Finite Sample Correction Research Articles

Finite sample corrections for average equivalence testing.

Average (bio)equivalence tests are used to assess if a parameter, like the mean difference in treatment response between two conditions for example, lies within a given equivalence interval, hence allowing to conclude that the conditions have "equivalent" means. The two one-sided tests (TOST) procedure, consisting in testing whether the target parameter is respectively significantly greater and lower than some pre-defined lower and upper equivalence limits, is typically used in this context, usually by checking whether the confidence interval for the target parameter lies within these limits. This intuitive and visual procedure is however known to be conservative, especially in the case of highly variable drugs, where it shows a rapid power loss, often reaching zero, hence making it impossible to conclude for equivalence when it is actually true. Here, we propose a finite sample correction of the TOST procedure, the -TOST, which consists in a correction of the significance level of the TOST allowing to guarantee a test size (or type-I error rate) of . This new procedure essentially corresponds to a finite sample and variability correction of the TOST procedure. We show that this procedure is uniformly more powerful than the TOST, easy to compute, and that its operating characteristics outperform the ones of its competitors. A case study about econazole nitrate deposition in porcine skin is used to illustrate the benefits of the proposed method and its advantages compared to other available procedures.

A nonparametric test for paired data

The paper proposes a weighted Kolmogorov–Smirnov type test for the two-sample problem for paired data. The asymptotic distribution of the test statistic under the null model is derived. The dependence of both the finite sample and the asymptotic distribution of the test statistic on the dependence structure of the data requires the use of the wild bootstrap technique for inference. The related wild bootstrap test turns out to be a consistent asymptotically level α test. With the finite sample correction applied, the test keeps the level well. An extensive simulation study demonstrates good finite sample behaviour of the test in comparison to the existing procedures. The main role in the proofs is played by tools from empirical processes. Additional simulation results, as well as an R code, which allow one to easily repeat the conducted numerical experiments, are attached as Supplementary Material.

Women Just Wanna Have Quotas: The Gender Divide on Affirmative Action in the Chilean Right

Objective/context: This article examines attitudes towards gender quotas by right-wing leadership in Chile and assesses gender gaps in supporting affirmative action. Methodology: The study uses original data from a survey of leaders of Chile Vamos, a right-wing political alliance in Chile. A series of logistic models with finite-sample corrections are estimated to examine the attitudes of right-wing leaders towards gender quotas and support for affirmative action policies. The models control for various demographic and political factors that may affect attitudes towards affirmative action. Conclusions: The findings for right-wing women in Chile are similar to those for Northern democracies. Right-wing elites show a significant gender gap on issues related to affirmative action and gender equality. Right-wing women are more likely to support affirmative action policies than their male counterparts. Originality: Quotas increase women’s autonomy and recognize that women are historically disadvantaged. The findings of this article support the importance of descriptive representation to the extent that attitudes of right-wing women differ significantly on issues close to their gender.

Phase I analysis of high-dimensional processes in the presence of outliers

One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I. This assessment is carried out in the absence and presence of outliers. We show that, in both cases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

The roles of ICT telecommunication infrastructure on foreign direct investment in Malaysia

The development of the digital economy and the emergence of new technologies are changing the way of doing business. In recent foreign direct investment (FDI) studies, factors in addition to conventional ownership-location-internalisation (OLI) factors have been explored to enrich the FDI model. This study looks at the roles of information and communications technology (ICT) telecommunication infrastructure on FDI in Malaysia. The two-step system generalised method of moments (GMM) approach is used. To overcome the limitations of the dynamic panel model on the “small groups” problem, this study uses five three-year average data for the period between 2002 to 2016, and the Windmeijer finite-sample correction, the robust standard errors for estimation. The results show a significant positive role of mobile telephony on FDI. Besides, institutional factors are found to have significant impacts on FDI. The findings indicate the importance of the institutional framework and ICT telecommunication infrastructure, which can be jointly used with the OLI paradigm to explain factors driving FDI in the new economy.

