Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models

• URL: http://arxiv.org/abs/2006.09587v6
• Date: Wed, 06 Nov 2024 20:42:55 GMT
• Title: Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models
• Authors: Christoph Breunig, Xiaohong Chen,
• Abstract summary: We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments.
• Score: 2.07706336594149
• License:
• Abstract: We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning parameters and Bonferroni adjusted chi-squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in $L^{2}$. That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in $L^{2}$ are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite-sample power greatly exceeds existing non-adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.

Related papers

• A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference) [3.622435665395788]
  We introduce a kernel-based measure for detecting differences between two conditional distributions. When the two conditional distributions are the same, the estimate has a Gaussian limit and its variance has a simple form that can be easily estimated from the data. We also provide a resampling based test using our estimate that applies to the conditional goodness-of-fit problem.
  arXiv  Detail & Related papers  (2024-07-23T15:04:38Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Uncertainty-Calibrated Test-Time Model Adaptation without Forgetting [55.17761802332469]
  Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and test data by adapting a given model w.r.t. any test sample. Prior methods perform backpropagation for each test sample, resulting in unbearable optimization costs to many applications. We propose an Efficient Anti-Forgetting Test-Time Adaptation (EATA) method which develops an active sample selection criterion to identify reliable and non-redundant samples.
  arXiv  Detail & Related papers  (2024-03-18T05:49:45Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Bootstrapped Edge Count Tests for Nonparametric Two-Sample Inference Under Heterogeneity [5.8010446129208155]
  We develop a new nonparametric testing procedure that accurately detects differences between the two samples. A comprehensive simulation study and an application to detecting user behaviors in online games demonstrates the excellent non-asymptotic performance of the proposed test.
  arXiv  Detail & Related papers  (2023-04-26T22:25:44Z)
• Minimax Instrumental Variable Regression and $L_2$ Convergence Guarantees without Identification or Closedness [71.42652863687117]
  We study nonparametric estimation of instrumental variable (IV) regressions. We propose a new penalized minimax estimator that can converge to a fixed IV solution. We derive a strong $L$ error rate for our estimator under lax conditions.
  arXiv  Detail & Related papers  (2023-02-10T18:08:49Z)
• A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates [1.1587112467663427]
  This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The test is scale-invariant and is robust to heteroskedastic errors. An empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed test.
  arXiv  Detail & Related papers  (2022-04-30T06:13:15Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing [87.17253904965372]
  We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. We show that these errors decrease exponentially with decay rates given by the measured relative entropies between the two states.
  arXiv  Detail & Related papers  (2021-04-30T00:52:48Z)
• Adaptive Estimation of Quadratic Functionals in Nonparametric Instrumental Variable Models [1.6539154611511273]
  This paper considers adaptive estimation of quadratic functionals in the nonparametric instrumental variables (NPIV) models. We first show that a leave-one-out, sieve NPIV estimator attains a convergence rate that coincides with the lower bound. The adaptive estimator attains the minimax optimal rate in the severely ill-posed case and in the regular, mildly ill-posed case, but up to a multiplicative $sqrtlog n$ in the irregular, mildly ill-posed case.
  arXiv  Detail & Related papers  (2021-01-28T21:14:02Z)
• Minimax Estimation of Conditional Moment Models [40.95498063465325]
  We introduce a min-max criterion function, under which the estimation problem can be thought of as solving a zero-sum game. We analyze the statistical estimation rate of the resulting estimator for arbitrary hypothesis spaces. We show how our modified mean squared error rate, combined with conditions that bound the ill-posedness of the inverse problem, lead to mean squared error rates.
  arXiv  Detail & Related papers  (2020-06-12T14:02:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.