Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiparametric Efficiency in Convexity Constrained Single Index Model   We consider estimation and inference in a single index regression model with
an unknown convex link function. We introduce a convex and Lipschitz
constrained least squares estimator (CLSE) for both the parametric and the
nonparametric components given independent and identically distributed
observations. We prove the consistency and find the rates of convergence of the
CLSE when the errors are assumed to have only $q \ge 2$ moments and are allowed
to depend on the covariates. When $q\ge 5$, we establish $n^{-1/2}$-rate of
convergence and asymptotic normality of the estimator of the parametric
component. Moreover, the CLSE is proved to be semiparametrically efficient if
the errors happen to be homoscedastic. {We develop and implement a numerically
stable and computationally fast algorithm to compute our proposed estimator in
the R package~\texttt{simest}}. We illustrate our methodology through extensive
simulations and data analysis. Finally, our proof of efficiency is geometric
and provides a general framework that can be used to prove efficiency of
estimators in a wide variety of semiparametric models even when they do not
satisfy the efficient score equation directly.

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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin