Corpus ID: 219792048

Inference for local parameters in convexity constrained models

@article{Deng2020InferenceFL,
  title={Inference for local parameters in convexity constrained models},
  author={Hang Deng and Qiyang Han and Bodhisattva Sen},
  journal={arXiv: Statistics Theory},
  year={2020}
}
We consider the problem of inference for local parameters of a convex regression function $f_0: [0,1] \to \mathbb{R}$ based on observations from a standard nonparametric regression model, using the convex least squares estimator (LSE) $\widehat{f}_n$. For $x_0 \in (0,1)$, the local parameters include the pointwise function value $f_0(x_0)$, the pointwise derivative $f_0'(x_0)$, and the anti-mode (i.e., the smallest minimizer) of $f_0$. The existing limiting distribution of the estimation error… Expand

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