Bootstrap Inference Research Articles

Bootstrap inference for linear time-varying coefficient models in locally stationary time series

Time-varying coefficient models can capture evolving relationships. However, constructing asymptotic confidence bands for coefficient curves in these models is challenging due to slow convergence rates and the presence of various nuisance parameters. A residual-based sieve bootstrap method has recently been proposed to address these issues. While it successfully produces confidence bands with accurate empirical coverage, its applicability is restricted to strictly stationary processes. We introduce a new bootstrap scheme, the local blockwise wild bootstrap (LBWB), that allows for locally stationary processes. The LBWB can replicate the distribution of the parameter estimates while automatically accounting for nuisance parameters. An extensive simulation study reveals the superior performance of the LBWB compared to various benchmark approaches. It also shows the potential applicability of the LBWB in broader scenarios, including time-varying cointegrating models. We then examine herding effects in the Chinese renewable energy market using the proposed methods. Our findings strongly support the presence of herding behaviors before 2016, aligning with earlier studies. However, contrary to previous research, we find no significant evidence of herding between around 2018 and 2021. Online supplementary materials are available for this article.

Bootstrap inference on a factor model based average treatment effects estimator

We propose a novel bootstrap procedure for conducting inference for factor model-based average treatment effects estimators. Our method overcomes bias inherent to existing bootstrap procedures and substantially improves upon existing large sample normal inference theory in small sample settings. The finite sample improvements arising from the use of our proposed procedure are illustrated via a set of Monte Carlo simulations, and formal justification for the procedure is outlined.

A doubly robust estimator for the Mann Whitney Wilcoxon rank sum test when applied for causal inference in observational studies

ABSTRACT The Mann–Whitney–Wilcoxon rank sum test (MWWRST) is a widely used method for comparing two treatment groups in randomized control trials, particularly when dealing with highly skewed data. However, when applied to observational study data, the MWWRST often yields invalid results for causal inference. To address this limitation, Wu et al. (Causal inference for Mann–Whitney–Wilcoxon rank sum and other nonparametric statistics, Stat. Med. 33 (2014), pp. 1261–1271) introduced an approach that incorporates inverse probability weighting (IPW) into this rank-based statistic to mitigate confounding effects. Subsequently, Mao (On causal estimation using U-statistics, Biometrika 105 (2018), pp. 215–220), Zhang et al. (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010), and Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) extended this IPW estimator to develop doubly robust estimators. Nevertheless, each of these approaches has notable limitations. Mao's method imposes stringent assumptions that may not align with real-world study data. Zhang et al.'s (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010) estimators rely on bootstrap inference, which suffers from computational inefficiency and lacks known asymptotic properties. Meanwhile, Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) primarily focus on testing the null hypothesis of equal distributions between two groups, which is a more stringent assumption that may not be well-suited to the primary practical application of MWWRST. In this paper, we aim to address these limitations by leveraging functional response models (FRM) to develop doubly robust estimators. We demonstrate the performance of our proposed approach using both simulated and real study data.

Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

Abstract This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.

Bootstrap for inference after model selection and model averaging for likelihood models

Bootstrap for inference after model selection and model averaging for likelihood models

Cross-section bootstrap for CCE regressions

The Common Correlated Effects (CCE) methodology is now well established for the analysis of factor-augmented panel data models. Yet, it is often neglected that the pooled variant is biased unless the cross-section dimension (N) of the dataset dominates the time series length (T). This is problematic for inference with typical macroeconomic datasets, where T is often equal or larger than N. In response, we establish in this paper the theoretical foundation of the cross-section (CS) bootstrap for inference with CCE estimators in large N and T panels with TN−1→τ<∞. This resampling scheme is often used to estimate standard errors, yet without theoretical justification, and with unused potential, as we show it also provides a solution to the bias problem. We derive conditions under which the scheme replicates the distribution of the CCE estimators, such that bias can be eliminated and asymptotically valid inference can ensue. In so doing, we also spend attention to the case where factors need not be common across the dependent and explanatory variables, or when slopes are heterogeneous. Since we find that the CS-bootstrap applies in each case, researchers can stay agnostic on these issues. Simulation experiments show that the asymptotic properties also translate well to finite samples.

Bootstrap inference in functional linear regression models with scalar response under heteroscedasticity

Bootstrap inference in functional linear regression models with scalar response under heteroscedasticity

Estimation and inference by stochastic optimization

In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into a fast resampling device. Two methods are introduced: a resampled Newton–Raphson (rnr) and a resampled quasi-Newton (rqn) algorithm. Both produce draws that can be used to compute consistent estimates, confidence intervals, and standard errors in a single run. The draws are generated by a gradient and Hessian (or an approximation) computed from batches of data that are resampled at each iteration. The proposed methods transition quickly from optimization to resampling when the objective is smooth and strictly convex. Simulated and empirical applications illustrate the properties of the methods on large scale and computationally intensive problems. Comparisons with frequentist and Bayesian methods highlight the features of the algorithms.

