Bias-corrected Version Research Articles

Fixed-[formula omitted] asymptotics for panel models with two-way clustering

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the “HAC of averages” estimator, and the “average of HACs” estimator. Based on this finding, we obtain a fixed-b asymptotic result for the CHS estimator and corresponding test statistics as the cross-section and time sample sizes jointly go to infinity. Furthermore, we propose two simple bias-corrected versions of the variance estimator and derive the fixed-b limits. In a simulation study, we find that the two bias-corrected variance estimators along with fixed-b critical values provide improvements in finite sample coverage probabilities. We illustrate the impact of bias-correction and use of the fixed-b critical values on inference in an empirical example on the relationship between industry profitability and market concentration.

A correction to Begg’s test for publication bias

Begg and Mazumdar proposed using a rank correlation test to test for publication bias when carrying out meta-analyses. The asymptotic variance of the rank correlation test statistic was derived under assumptions unmet by this application, often resulting in a loss of power. Low power when Begg’s test is used to screen for publication bias may lead to false positives in a subsequent meta-analysis. We obtain the asymptotic bias under the common conditionally normal model as a function of the distribution of primary study variances. In simulations, we consider the performance of Begg’s test using an approximation to the correct asymptotic variance. We consider this performance under the common fixed effects and random effects frameworks. We then examine several meta-analyses drawn from the literature where the standard and bias-corrected versions of Begg’s test lead to different conclusions.

Estimation in the Presence of Heteroskedasticity of Unknown Form: A Lasso-based Approach

Abstract We study the Feasible Generalized Least-Squares (FGLS) estimation of the parameters of a linear regression model in the presence of heteroskedasticity of unknown form in the errors. We suggest a Lasso based procedure to estimate the skedastic function of the residuals. The advantage of using Lasso is that it can handle a large number of potential covariates, yet still yields a parsimonious specification. Using extensive simulation experiments, we show that our suggested procedure always provide some improvements in the precision of the parameter of interest (lower Mean-Squared Errors) when heteroskedasticity is present and is equivalent to OLS when there is none. It also performs better than previously suggested procedures. Since the fitted value of the skedastic function falls short of the true specification, we form confidence intervals using a bias-corrected version of the usual heteroskedasticity-robust covariance matrix estimator. These have the correct size and substantially shorter length than when using OLS. Our method is applicable to both cross-section (with a random sample) and time series models, though here we concentrate on the former.

Impact of Bias Correction of the Least Squares Estimation on Bootstrap Confidence Intervals for Bifurcating Autoregressive Models

The least squares (LS) estimator of the autoregressive coefficient in the bifurcating autoregressive (BAR) model was recently shown to suffer from substantial bias, especially for small to moderate samples. This study investigates the impact of the bias in the LS estimator on the behavior of various types of bootstrap confidence intervals for the autoregressive coefficient and introduces methods for constructing bias-corrected bootstrap confidence intervals. We first describe several bootstrap confidence interval procedures for the autoregressive coefficient of the BAR model and present their bias-corrected versions. The behavior of uncorrected and corrected confidence interval procedures is studied empirically through extensive Monte Carlo simulations and two real cell lineage data applications. The empirical results show that the bias in the LS estimator can have a significant negative impact on the behavior of bootstrap confidence intervals and that bias correction can significantly improve the performance of bootstrap confidence intervals in terms of coverage, width, and symmetry.

Crtrest: A command for ratio estimators of intervention effects on event rates in cluster randomized trials

We describe five asymptotically unbiased estimators of intervention effects on event rates in nonmatched and matched-pair cluster randomized trials, and we present a bias-corrected version of the estimators for use when the number of clusters is small. The estimators are the ratio of mean counts ( r 1), ratio of mean cluster-level event rates ( r 2), ratio of event rates ( r 3), double ratio of counts ( r 4), and double ratio of event rates ( r 5). r 1, r 2, and r 3 estimate the total effect, which comprises the direct and indirect effects; r 4 and r 5 estimate the direct effect. We describe a new command, crtrest, that provides these ratio estimators and their standard errors in nonmatched and matched-pair cluster randomized trials.

Statistical Inference for Method of Moments Estimators of a Semi-Supervised Two-Component Mixture Model

ABSTRACT A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we investigate asymptotic properties of method of moment estimators for the treatment effect based on a semi-supervised two-component mixture model. From these properties, we develop asymptotic confidence intervals and demonstrate their superior statistical inference performance compared to the computationally intensive bootstrap intervals and their Bias-Corrected versions.

Finite-sample properties of estimators for first and second order autoregressive processes

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying R-package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

Backward mean transformation in unit root panel data models

The effectiveness of an orthogonal to backward mean transformation is investigated in the context of a non-stationary panel data model. It is shown that the corresponding estimator is as efficient as Transformed Maximum Likelihood when the autoregressive parameter is equal to unity. Furthermore, a recently introduced bias-corrected version is almost as efficient as the Pooled Least Squares estimator.

