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

Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1