The case for CASE: Estimating heterogeneous systemic effects

The Basel Committee and the Financial Stability Board require a consensus on the identification of characteristics that make a financial institution more prone than others to be severely hit by systemic shocks. This paper introduces a new tool to achieve this goal: a model for the Conditional Average Systemic Effects (CASE). The CASE quantifies the average effect of a system wide shock or market downturn on the profit and loss account of a bank, a firm or on the return of an asset. We propose a linear model for CASE with heterogeneous effects in observable characteristics. These models complement alternative measures of systemic risk and allow researchers to identify the determinants of the vulnerability of a given financial institution. We develop bootstrap inference that accounts for both estimation risk and model misspecification risk, and show the utility of our results in Monte Carlo simulations and an empirical application to 100 large U.S. financial firms.

Bootstrap inference in functional linear regression models with scalar response

Bootstrap inference in functional linear regression models with scalar response

Bootstrap Inference in Cointegrating Regressions: Traditional and Self-Normalized Test Statistics

Traditional tests of hypotheses on the cointegrating vector are well known to suffer from severe size distortions in finite samples, especially when the data are characterized by large levels of endogeneity or error serial correlation. To address this issue, we combine a vector autoregressive (VAR) sieve bootstrap to construct critical values with a self-normalization approach that avoids direct estimation of long-run variance parameters when computing test statistics. To asymptotically justify this method, we prove bootstrap consistency for the self-normalized test statistics under mild conditions. In addition, the underlying bootstrap invariance principle allows us to prove bootstrap consistency also for traditional test statistics based on popular modified OLS estimators. Simulation results show that using bootstrap critical values instead of asymptotic critical values reduces size distortions associated with traditional test statistics considerably, but combining the VAR sieve bootstrap with self-normalization can lead to even less size distorted tests at the cost of only small power losses. We illustrate the usefulness of the VAR sieve bootstrap in empirical applications by analyzing the validity of the Fisher effect in 19 OECD countries.

Comparative Effectiveness Analysis of Lumpectomy and Mastectomy for Elderly Female Breast Cancer Patients: A Deep Learning-based Big Data Analysis.

Objectives: To evaluate the comparative effectiveness of treatments, a randomized clinical trial remains the gold standard but can be challenged by a high cost, a limited sample size, an inability to fully reflect the real world, and feasibility concerns. The objective is to showcase a big data approach that takes advantage of large electronic medical record (EMR) data to emulate clinical trials. To overcome the limitations of regression analysis, a deep learning-based analysis pipeline was developed. Study Design and Setting: Lumpectomy (breast-conserving surgery) and mastectomy are the two most commonly used surgical procedures for early-stage female breast cancer patients. An emulation trial was designed using the Surveillance, Epidemiology, and End Results (SEER)-Medicare data to evaluate their relative effectiveness in overall survival. The analysis pipeline consisted of a propensity score step, a weighted survival analysis step, and a bootstrap inference step. Results: A total of 65,997 subjects were enrolled in the emulated trial, with 50,704 and 15,293 in the lumpectomy and mastectomy arms, respectively. The two surgery procedures had comparable effects in terms of overall survival (survival year change = 0.08, 95% confidence interval (CI): -0.08, 0.25) for the elderly SEER-Medicare early-stage female breast cancer patients. Conclusion: This study demonstrated the power of "mining large EMR data + deep learning-based analysis," and the proposed analysis strategy and technique can be potentially broadly applicable. It provided convincing evidence of the comparative effectiveness of lumpectomy and mastectomy.

Econometric inference on a large Bayesian game with heterogeneous beliefs

Econometric models of strategic interactions among people or firms have received a great deal of attention in the literature. Less attention has been paid to the role of the underlying assumptions about the way agents form beliefs about other agents. We focus on a single large Bayesian game with idiosyncratic strategic neighborhoods and develop an approach of empirical modeling that relaxes the assumption of rational expectations and allows the players to form beliefs differently. By drawing on the main intuition of Kalai (2004), we introduce the notion of hindsight regret, which measures each player’s ex-post value of other players’ type information, and obtain the belief-free bound for the hindsight regret. Using this bound, we derive testable implications and develop a bootstrap inference procedure for the structural parameters. Our inference method is uniformly valid regardless of the size of strategic neighborhoods and tends to exhibit high power when the neighborhoods are large. We demonstrate the finite sample performance of the method through Monte Carlo simulations.

Consumer and critic reception of video game platforms: Trends from 2002–2022

For the last 21 years, there have been four dominant video game platforms: personal computer (PC), Playstation, Nintendo, and Xbox. This paper compares the most satisfying “basket” of games each platform provided as determined via quantile regression, as well as the sheer number of “top-shelf” games each platform provided as determined via bootstrap inference. Trends in gamer satisfaction for each platform are analyzed, and which and when each platform delivered the most well-received gaming experience is identified. Furthermore, this paper analyzes the reception of games that were ported to multiple platforms to provide a very direct cross-platform comparison as determined via ordinary linear regression. Reception was measured by review scores from professionals and users as aggregated by website Metacritic. The results suggest that PC and Nintendo platforms provided fairly consistently satisfying games from 2002–2022, whereas Playstation and Xbox appear to have deteriorated in that sense, and gaming as a whole appears to have declined according to users. PC had the most top-shelf games, and Nintendo the fewest. Xbox had most well-received ports. Generally, users tended to be less charitable in their assessments than professionals, and that difference increased over time.

