Pub Date : 2022-10-02DOI: 10.1080/07350015.2022.2102021
J. Rubio-Ramirez
The views expressed in this paper are solely those of the author and do not necessarily reflect the views of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any errors or omissions are the responsibility of the author. No statements here should be treated as legal advice. Preliminary and Incomplete. Do not circulate without consent from the author.
{"title":"Comments on “Narrative Restrictions and Proxies” by Giacomini, Kitagawa, and Read","authors":"J. Rubio-Ramirez","doi":"10.1080/07350015.2022.2102021","DOIUrl":"https://doi.org/10.1080/07350015.2022.2102021","url":null,"abstract":"The views expressed in this paper are solely those of the author and do not necessarily reflect the views of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any errors or omissions are the responsibility of the author. No statements here should be treated as legal advice. Preliminary and Incomplete. Do not circulate without consent from the author.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46153207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-02DOI: 10.1080/07350015.2022.2096042
Mikkel Plagborg-Møller
I am grateful for the chance to discuss this characteristically insightful paper by Giacomini, Kitagawa, and Read (hence-forth GKR). Since the seminal contribution of Antolín-Díaz and Rubio-Ramírez (2018), narrative restrictions have rapidly become one of the go-to tools for sharpening causal inference in SVAR analysis. Giacomini, Kitagawa, and Read (2021) con-tributed greatly to our understanding of the role of subjective prior beliefs and the appropriate form of the likelihood function when exploiting such narrative information. In the new paper that is the topic of this discussion, GKR compare their pre-ferred prior-robust Bayesian inference procedure with an alter-native approach that constructs categorical proxy variables from the narrative information and uses these to estimate impulse responses via instrumental variable (IV) regressions. GKR argue that the proxy approach will likely suffer from weak IV problems when we only have narrative restrictions for a few time periods, as is often the case in practice. To add insult to injury, this cannot be addressed using existing techniques for weak-IV-robust inference in SVARs (Montiel Olea, Stock, and Watson 2021).Inthe following I will make two points. First, the proxy approach to exploiting narrative information has several appeal-ing robustness properties relative to the likelihood approaches of Antolín-Díaz and Rubio-Ramírez (2018) and Giacomini, Kita-gawa, and Read (2021): The proxy approach allows the narrative signals to be imperfect and arrive non-randomly, and further-more, the economic shocks are allowed to be non-invertible (also known as non-fundamental). Second, the weak IV prob-lem that GKR discuss can be overcome by using procedures designed for small samples, such as permutation tests.
{"title":"Discussion of “Narrative Restrictions and Proxies” by Raffaella Giacomini, Toru Kitagawa, and Matthew Read","authors":"Mikkel Plagborg-Møller","doi":"10.1080/07350015.2022.2096042","DOIUrl":"https://doi.org/10.1080/07350015.2022.2096042","url":null,"abstract":"I am grateful for the chance to discuss this characteristically insightful paper by Giacomini, Kitagawa, and Read (hence-forth GKR). Since the seminal contribution of Antolín-Díaz and Rubio-Ramírez (2018), narrative restrictions have rapidly become one of the go-to tools for sharpening causal inference in SVAR analysis. Giacomini, Kitagawa, and Read (2021) con-tributed greatly to our understanding of the role of subjective prior beliefs and the appropriate form of the likelihood function when exploiting such narrative information. In the new paper that is the topic of this discussion, GKR compare their pre-ferred prior-robust Bayesian inference procedure with an alter-native approach that constructs categorical proxy variables from the narrative information and uses these to estimate impulse responses via instrumental variable (IV) regressions. GKR argue that the proxy approach will likely suffer from weak IV problems when we only have narrative restrictions for a few time periods, as is often the case in practice. To add insult to injury, this cannot be addressed using existing techniques for weak-IV-robust inference in SVARs (Montiel Olea, Stock, and Watson 2021).Inthe following I will make two points. First, the proxy approach to exploiting narrative information has several appeal-ing robustness properties relative to the likelihood approaches of Antolín-Díaz and Rubio-Ramírez (2018) and Giacomini, Kita-gawa, and Read (2021): The proxy approach allows the narrative signals to be imperfect and arrive non-randomly, and further-more, the economic shocks are allowed to be non-invertible (also known as non-fundamental). Second, the weak IV prob-lem that GKR discuss can be overcome by using procedures designed for small samples, such as permutation tests.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43379665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-23DOI: 10.1080/07350015.2022.2127737
Ulrich K. Müller, M. Watson
Abstract We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the recently suggested SCPC method that addresses this challenge. We find that the method has good size properties in a wide range of Monte Carlo designs that are calibrated to real world applications, both in a pure cross sectional setting, but also for spatially correlated panel data. We provide numerically efficient methods for computing the associated spatial-correlation robust test statistics, critical values, and confidence intervals.
