Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing

Existing asymptotic theory for inference in nonparametric series estimation typically imposes an undersmoothing condition that the number of series terms is sufficiently large to make bias asymptotically negligible. However, there is no formally justified data-dependent method for this in practice. This paper constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide an empirical process theory for the t-statistics indexed by the number of series terms. Using this result, I show that test based on the infimum of the t-statistics and its asymptotic critical value controls asymptotic size with undersmoothing condition. Using this test, we can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Allowing asymptotic bias without the undersmoothing condition, I show that CI based on the infimum of the t-statistics bounds coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on the standard CI with the possible ad hoc choice of series terms

Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing

Existing asymptotic theory for inference in nonparametric series estimation typically imposes an undersmoothing condition that the number of series terms is sufficiently large to make bias asymptotically negligible. However, there is no formally justified data-dependent method for this in practice. This paper constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide an empirical process theory for the t-statistics indexed by the number of series terms. Using this result, I show that test based on the infimum of the t-statistics and its asymptotic critical value controls asymptotic size with undersmoothing condition. Using this test, we can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Allowing asymptotic bias without the undersmoothing condition, I show that CI based on the infimum of the t-statistics bounds coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on the standard CI with the possible ad hoc choice of series terms

Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms

Nonparametric series estimation often involves specification search over the different number of series terms due to the unknown smoothness of underlying function. This paper considers pointwise inference in the nonparametric series regression for the conditional mean and introduces test based on the supremum of t-statistics over different series terms. I show that proposed test has correct asymptotic size and it can be used to construct confidence intervals that have correct asymptotic coverage probability uniform in the number of series terms. With possibly large bias in this setup, I also consider infimum of the t-statistics which is shown to reduce size distortions in such case. Asymptotic distribution of the test statistics, asymptotic size, and local power results are derived. I investigate the performance of the proposed tests and CIs in various simulation setups as well as an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002). I also extend our inference methods to the partially linear model setup

Higher Order Approximation of IV Estimators with Invalid Instruments

This paper considers the instrument selection problem in instrumental variable (IV) regression model when there is a large set of instruments with potential invalidity. I derive higher-order mean square error (MSE) approximation of two-stage least squares (2SLS), limited information maximum likelihood (LIML), Fuller (FULL) and bias-adjusted 2SLS (B2SLS) estimators with allowing for local violation of the instrument-exogeneity conditions. Based on the approximation to the higher-order MSE, I propose instrument selection criteria that are robust to potential invalidity of instruments. Furthermore, I also show the optimality results of instrument selection criteria in Donald and Newey (2001, Econometrica) under faster than N^(-1/2) locally invalid instruments specication

Essays on nonparametric inference and instrument selection

My dissertation consists of two chapters on nonparametric inference and model selection in econometric models. Researchers in economics and social science need reliable models and statistical tools to quantify economic relationships and uncertainty associated with data. In practice, researchers often evaluate their object of interests with various specifications in the first stage of analysis or select model by some criteria. Unfortunately, commonly used statistical methods may fail to assess uncertainty inherent in the first step specification search. Moreover, some existing model selection criteria may be fragile due to model misspecification errors. All these methods can lead to misleading conclusions without valid, robust corrections. To quantify and test economic theories more accurately in such cases, researchers and policy makers need more reliable and robust methods. My research investigates these issues and provides practical methods in empirical research with rigorous theoretical justifications. First chapter provides new inference methods in nonparametric series regression with data dependent number of series terms. Nonparametric series estimation have increased their popularity as it gives flexible method addressing potential misspecification of the parametric model. However, implementation in practice requires a choice of the number of series terms and the estimation and inference may largely depend on its choice. Existing asymptotic theory for inference in nonparametric series estimation typically imposes an undersmoothing condition that the number of series terms is sufficiently large to make bias asymptotically negligible. However, there is no formally justified data-dependent method for this in practice. This chapter constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide a uniform asymptotic theory for the t-statistic process indexed by the number of series terms. Using this result, I show that the test based on the infimum of the t-statistics and its asymptotic critical value controls the asymptotic size with the undersmoothing condition. We can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Even when asymptotic bias terms are present without the undersmoothing condition, I show that the CI based on the infimum of the t-statistics bounds the coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on existing methods with possibly ad hoc choice of series terms. Second chapter provides instrument selection criteria in instrumental variable (IV) regression model when there is a large set of instruments with potential invalidity. Economic data identified by IV model sometimes involve large sets of potential instruments and debates about their validity. Existing methods for instrument selection are largely based on a priori assumption of an instrument’s validity and/or based on the first-order asymptotics, which may lead to a large finite sample bias with many and invalid instruments. First, I derive higher-order mean square error (MSE) approximation for two-stage least squares (2SLS), limited information maximum likelihood (LIML), modified Fuller (FULL) and bias-adjusted 2SLS (B2SLS) estimator allowing locally invalid instruments. Based on the approximation to the higher-order MSE, I propose an invalidity-robust instrument selection criteria (IRC) that capture two sources of finite sample bias at the same time: bias from using many instruments and bias from invalid instruments. I also show optimality result of choice of instruments based on the criteria of Donald and Newey (2001) under certain locally invalid instruments specification

A Doubly Corrected Robust Variance Estimator for Linear GMM

We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. Formal stochastic expansions are derived to show the proposed double correction estimates the variance of some higher-order terms in the expansion. In addition, the proposed double correction provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time

Lord of the x86 Rings: A Portable User Mode Privilege Separation Architecture on x86

Modern applications often involve processing of sensitive information. However, the lack of privilege separation within the user space leaves sensitive application secret such as cryptographic keys just as unprotected as a "hello world" string. Cutting-edge hardware-supported security features are being introduced. However, the features are often vendor-specific or lack compatibility with older generations of the processors. The situation leaves developers with no portable solution to incorporate protection for the sensitive application component. We propose LOTRx86, a fundamental and portable approach for user-space privilege separation. Our approach creates a more privileged user execution layer called PrivUser by harnessing the underused intermediate privilege levels on the x86 architecture. The PrivUser memory space, a set of pages within process address space that are inaccessible to user mode, is a safe place for application secrets and routines that access them. We implement the LOTRx86 ABI that exports the privcall interface to users to invoke secret handling routines in PrivUser. This way, sensitive application operations that involve the secrets are performed in a strictly controlled manner. The memory access control in our architecture is privilege-based, accessing the protected application secret only requires a change in the privilege, eliminating the need for costly remote procedure calls or change in address space. We evaluated our platform by developing a proof-of-concept LOTRx86-enabled web server that employs our architecture to securely access its private key during an SSL connection. We conducted a set of experiments including a performance measurement on the PoC on both Intel and AMD PCs, and confirmed that LOTRx86 incurs only a limited performance overhead