A smoothed p-value test when there is a nuisance parameter under the alternative

We present a new test when there is a nuisance parameter λ under the alternative hypothesis. The test exploits the p-value occupation time [PVOT], the measure of the subset of λ on which a p-value test based on a test statistic Tn(λ) rejects the null hypothesis. Key contributions are: (i) An asymptotic critical value upper bound for our test is the significance level α, making inference easy. (ii) We only require Tn(λ) to have a known or bootstrappable limit distribution, hence we do not require n-Gaussian asymptotics, allowing for weak or non-identification, boundary values, heavy tails, infill asymptotics, and so on. (iii) A test based on the transformed p-value supλ∈Λpn(λ) may be conservative and in some cases have trivial power, while the PVOT naturally controls for this by smoothing over the nuisance parameter space. Finally, (iv) the PVOT uniquely allows for bootstrap inference in the presence of nuisance parameters when some estimated parameters may not be identified.

Lgrgtest: Lagrange multiplier test after constrained maximum-likelihood estimation

Besides the Wald and likelihood-ratio tests, the Lagrange multiplier test (Rao, 1948, Mathematical Proceedings of the Cambridge Philosophical Society 44: 50–57; Aitchison and Silvey, 1958, Annals of Mathematical Statistics 29: 813–828; Silvey, 1959, Annals of Mathematical Statistics 30: 389–407) is the third canonical approach to testing hypotheses after maximum likelihood estimation. While the Stata commands test and lrtest implement the first two, Stata does not have an official command for implementing the third. The community-contributed boottest package (Roodman et al., 2019, Stata Journal 19: 4–60) focuses on methods of bootstrap inference and also implements the Lagrange multiplier test functionality. In this article, I introduce the new community-contributed postestimation command lgrgtest, which allows for straightforwardly using the Lagrange multiplier test after constrained maximum-likelihood estimation. lgrgtest is intended to be compatible with all Stata estimation commands that use maximum likelihood and allow for the options constraints(), iterate(), and from(). lgrgtest can also be used after cnsreg.

Bootstrap inference for skew-normal unbalanced heteroscedastic one-way classification random effects model

In this paper, the one-sided hypothesis testing and interval estimation problems for the fixed effect and variance component functions are considered in the skew-normal unbalanced heteroscedastic one-way classification random effects model. Firstly, the Bootstrap approach is used to establish test statistic for fixed effect. Secondly, the test statistics and confidence intervals for variance component functions are constructed by Bootstrap approach and generalized approach, and their theoretical properties are discussed. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with two real examples of the annual average concentrations of fine particulate matter and nitrogen dioxide.

Social threshold regression

This paper develops a threshold social interaction model which introduces group-specific endogenous effects as well as contextual effects into a conventional spatial Durbin model. We propose a two-step GMM estimator for the threshold and regression parameters, derive asymptotic theory, and provide bootstrap inference. Finally, we assess the performance of our methods using a Monte Carlo simulation and provide an empirical application on the role of peer effects on student academic achievement using Add Health data.

Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models

We study the bootstrap inference on the goodness-of-fit test for generalized autoregressive conditional heteroskedastic (GARCH) models. Note that the commonly-used portmanteau tests for model adequacy checking necessarily impose moment conditions on innovations, we hence construct the test on the sample autocorrelations of a bounded transformation of absolute residuals, which are obtained by the least absolute deviation estimation from a fitted GARCH model. Specifically, we employ the empirical distribution function of absolute residuals as the transformation. Thus the corresponding portmanteau tests are applicable for very heavy-tailed innovations with only finite fractional moments. We bootstrap both the estimation equation and sample autocorrelations of transformed residuals to approximate the test statistics. The asymptotic validity of the bootstrap procedure is established. Monte Carlo experiments compare the finite-sample performance of the proposed bootstrap-based test with other existing tests. An empirical analysis of modeling exchange rates illustrates its usefulness.

Fast estimation of mixed-effects location-scale regression models.

As a result of advances in data collection technology and study design, modern longitudinal datasets can be much larger than they historically have been. Such "intensive" longitudinal datasets are rich enough to allow for detailed modeling of the variance of a response as well as the mean, and a flexible class of models called mixed-effects location-scale (MELS) regression models are commonly used to do so. However, fitting MELS models can pose computational challenges related to the numerical evaluation of multi-dimensional integrals; the slow runtime of current methods is inconvenient for data analysis and makes bootstrap inference impractical. In this paper, we introduce a new fitting technique, called FastRegLS, that is considerably faster than existing techniques while still providing consistent estimators for the model parameters.