Modifying the linear two-step Windmeijer correction for the presence of spatial error dependence

The aim in the paper is to show how the presence of spatial dependence affects the often-adopted Windmeijer (J Econom 126:25–51, 2005) finite sample correction (For example it is an option facilitating robust estimation in the software package Stata, which is used by many applied econometricians and data analysts.), which corrects the downward bias in estimated parameter standard errors. Windmeijer (2005) explains why, with numerous instruments, the estimated asymptotic standard errors of the efficient, two-step, GMM estimator are downward biased in small samples. GMM estimation is based on an estimated optimal weight matrix, which is the inverse of the covariance of the sample moments, and the bias results from the weight matrix being evaluated at estimated, rather than the true values of parameters. Hwang et al. (J Econom 229(2):276–298, 2022) provide a correction to the Windmeijer (2005) finite sample correction to allow for over-identification bias. The novel contribution of the current paper is to show how the Windmeijer (2005) correction can be modified given spatial dependence in the error term of a model with moments conditions that are linear in parameters estimated by GMM, leading to corrected standard errors and therefore more accurate inference. Monte Carlo simulations are used to demonstrate the effect of the modification and two examples using real data shows how inference may be affected by ignoring the effect of spatial error dependence.

Cointegration in large VARs

The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from overrejection. This is achieved through novel asymptotic theorems for eigenvalues of matrices in the test statistic in the regime of proportionally growing N and T. Our theoretical findings are supported by Monte Carlo simulations and an empirical illustration. Moreover, we find a surprising connection with multivariate analysis of variance (MANOVA) and explain why it emerges.

OLA strategy for ARDS: Its effect on mortality depends on achieved recruitment (PaO2/FiO2) and mechanical power. Systematic review and meta-analysis with meta-regression.

The "Open Lung Approach" (OLA), that includes high levels of positive end-expiratory pressure coupled with limited tidal volumes, is considered optimal for adult patients with ARDS. However, many previous meta-analyses have shown only marginal benefits of OLA on mortality but with statistical heterogeneity. It is crucial to identify the most likely moderators of this effect. To determine the effect of OLA strategy on mortality of ventilated ARDS patients. We hypothesized that the degree of recruitment achieved in the control group (PaO2/FiO2 ratio on day 3 of ventilation), and the difference in Mechanical Power (MP) or Driving Pressure (DP) between experimental and control groups will be the most likely sources of heterogeneity. A Systematic Review and Meta-analysis was performed according to PRISMA statement and registered in PROSPERO database. We searched only for randomized controlled trials (RCTs). GRADE guidelines were used for rating the quality of evidence. Publication bias was assessed. For the Meta-analysis, we used a Random Effects Model. Sources of heterogeneity were explored with Meta-Regression, using a priori proposed set of possible moderators. For model comparison, Akaike's Information Criterion with the finite sample correction (AICc) was used. Not applicable. Fourteen RCTs were included in the study. Not applicable. Not applicable. Evidence of publication bias was detected, and quality of evidence was downgraded. Pooled analysis did not show a significant difference in the 28-day mortality between OLA strategy and control groups. Overall risk of bias was low. The analysis detected statistical heterogeneity. The two "best" explicative meta-regression models were those that used control PaO2/FiO2 on day 3 and difference in MP between experimental and control groups. The DP and MP models were highly correlated. There is no clear benefit of OLA strategy on mortality of ARDS patients, with significant heterogeneity among RCTs. Mortality effect of OLA is mediated by lung recruitment and mechanical power.