{"title":"Spatial Correlation Robust Inference in Linear Regression and Panel Models","authors":"Ulrich K. Müller, M. Watson","doi":"10.1080/07350015.2022.2127737","DOIUrl":"https://doi.org/10.1080/07350015.2022.2127737","url":null,"abstract":"Abstract We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the recently suggested SCPC method that addresses this challenge. We find that the method has good size properties in a wide range of Monte Carlo designs that are calibrated to real world applications, both in a pure cross sectional setting, but also for spatially correlated panel data. We provide numerically efficient methods for computing the associated spatial-correlation robust test statistics, critical values, and confidence intervals.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41738828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-20DOI: 10.1080/07350015.2022.2126845
Michael Carr, R. Moffitt, E. Wiemers
Abstract As part of a set of papers using the same methods and sample selection criteria to estimate trends in male earnings volatility across survey and administrative datasets, we conduct a new investigation of male earnings volatility using data from the Survey of Income and Program Participation (SIPP) survey and SIPP-linked administrative earnings data (SIPP GSF). We find that the level of volatility is higher in the administrative earnings histories in the SIPP GSF than in the SIPP survey but that the trends are similar. Between 1984 and 2012, volatility in the SIPP survey declines slightly while volatility in the SIPP GSF increases slightly. Including imputations due to unit nonresponse in the SIPP survey data increases both the level and upward trend in volatility and poses a challenge for estimating a consistent series in the SIPP survey data. Because the density of low earnings differs considerably across datasets, and volatility may vary across the earnings distribution, we also estimate trends in volatility where we hold the earnings distribution fixed across the two data sources. Differences in the underlying earnings distribution explain much of the difference in the level of and trends in volatility between the SIPP survey and SIPP GSF.
{"title":"Reconciling Trends in Male Earnings Volatility: Evidence from the SIPP Survey and Administrative Data","authors":"Michael Carr, R. Moffitt, E. Wiemers","doi":"10.1080/07350015.2022.2126845","DOIUrl":"https://doi.org/10.1080/07350015.2022.2126845","url":null,"abstract":"Abstract As part of a set of papers using the same methods and sample selection criteria to estimate trends in male earnings volatility across survey and administrative datasets, we conduct a new investigation of male earnings volatility using data from the Survey of Income and Program Participation (SIPP) survey and SIPP-linked administrative earnings data (SIPP GSF). We find that the level of volatility is higher in the administrative earnings histories in the SIPP GSF than in the SIPP survey but that the trends are similar. Between 1984 and 2012, volatility in the SIPP survey declines slightly while volatility in the SIPP GSF increases slightly. Including imputations due to unit nonresponse in the SIPP survey data increases both the level and upward trend in volatility and poses a challenge for estimating a consistent series in the SIPP survey data. Because the density of low earnings differs considerably across datasets, and volatility may vary across the earnings distribution, we also estimate trends in volatility where we hold the earnings distribution fixed across the two data sources. Differences in the underlying earnings distribution explain much of the difference in the level of and trends in volatility between the SIPP survey and SIPP GSF.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42061814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-19DOI: 10.1080/07350015.2022.2126480
Bryan S. Graham, Geert Ridder, Petra Thiemann, Gema Zamarro
Abstract
We study the effects of counterfactual teacher-to-classroom assignments on average student achievement in U.S. elementary and middle schools. We use the Measures of Effective Teaching (MET) experiment to semiparametrically identify the average reallocation effects (AREs) of such assignments. Our identification strategy exploits the random assignment of teachers to classrooms in MET schools. To account for non-compliance of some students and teachers to the random assignment, we develop and implement a semiparametric instrumental variables estimator. We find that changes in within-district teacher assignments could have appreciable effects on student achievement. Unlike policies that aim at changing the pool of teachers (e.g., teacher tenure policies or class-size reduction measures), alternative teacher-to-classroom assignments do not require that districts hire new teachers or lay off existing ones; they raise student achievement through a more efficient deployment of existing teachers.