Reanalysis datasets outperform other gridded climate products in vegetation change analysis in peripheral conservation areas of Central Asia

Global environmental research requires long-term climate data. Yet, meteorological infrastructure is missing in the vast majority of the world’s protected areas. Therefore, gridded products are frequently used as the only available climate data source in peripheral regions. However, associated evaluations are commonly biased towards well observed areas and consequently, station-based datasets. As evaluations on vegetation monitoring abilities are lacking for regions with poor data availability, we analyzed the potential of several state-of-the-art climate datasets (CHIRPS, CRU, ERA5-Land, GPCC-Monitoring-Product, IMERG-GPM, MERRA-2, MODIS-MOD10A1) for assessing NDVI anomalies (MODIS-MOD13Q1) in two particularly suitable remote conservation areas. We calculated anomalies of 156 climate variables and seasonal periods during 2001–2018, correlated these with vegetation anomalies while taking the multiple comparison problem into consideration, and computed their spatial performance to derive suitable parameters. Our results showed that four datasets (MERRA-2, ERA5-Land, MOD10A1, CRU) were suitable for vegetation analysis in both regions, by showing significant correlations controlled at a false discovery rate < 5% and in more than half of the analyzed areas. Cross-validated variable selection and importance assessment based on the Boruta algorithm indicated high importance of the reanalysis datasets ERA5-Land and MERRA-2 in both areas but higher differences and variability between the regions with all other products. CHIRPS, GPCC and the bias-corrected version of MERRA-2 were unsuitable and not important in both regions. We provide evidence that reanalysis datasets are most suitable for spatiotemporally consistent environmental analysis whereas gauge- or satellite-based products and their combinations are highly variable and may not be applicable in peripheral areas.

Contribution of the Amazon River Discharge to Regional Sea Level in the Tropical Atlantic Ocean

The Amazon River is by far the largest river by volume of water in the world, representing around 17% of the global riverine discharge to the oceans. Recent studies suggested that its impact on sea level is potentially important at global and regional scales. This study uses a set of regional simulations based on the ocean model NEMO to quantify the influence of the Amazon runoff on sea level in the Tropical Atlantic Ocean. The model is forced at its boundaries with daily fields from the ocean reanalysis GLORYS2V4. Air-sea fluxes are computed using atmospheric variables from DFS5.2, which is a bias-corrected version of ERAinterim reanalysis. The particularity of this study is that interannual daily runoffs from the up-to-date ISBA-CTRIP land surface model are used. Firstly, mean state of sea level is investigated through a comparison between a simulation with an interannual river discharge and a simulation without any Amazon runoff. Then, the impact of the Amazon River on seasonal and interannual variability of sea level is examined. It was shown that the Amazon River has a local contribution to the mean state sea level at the river mouth but also a remote contribution of 3.3 cm around the whole Caribbean Archipelago, a region threatened by the actual sea level rise. This effect is mostly due to a halosteric sea level contribution for the upper 250 m of the ocean. This occurs in response to the large scale advection of the plume and the downward mixing of subsurface waters at winter time. The Amazon discharge also induces an indirect thermosteric sea level contribution. However, this contribution is of second order and tends to counterbalance the halosteric sea level contribution. Regional mass redistributions are also observed and consist in a 8 cm decrease of the sea level at the river mouth and a 4.5 increases on continental shelves of the Gulf of Mexico and Caribbean Sea. In terms of variability, simulations indicate that the Amazon discharge may contributes to 23% and 12% of the seasonal and interannual sea level variances in the Caribbean Archipelago area. These variances are first explained by the Amazon time mean discharge and show very weak sensitivity to the seasonal and interannual variability of the Amazon runoff.

A general theory of purely sequential minimum risk point estimation (MRPE) of a function of the mean in a normal distribution

A purely sequential minimum risk point estimation (MRPE) methodology with associated stopping time N is designed to come up with a useful estimation strategy. We work under an appropriately formulated weighted squared error loss (SEL) due to estimation of a function of μ, with plus linear cost of sampling from a population having both parameters unknown. A series of important first-order and second-order asymptotic (as c, the cost per unit sample, ) results is laid out including the first-order and second-order efficiency properties. Then, accurate sequential risk calculations are launched, which are then followed by two main results: (i) Theorem 4.1 shows an asymptotic risk efficiency property, and (ii) Theorem 5.1 shows an asymptotic second-order regret expansion associated with the proposed purely sequential MRPE strategy assuming suitable conditions on g(.). We also provide a bias-corrected version of the terminal estimator, We follow up with a number of interesting illustrations where Theorems 4.1–5.1 are readily exploited to conclude an asymptotic risk efficiency property and second-order regret expansion, respectively. A number of other interesting illustrations are highlighted where it is possible to verify the conclusions from Theorems 4.1–5.1 more directly with less stringent assumptions on the pilot sample size.

Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes

Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a pre-asymptotic version for such observation schemes. For max-stable processes with Frechet margins we provide conditions, such that the empirical extremogram (or a bias-corrected version) centred by its true version is asymptotically normal. In a second step, for a parametric extremogram model, we fit the parameters by generalised least squares estimation and prove consistency and asymptotic normality of the estimates. We propose subsampling procedures to obtain asymptotically correct confidence intervals. Finally, we apply our results to a variety of Brown-Resnick processes. A simulation study shows that the procedure works well also for moderate sample sizes.