OLA strategy for ARDS: Its effect on mortality depends on achieved recruitment (PaO2/FiO2) and mechanical power. Systematic review and meta-analysis with meta-regression

ObjectiveThe “Open Lung Approach” (OLA), that includes high levels of positive end-expiratory pressure coupled with limited tidal volumes, is considered optimal for adult patients with ARDS. However, many previous meta-analyses have shown only marginal benefits of OLA on mortality but with statistical heterogeneity. It is crucial to identify the most likely moderators of this effect.To determine the effect of OLA strategy on mortality of ventilated ARDS patients. We hypothesized that the degree of recruitment achieved in the control group (PaO2/FiO2 ratio on day 3 of ventilation), and the difference in Mechanical Power (MP) or Driving Pressure (DP) between experimental and control groups will be the most likely sources of heterogeneity. DesignA Systematic Review and Meta-analysis was performed according to PRISMA statement and registered in PROSPERO database. We searched only for randomized controlled trials (RCTs). GRADE guidelines were used for rating the quality of evidence. Publication bias was assessed. For the Meta-analysis, we used a Random Effects Model. Sources of heterogeneity were explored with Meta-Regression, using a priori proposed set of possible moderators. For model comparison, Akaike's Information Criterion with the finite sample correction (AICc) was used. SettingNot applicable. PatientsFourteen RCTs were included in the study. InterventionsNot applicable. Main variables of interestNot applicable. ResultsEvidence of publication bias was detected, and quality of evidence was downgraded. Pooled analysis did not show a significant difference in the 28-day mortality between OLA strategy and control groups. Overall risk of bias was low. The analysis detected statistical heterogeneity. The two “best” explicative meta-regression models were those that used control PaO2/FiO2 on day 3 and difference in MP between experimental and control groups. The DP and MP models were highly correlated. ConclusionsThere is no clear benefit of OLA strategy on mortality of ARDS patients, with significant heterogeneity among RCTs. Mortality effect of OLA is mediated by lung recruitment and mechanical power.

China’s outward FDI and environmental sustainability in belt and road countries: does the quality of institutions matter?

This study aims to unravel the environmental effects of institutional quality in relationship with China’s Foreign Direct Investment (FDI) in Belt and Road Initiative (BRI) countries. The empirical analysis is conducted over the period 2003–2018, using the System-GMM approach with the Windmeijer finite-sample correction. We infer that China’s FDI has a detrimental effect on environmental quality, which validates the ‘pollution haven hypothesis’ in the BRI region. Importantly, the interaction effect of China’s FDI with indicators of institutional quality yields negative and significant results. This entails that strong institutions can boost the quality of the environment through FDI attractiveness. In further assessment, the threshold levels of institutional quality are calculated, beyond which China’s FDI can reduce carbon emissions in the BRI region. This substantiates both the pollution haven and pollution halo hypotheses. The study underscores the importance of institutional reform in the quest for sustainable development, owing to the fact that most economies prioritize FDI-led growth strategies.

A finite sample correction for the panel Durbin–Watson test

ABSTRACT This study shows that the panel Durbin–Watson test is incapable of distinguishing temporal heteroskedasticity and serial correlation with short time series. The study proposes a new finite sample correction for solving this weakness of the panel Durbin–Watson test. Monte Carlo simulations demonstrate that the corrected statistic performs better in terms of size and power than the extant panel tests. It leads to more accurate inferences in empirical studies.

Sample size estimation for modified Poisson analysis of cluster randomized trials with a binary outcome.

The modified Poisson regression coupled with a robust sandwich variance has become a viable alternative to log-binomial regression for estimating the marginal relative risk in cluster randomized trials. However, a corresponding sample size formula for relative risk regression via the modified Poisson model is currently not available for cluster randomized trials. Through analytical derivations, we show that there is no loss of asymptotic efficiency for estimating the marginal relative risk via the modified Poisson regression relative to the log-binomial regression. This finding holds both under the independence working correlation and under the exchangeable working correlation provided a simple modification is used to obtain the consistent intraclass correlation coefficient estimate. Therefore, the sample size formulas developed for log-binomial regression naturally apply to the modified Poisson regression in cluster randomized trials. We further extend the sample size formulas to accommodate variable cluster sizes. An extensive Monte Carlo simulation study is carried out to validate the proposed formulas. We find that the proposed formulas have satisfactory performance across a range of cluster size variability, as long as suitable finite-sample corrections are applied to the sandwich variance estimator and the number of clusters is at least 10. Our findings also suggest that the sample size estimate under the exchangeable working correlation is more robust to cluster size variability, and recommend the use of an exchangeable working correlation over an independence working correlation for both design and analysis. The proposed sample size formulas are illustrated using the Stop Colorectal Cancer (STOP CRC) trial.

