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University of Washington

1. Shi, Xuetao. Uniform Inference when Parameters are Subject to Linear Inequality Constraints.

Degree: PhD, 2021, University of Washington

URL: http://hdl.handle.net/1773/46774

This dissertation studies the problem of uniform inference when model parameters are sub- ject to linear inequality constraints. Linear inequality constraints such as non-negativity and monotonicity are often implied by nature of the parameters or imposed by economic theory. Chapter 1 seeks to develop Wald-type, QLR, and score-type tests for testing linear equality constraints against two-sided alternative hypotheses in a general class of extremum estimation problems. The null asymptotic distributions of Wald and QLR statistics are discontinuous in model parameters demanding for uniform inference, and the one of score statistic depends on a polytope projection. For each test, we provide steps on obtaining the critical value and conditions under which the asymptotic size is controlled and the test is consistent. Linear inequality constraints are particularly common in models for random inter- vals. Chapter 2 develops asymptotically uniformly valid tests for linear equality constraints on the parameters in the interval data model. Moreover, based on interval arithmetic, we introduce a new interval data model to extend and generalize the commonly used one, and propose a coefficient of determination.More specifically, the first chapter develops Wald-type, QLR, and score-type tests for linear equality constraints against two-sided alternative hypotheses in a general class of ex- tremum estimation problems, where the parameter space is characterized by a finite number of linear equality and inequality constraints. It shows that the null asymptotic distribu-
tions of the Wald and QLR statistics are discontinuous in an implicit nuisance parameter and proposes an algorithm to identify it. In contrast, the null asymptotic distribution of the score statistic is not discontinuous in any model parameter but depends on a polytope projection. The chapter presents an algorithm based on the Fourier-Motzkin elimination to compute such projection. It studies consistency and local power properties of the three tests, and finds that the score test may be inconsistent due to the use of partial information in the parameter space through projection. Numerical results from a Monte Carlo study of the finite sample performance of our tests are presented. An empirical illustration on Mincer earnings regression is conducted.
Via generalized interval arithmetic, the second chapter proposes a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals in which parameters in the model satisfy linear inequality constraints. It extends the commonly used Center and Range (CR) model in several directions. For the GIA-CR model, this chapter constructs a constrained estimator of the parameter vector and proposes a coefficient of determination. It develops asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. At last, this chapter conducts a simulation study to examine the finite sample performance of the estimator and test for the correct specification of the CR model against the…
*Advisors/Committee Members: Fan, Yanqin (advisor).*

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APA (6^{th} Edition):

Shi, X. (2021). Uniform Inference when Parameters are Subject to Linear Inequality Constraints. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/46774

Chicago Manual of Style (16^{th} Edition):

Shi, Xuetao. “Uniform Inference when Parameters are Subject to Linear Inequality Constraints.” 2021. Doctoral Dissertation, University of Washington. Accessed April 22, 2021. http://hdl.handle.net/1773/46774.

MLA Handbook (7^{th} Edition):

Shi, Xuetao. “Uniform Inference when Parameters are Subject to Linear Inequality Constraints.” 2021. Web. 22 Apr 2021.

Vancouver:

Shi X. Uniform Inference when Parameters are Subject to Linear Inequality Constraints. [Internet] [Doctoral dissertation]. University of Washington; 2021. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/1773/46774.

Council of Science Editors:

Shi X. Uniform Inference when Parameters are Subject to Linear Inequality Constraints. [Doctoral Dissertation]. University of Washington; 2021. Available from: http://hdl.handle.net/1773/46774