摘要 我们研究了美国中小学教师对班级的反事实分配对学生平均成绩的影响。我们利用 "有效教学措施（MET）"实验，以半参数方法确定了这种分配的平均再分配效应（AREs）。我们的识别策略利用了随机分配教师到 MET 学校教室的方法。为了解释部分学生和教师不遵守随机分配的情况，我们开发并实施了一个半参数工具变量估计器。我们发现，区内教师分配的变化会对学生成绩产生显著影响。与那些旨在改变教师队伍的政策（如教师终身制政策或缩小班级规模的措施）不同，替代性的教师到教室分配不要求学区聘用新教师或解雇现有教师；它们通过更有效地调配现有教师来提高学生成绩。
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Pub Date : 2022-09-07DOI: 10.1080/07350015.2022.2120485
Lajos Horváth, Lorenzo Trapani
Abstract We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Similarly, our tests can be applied even when the error term and the stochastic part of the autoregressive coefficient are non iid, covering the cases of conditional volatility and shifts in the variance, again without requiring any prior knowledge as to the presence or type thereof. In order to ensure the ability to detect breaks at sample endpoints, we propose weighted CUSUM statistics, deriving the asymptotics for virtually all possible weighing schemes, including the standardized CUSUM process (for which we derive a Darling-Erdős theorem) and even heavier weights (so-called Rényi statistics). Simulations show that our procedures work very well in finite samples. We complement our theory with an application to several financial time series.
{"title":"Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models","authors":"Lajos Horváth, Lorenzo Trapani","doi":"10.1080/07350015.2022.2120485","DOIUrl":"https://doi.org/10.1080/07350015.2022.2120485","url":null,"abstract":"Abstract We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Similarly, our tests can be applied even when the error term and the stochastic part of the autoregressive coefficient are non iid, covering the cases of conditional volatility and shifts in the variance, again without requiring any prior knowledge as to the presence or type thereof. In order to ensure the ability to detect breaks at sample endpoints, we propose weighted CUSUM statistics, deriving the asymptotics for virtually all possible weighing schemes, including the standardized CUSUM process (for which we derive a Darling-Erdős theorem) and even heavier weights (so-called Rényi statistics). Simulations show that our procedures work very well in finite samples. We complement our theory with an application to several financial time series.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44037267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-07DOI: 10.1080/07350015.2022.2120484
Shaobo Li, Shaonan Tian, Yan Yu, Xiaorui Zhu, Heng Lian
Abstract Corporate probability of default (PD) prediction is vitally important for risk management and asset pricing. In search of accurate PD prediction, we propose a flexible yet easy-to-interpret default-prediction single-index hazard model (DSI). By applying it to a comprehensive U.S. corporate bankruptcy database we constructed, we discover an interesting V-shaped relationship, indicating a violation of the common linear hazard specification. Most importantly, the single-index hazard model passes the Hosmer-Lemeshow goodness-of-fit calibration test while neither does a state-of-the-art linear hazard model in finance nor a parametric class of Box-Cox transformation survival models. In an economic value analysis, we find that this may translate to as much as three times of profit compared to the linear hazard model. In model estimation, we adopt a penalized-spline approximation for the unknown function and propose an efficient algorithm. With a diverging number of spline knots, we establish consistency and asymptotic theories for the penalized-spline likelihood estimators. Furthermore, we reexamine the distress risk anomaly, that is, higher financially distressed stocks deliver anomalously lower excess returns. Based on the PDs from the proposed single-index hazard model, we find that the distress risk anomaly has weakened or even disappeared during the extended period.