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 also corrects the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005), which corrects the bias from estimating the efficient weight matrix, so is doubly corrected. An important feature of the proposed double correction is that it automatically 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 double correction formula proposed in this paper provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.

Wrong skewness and finite sample correction in the normal-half normal stochastic frontier model

In parametric stochastic frontier models, the composed error is specified as the sum of a two-sided noise component and a one-sided inefficiency component, which is usually assumed to be half-normal, implying that the error distribution is skewed in one direction. In practice, however, estimation residuals may display skewness in the wrong direction. Model respecification or pulling a new sample is often prescribed. Since wrong skewness may manifest as a finite sample problem, this paper proposes a finite sample adjustment to existing estimators to obtain the desired direction of residual skewness. This provides an alternative empirical approach to deal with the wrong skewness problem that does not require respecification of the model.

The impact of corporate social responsibility on the risk of commercial banks with different levels of financial constraint

PurposeThis research investigates the link between corporate social responsibility (CSR) activities and bank risk-taking in Vietnam and introduces the constraint factor to see whether this link alters with different levels of constraint.Design/methodology/approachUsing a sample of commercial banks in Vietnam from 2008 to 2017, this study employs two-step system generalized method of moments (Sys GMM) with a finite sample correction mechanism to estimate the models.FindingsThe results suggest that CSR activities reduce bank risk-taking, and this relationship is only present in the case of financially constrained banks. Unconstrained banks, on the other hand, are more likely to invest in unnecessary CSR, thus reducing bank performance and increasing bank risk-taking.Research limitations/implicationsThe first implication from this study is that CSR activities might be considered as a risk-mitigating tool and should be invested in that respect. Secondly, regulatory units and investors should be more cautious about CSR expenditures since this type of spending could increase default risk, especially for banks with easy access to external financing. One particular limitation of this study is the low number of observations available for banks in Vietnam. Future studies could use texture analysis to expand the sample or consider macro-level governance characteristics to examine which factors might modify the relationship between CSR and bank risk.Originality/valueVery limited studies discussed the link between corporate social responsibility and bank performance and bank risk. There are even fewer papers examining the relationship between CSR and risk, and most of these papers deal with advanced economies. Furthermore, no studies investigate the interaction effect of CSR and financial constraint, which should be prevalent in developing countries on bank risk. As a consequence, the current study seeks to verify the impact of financial constraints on the link between CSR and bank risk.

Reopening the debate on the relationship among remittances, household consumption stability and economic growth in emerging markets

PurposeThe impact of remittances on household consumption stability and economic growth is not quite clear. This paper attempts to reopen the debate on the relationship among these three variables. The current remittance literature suggests that a decrease in household consumption volatility, induced by remittances, automatically leads to economic growth. This paper challenges these arguments by stating that, under certain circumstances, there is no automatic relationship among remittances, household consumption stability and growth.Design/methodology/approachThe authors approach the question from the perspective of emerging Central, Eastern and Southeastern European (CESEE) countries. The authors use the two-step system generalized method of moments (GMM) estimator with the Windmeijer (2005) finite-sample correction. To test the existence of the possible non-linear effects of remittances on household consumption stability and economic growth, the authors use threshold regressions.FindingsThe authors find that remittances significantly reduce household consumption volatility. They exhibit a consumption-smoothing effect on recipient households. This stabilizing effect happens not through the preventive role of remittances, but rather through their compensatory role. Remittances produce a weaker stabilizing effect on household consumption when the remittance to GDP ratio of the recipient country is above the estimated threshold level of 4.5%. The authors also find that there is a negatively significant and linear impact of remittances on growth. There is no evidence to suggest that remittances can foster productive investment and therefore promote economic growth in CESEE countries, which means that: (1) the remittances cannot be treated as a source of funds to invest in human and physical capital and (2) the remittances are compensatory rather than profit-oriented.Originality/valueAs far as the authors are aware, this is the first study that investigates the impact of remittances on both household consumption stability and economic growth simultaneously.