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants.

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for models with more than two states-for example DNA sequence alignments with four-state models-we find that methods which rely on phylogenetic invariants are incapable of satisfying all three of the stated statistical properties. This is because in these cases the relevant Markov invariants belong to a class of polynomials independent from the phylogenetic invariants.

Asymptotically optimal differenced estimators of error variance in nonparametric regression

The existing differenced estimators of error variance in nonparametric regression are interpreted as kernel estimators, and some requirements for a “good” estimator of error variance are specified. A new differenced method is then proposed that estimates the errors as the intercepts in a sequence of simple linear regressions and constructs a variance estimator based on estimated errors. The new estimator satisfies the requirements for a “good” estimator and achieves the asymptotically optimal mean square error. A feasible difference order is also derived, which makes the estimator more applicable. To improve the finite-sample performance, two bias-corrected versions are further proposed. All three estimators are equivalent to some local polynomial estimators and thus can be interpreted as kernel estimators. To determine which of the three estimators to be used in practice, a rule of thumb is provided by analysis of the mean square error, which solves an open problem in error variance estimation which difference sequence to be used in finite samples. Simulation studies and a real data application corroborate the theoretical results and illustrate the advantages of the new method compared with the existing methods.

Rainfall characteristics and their implications for rain-fed agriculture: a case study in the Upper Zambezi River Basin

ABSTRACTThis study investigates rainfall characteristics in the Upper Zambezi River Basin and implications for rain-fed agriculture. Seventeen indices describing the character of each rainy season were calculated using a bias-corrected version of TRMM-B42 v6 rainfall estimate for 1998–2010. These were correlated with maize yields obtained by applying a SVATmodel. Finally, a self-organizing map (SOM) was trained to examine multivariate relationships. The results reveal a significant spatio‐temporal variability of rainfall indices and yields, with a gradient from north to south. Yields greater than 1 t/ha are found to be only achievable with rainy seasons longer than 160 days. For shorter durations, the interplay of total rainfall, dry spell frequency and maximum dry/wet spell durations determines agricultural success. Using total rainfall alone or wet day frequency as estimators for yields is insufficient. Alternating wet and dry spells affect yields most negatively. The results have significance in the context of agricultural planning under changing climatic conditions and agricultural planning, as well as for the development of forecasting mechanisms.EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR A. Efstratiadis

DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide a bias-corrected LS estimator. We also present bias-corrected versions of the three classical test statistics (Wald, LR, and LM test) and show their asymptotic distribution is a χ2-distribution. Monte Carlo simulations show the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes.

A Note on Performance of Conditional Akaike Information Criteria in Linear Mixed Models

It is not easy to select a linear mixed model since the main interest for model building could be different and the number of parameters in the model could not be clearly defined. In this paper, performance of conditional Akaike Information Criteria and its bias-corrected version are compared with marginal Bayesian and Akaike Information Criteria through a simulation study. The results from the simulation study indicate that bias-corrected conditional Akaike Information Criteria shows promising performance when candidate models exclude large models containing the true model, but bias-corrected one prefers over-parametrized models more intensively when a set of candidate models increases. Marginal Bayesian and Akaike Information Criteria also have some difficulty to select the true model when the design for random effects is nested.

Improved inferences for spatial regression models

The quasi-maximum likelihood (QML) method is popular in the estimation and inference for spatial regression models. However, the QML estimators (QMLEs) of the spatial parameters can be quite biased and hence the standard inferences for the regression coefficients (based on t-ratios) can be seriously affected. This issue, however, has not been addressed. The QMLEs of the spatial parameters can be bias-corrected based on the general method of Yang (2015b, J. of Econometrics 186, 178–200). In this paper, we demonstrate that by simply replacing the QMLEs of the spatial parameters by their bias-corrected versions, the usual t-ratios for the regression coefficients can be greatly improved. We propose further corrections on the standard errors of the QMLEs of the regression coefficients, and the resulted t-ratios perform superbly, leading to much more reliable inferences.

Is First-Order Vector Autoregressive Model Optimal for fMRI Data?

We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types--a resting state, an event-related design, and a block design data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.

Influence of differences in current GOSATXCO2retrievals on surface flux estimation

We investigated differences in the five currently-available datasets of column-integrated CO2 concentrations (XCO2) retrieved from spectral soundings collected by Greenhouse gases Observing SATellite (GOSAT) and assessed their impact on regional CO2 flux estimates. We did so by estimating the fluxes from each of the five XCO2 datasets combined with surface-based CO2 data, using a single inversion system. The five XCO2 datasets are available in raw and bias-corrected versions, and we found that the bias corrections diminish the range of the five coincident values by ~30% on average. The departures of the five individual inversion results (annual-mean regional fluxes based on XCO2-surface combined data) from the surface-data-only results were close to one another in some terrestrial regions where spatial coverage by each XCO2 dataset was similar. The mean of the five annual global land uptakes was 1.7 ± 0.3 GtC yr−1, and they were all smaller than the value estimated from the surface-based data alone.