{"title":"Corporate Probability of Default: A Single-Index Hazard Model Approach","authors":"Shaobo Li, Shaonan Tian, Yan Yu, Xiaorui Zhu, Heng Lian","doi":"10.1080/07350015.2022.2120484","DOIUrl":"https://doi.org/10.1080/07350015.2022.2120484","url":null,"abstract":"Abstract Corporate probability of default (PD) prediction is vitally important for risk management and asset pricing. In search of accurate PD prediction, we propose a flexible yet easy-to-interpret default-prediction single-index hazard model (DSI). By applying it to a comprehensive U.S. corporate bankruptcy database we constructed, we discover an interesting V-shaped relationship, indicating a violation of the common linear hazard specification. Most importantly, the single-index hazard model passes the Hosmer-Lemeshow goodness-of-fit calibration test while neither does a state-of-the-art linear hazard model in finance nor a parametric class of Box-Cox transformation survival models. In an economic value analysis, we find that this may translate to as much as three times of profit compared to the linear hazard model. In model estimation, we adopt a penalized-spline approximation for the unknown function and propose an efficient algorithm. With a diverging number of spline knots, we establish consistency and asymptotic theories for the penalized-spline likelihood estimators. Furthermore, we reexamine the distress risk anomaly, that is, higher financially distressed stocks deliver anomalously lower excess returns. Based on the PDs from the proposed single-index hazard model, we find that the distress risk anomaly has weakened or even disappeared during the extended period.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43809645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-02DOI: 10.1080/07350015.2022.2120486
C. Gouriéroux, J. Jasiak
ABSTRACT We consider a class of semi-parametric dynamic models with iid errors, including the nonlinear mixed causal-noncausal Vector Autoregressive (VAR), Double-Autoregressive (DAR) and stochastic volatility models. To estimate the parameters characterizing the (nonlinear) serial dependence, we introduce a generic Generalized Covariance (GCov) estimator, which minimizes a residual-based multivariate portmanteau statistic. In comparison to the standard methods of moments, the GCov estimator has an interpretable objective function, circumvents the inversion of high-dimensional matrices, and achieves semi-parametric efficiency in one step. We derive the asymptotic properties of the GCov estimator and show its semi-parametric efficiency. We also prove that the associated residual-based portmanteau statistic is asymptotically chi-square distributed. The finite sample performance of the GCov estimator is illustrated in a simulation study. The estimator is then applied to a dynamic model of commodity futures.
{"title":"Generalized Covariance Estimator","authors":"C. Gouriéroux, J. Jasiak","doi":"10.1080/07350015.2022.2120486","DOIUrl":"https://doi.org/10.1080/07350015.2022.2120486","url":null,"abstract":"ABSTRACT We consider a class of semi-parametric dynamic models with iid errors, including the nonlinear mixed causal-noncausal Vector Autoregressive (VAR), Double-Autoregressive (DAR) and stochastic volatility models. To estimate the parameters characterizing the (nonlinear) serial dependence, we introduce a generic Generalized Covariance (GCov) estimator, which minimizes a residual-based multivariate portmanteau statistic. In comparison to the standard methods of moments, the GCov estimator has an interpretable objective function, circumvents the inversion of high-dimensional matrices, and achieves semi-parametric efficiency in one step. We derive the asymptotic properties of the GCov estimator and show its semi-parametric efficiency. We also prove that the associated residual-based portmanteau statistic is asymptotically chi-square distributed. The finite sample performance of the GCov estimator is illustrated in a simulation study. The estimator is then applied to a dynamic model of commodity futures.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45785099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-01DOI: 10.1080/07350015.2022.2118127
Lajos Horváth, Zhenya Liu, Gregory Rice, Shixuan Wang, Yaosong Zhan
Abstract Many sequentially observed functional data objects are available only at the times of certain events. For example, the trajectory of stock prices of companies after their initial public offering (IPO) can be observed when the offering occurs, and the resulting data may be affected by changing circumstances. It is of interest to investigate whether the mean behavior of such functions is stable over time, and if not, to estimate the times at which apparent changes occur. Since the frequency of events may fluctuates over time, we propose a change point analysis that has two steps. In the first step, we segment the series into segments in which the frequency of events is approximately homogeneous using a new binary segmentation procedure for event frequencies. After adjusting the observed curves in each segment based on the frequency of events, we proceed in the second step by developing a method to test for and estimate change points in the mean of the observed functional data objects. We establish the consistency and asymptotic distribution of the change point detector and estimator in both steps, and study their performance using Monte Carlo simulations. An application to IPO performance data illustrates the proposed methods.
