# A Unifying Framework for Testing Shape Restrictions

@inproceedings{Fang2021AUF, title={A Unifying Framework for Testing Shape Restrictions}, author={Zheng Fang}, year={2021} }

This paper makes the following original contributions. First, we develop a unifying framework for testing shape restrictions based on the Wald principle. The test has asymptotic uniform size control and is uniformly consistent. Second, we examine the applicability and usefulness of some prominent shape enforcing operators in implementing our framework. In particular, in stark contrast to its use in point and interval estimation, the rearrangement operator is inapplicable due to a lack of…

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SHOWING 1-10 OF 66 REFERENCES

Shape-Enforcing Operators for Point and Interval Estimators

- Mathematics, Economics
- 2018

A common problem in econometrics, statistics, and machine learning is to estimate and make inference on functions that satisfy shape restrictions. For example, distribution functions are…

Inference on Directionally Differentiable Functions

- Mathematics, EconomicsThe Review of Economic Studies
- 2018

This paper studies an asymptotic framework for conducting inference on parameters of the form ( 0), where is a known directionally dierentiable function and 0 is estimated by ^ n. In these settings,…

Constrained conditional moment restriction models

- Mathematics
- 2015

This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least…

Refinements of the Kiefer-Wolfowitz theorem and a test of concavity

- Mathematics, EconomicsElectronic Journal of Statistics
- 2019

This paper studies estimation of and inference on a distribution function $F$ that is concave on the nonnegative half line and admits a density function $f$ with potentially unbounded support. When…

Testing Regression Monotonicity in Econometric Models

- Economics
- 2012

Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design eff ective and practical econometric…

Inference in nonparametric/semiparametric moment equality models with shape restrictions

- Mathematics, Economics
- 2020

This paper studies the inference problem of an infinite-dimensional parameter with a shape restriction. This parameter is identified by arbitrarily many unconditional moment equalities. The shape…

Intersection Bounds: Estimation and Inference

- Mathematics, Computer Science
- 2009

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the…

Quantile and Probability Curves without Crossing

- Mathematics, Economics
- 2007

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem.…

Inference Based on Conditional Moment Inequalities

- Mathematics
- 2011

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that…