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Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1

Shakeeb Khan, Xiaoying Lan, Elie Tamer, Qingsong Yao

arXiv 8 Oct 2021 · Econometrics · 1 citations (OpenAlex)

arXiv:2110.04388 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric transformation, and duration models. A main advantage of our approach is computational. For instance, rank estimation procedures such as those proposed in Han (1987) and Cavanagh and Sherman (1998) that optimize a nonsmooth, non convex objective function are difficult to use with more than a few regressors and so limits their use in with economic data sets. For such monotone index models with increasing dimension, we propose to use a new class of estimators based on batched gradient descent (BGD) involving nonparametric methods such as kernel estimation or sieve estimation, and study their asymptotic properties. The BGD algorithm uses an iterative procedure where the key step exploits a strictly convex objective function, resulting in computational advantages. A contribution of our approach is that our model is large dimensional and semiparametric and so does not require the use of parametric distributional assumptions.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1James L Powell, James H Stock, and Thomas M Stoker (1989) Semiparametric estimation of index coefficients0.7373367%
2Aaron K Han (1987) Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator0.73732100%
3Hidehiko Ichimura (1993) Semiparametric least squares (sls) and weighted sls estimation of single-index models0.73732100%
4Victor Chernozhukov, Denis Chetverikov, and Kengo Kato (2017) Central limit theorems and bootstrap in high dimensions0.64422100%
5Roger W Klein and Richard H Spady (1993) An efficient semiparametric estimator for binary response models0.64422100%
6Thomas M Stoker (1986) Consistent estimation of scaled coefficients0.64422100%
7Yanqin Fan, Fang Han, Wei Li, and Xiao-Hua Zhou (2020) On rank estimators in increasing dimensions0.58531100%
8Pragya Sur and Emmanuel J Candès (2019) A modern maximum-likelihood theory for high-dimensional logistic regression0.51121100%
9Y. Shin and Z. Todorov (2021) Exact computation of the maximum rank correlation estimator0.40511100%
10Alekh Agarwal, Sham Kakade, Nikos Karampatziakis, Le Song, and Grego… (2014) Least squares revisited: Scalable approaches for multi-class prediction0.40511100%

Showing the top 10 of 25 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Stochastic Learning of Semiparametric Monotone Index Models with Large Sample Size0.817115