{"title":"Testing Stability in Functional Event Observations with an Application to IPO Performance","authors":"Lajos Horváth, Zhenya Liu, Gregory Rice, Shixuan Wang, Yaosong Zhan","doi":"10.1080/07350015.2022.2118127","DOIUrl":"https://doi.org/10.1080/07350015.2022.2118127","url":null,"abstract":"Abstract Many sequentially observed functional data objects are available only at the times of certain events. For example, the trajectory of stock prices of companies after their initial public offering (IPO) can be observed when the offering occurs, and the resulting data may be affected by changing circumstances. It is of interest to investigate whether the mean behavior of such functions is stable over time, and if not, to estimate the times at which apparent changes occur. Since the frequency of events may fluctuates over time, we propose a change point analysis that has two steps. In the first step, we segment the series into segments in which the frequency of events is approximately homogeneous using a new binary segmentation procedure for event frequencies. After adjusting the observed curves in each segment based on the frequency of events, we proceed in the second step by developing a method to test for and estimate change points in the mean of the observed functional data objects. We establish the consistency and asymptotic distribution of the change point detector and estimator in both steps, and study their performance using Monte Carlo simulations. An application to IPO performance data illustrates the proposed methods.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43304873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-23DOI: 10.1080/07350015.2022.2116442
Rong Zhu, Haiying Wang, Xinyu Zhang, Hua Liang
Abstract Frequentist model averaging is an effective technique to handle model uncertainty. However, calculation of the weights for averaging is extremely difficult, if not impossible, even when the dimension of the predictor vector, p, is moderate, because we may have candidate models. The exponential size of the candidate model set makes it difficult to estimate all candidate models, and brings additional numeric errors when calculating the weights. This article proposes a scalable frequentist model averaging method, which is statistically and computationally efficient, to overcome this problem by transforming the original model using the singular value decomposition. The method enables us to find the optimal weights by considering at most p candidate models. We prove that the minimum loss of the scalable model averaging estimator is asymptotically equal to that of the traditional model averaging estimator. We apply the Mallows and Jackknife criteria to the scalable model averaging estimator and prove that they are asymptotically optimal estimators. We further extend the method to the high-dimensional case (i.e., ). Numerical studies illustrate the superiority of the proposed method in terms of both statistical efficiency and computational cost.
{"title":"A Scalable Frequentist Model Averaging Method","authors":"Rong Zhu, Haiying Wang, Xinyu Zhang, Hua Liang","doi":"10.1080/07350015.2022.2116442","DOIUrl":"https://doi.org/10.1080/07350015.2022.2116442","url":null,"abstract":"Abstract Frequentist model averaging is an effective technique to handle model uncertainty. However, calculation of the weights for averaging is extremely difficult, if not impossible, even when the dimension of the predictor vector, p, is moderate, because we may have candidate models. The exponential size of the candidate model set makes it difficult to estimate all candidate models, and brings additional numeric errors when calculating the weights. This article proposes a scalable frequentist model averaging method, which is statistically and computationally efficient, to overcome this problem by transforming the original model using the singular value decomposition. The method enables us to find the optimal weights by considering at most p candidate models. We prove that the minimum loss of the scalable model averaging estimator is asymptotically equal to that of the traditional model averaging estimator. We apply the Mallows and Jackknife criteria to the scalable model averaging estimator and prove that they are asymptotically optimal estimators. We further extend the method to the high-dimensional case (i.e., ). Numerical studies illustrate the superiority of the proposed method in terms of both statistical efficiency and computational cost.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44128430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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