterative smoothing. We specify an adaptive choice of kernel smoother with a sequentially shrinking bandwidth to achieve the superlinear improvement of the optimization error over the multiple iterations. The improved statistical accuracy per iteration is derived, and a quadratic convergence up to the optimal statistical error rate is established. We further provide two generalizations to handle the heterogeneity of datasets and high-dimensional problems where the parameter of interest is sparse.