FINITE-SAMPLE SIZE CONTROL OF IVX-BASED TESTS IN PREDICTIVE REGRESSIONS

In predictive regressions with variables of unknown persistence, the use of extended IV (IVX) instruments leads to asymptotically valid inference. Under highly persistent regressors, the standard normal or chi-squared limiting distributions for the usual t and Wald statistics may, however, differ markedly from the actual finite-sample distributions which exhibit in particular noncentrality. Convergence to the limiting distributions is shown to occur at a rate depending on the choice of the IVX tuning parameters and can be very slow in practice. A characterization of the leading higher-order terms of the t statistic is provided for the simple regression case, which motivates finite-sample corrections. Monte Carlo simulations confirm the usefulness of the proposed methods.

Xtgeebcv: A command for bias-corrected sandwich variance estimation for GEE analyses of cluster randomized trials.

Cluster randomized trials, where clusters (for example, schools or clinics) are randomized to comparison arms but measurements are taken on individuals, are commonly used to evaluate interventions in public health, education, and the social sciences. Analysis is often conducted on individual-level outcomes, and such analysis methods must consider that outcomes for members of the same cluster tend to be more similar than outcomes for members of other clusters. A popular individual-level analysis technique is generalized estimating equations (GEE). However, it is common to randomize a small number of clusters (for example, 30 or fewer), and in this case, the GEE standard errors obtained from the sandwich variance estimator will be biased, leading to inflated type I errors. Some bias-corrected standard errors have been proposed and studied to account for this finite-sample bias, but none has yet been implemented in Stata. In this article, we describe several popular bias corrections to the robust sandwich variance. We then introduce our newly created command, xtgeebcv, which will allow Stata users to easily apply finite-sample corrections to standard errors obtained from GEE models. We then provide examples to demonstrate the use of xtgeebcv. Finally, we discuss suggestions about which finite-sample corrections to use in which situations and consider areas of future research that may improve xtgeebcv.

The environmental effects of trade openness in developing countries: conflict or cooperation?

Identifying environmental consequences of international trade has a crucial role in constructing and planning strategies of any country, especially in developing countries that are currently witnessing a significant increase in trade openness; however, little efforts are made to investigate the environmental consequences of trade openness. The paper attempts to investigate the dynamic relationship between trade openness and environmental pollutants incorporating potential factors affecting environmental quality in 66 developing economies over the period 1971-2017. This article employs the powerful approach two-step generalized method of moment's estimators with a finite sample correction to obtain more accurate inference. The key empirical results are as follows: (1) trade openness may be harmful for the environment while confirming the existence of an environmental Kuznets curve hypothesis. (2) An increase in pollutants, namely carbon dioxide emissions, ambient particulate matter and nitrous oxide emissions in the previous period, is associated with a rise in pollutants in the future suggesting that if no action in reducing pollutants is taken, environmental quality is worse. (3) Energy consumption, financial development and industrialization have a significant contribution to deteriorating environment. The implications of these results also are discussed and proposed for developing economies in this research.

Statistical properties of estimators for the log-optimal portfolio

The best constant re-balanced portfolio represents the standard estimator for the log-optimal portfolio. It is shown that a quadratic approximation of log-returns works very well on a daily basis and a mean-variance estimator is proposed as an alternative to the best constant re-balanced portfolio. It can easily be computed and the numerical algorithm is very fast even if the number of dimensions is high. Some small-sample and the basic large-sample properties of the estimators are derived. The asymptotic results can be used for constructing hypothesis tests and for computing confidence regions. For this purpose, one should apply a finite-sample correction, which substantially improves the large-sample approximation. However, it is shown that the impact of estimation errors concerning the expected asset returns is serious. The given results confirm a general rule, which has become folklore during the last decades, namely that portfolio optimization typically fails on estimating expected asset returns.