2021/10/08 by Shakeeb Khan, Xiaoying Lan, Khan, Shakeeb +4 · 1 citation
Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2110.04388
openalex publication_date 2021/10/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper we propose new approaches to estimating large dimensional\nmonotone index models. This class of models has been popular in the applied and\ntheoretical econometrics literatures as it includes discrete choice,\nnonparametric transformation, and duration models. A main advantage of our\napproach is computational. For instance, rank estimation procedures such as\nthose proposed in Han (1987) and Cavanagh and Sherman (1998) that optimize a\nnonsmooth, non convex objective function are difficult to use with more than a\nfew regressors and so limits their use in with economic data sets. For such\nmonotone index models with increasing dimension, we propose to use a new class\nof estimators based on batched gradient descent (BGD) involving nonparametric\nmethods such as kernel estimation or sieve estimation, and study their\nasymptotic properties. The BGD algorithm uses an iterative procedure where the\nkey step exploits a strictly convex objective function, resulting in\ncomputational advantages. A contribution of our approach is that our model is\nlarge dimensional and semiparametric and so does not require the use of\nparametric distributional assumptions.\n