Asymptotic Bias Research Articles

Measuring Dispersion and Serial Dependence in Ordinal Time Series Based on the Cumulative Paired ϕ-Entropy

The family of cumulative paired -entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s , with the weights being related to the actual choice of . Again, the asymptotic distribution of the corresponding sample is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel -entropy-related measures are applied to an ordinal time series on the daily level of air quality.

Optimal Covariate Balancing Conditions in Propensity Score Estimation

Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pretreatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the covariate balancing propensity score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.

Improved shrinkage estimators in zero-inflated negative binomial regression model

‎Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. ‎This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, ‎so that some of them have not influence on the response variable. ‎We proposed parameter estimation based on the linear shrinkage, ‎pretest, ‎shrinkage pretest, ‎Stein-type, ‎and positive Stein-type estimators. ‎We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. ‎‎We also conducted a Monte Carlo simulation study ‎to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion.‎‎ ‎The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. ‎The suggested estimators were applied to the wildlife fish data to appraise their performance.

Debiased learning and forecasting of first derivative

In the era of big data, there are many data sets recorded in equal intervals of time. To model the change rate of such data, one often constructs a nonparametric regression model and then estimates the first derivative of the mean function. Along this direction, we propose a symmetric two-sided local constant regression for interior points, an asymmetric two-sided local polynomial regression for boundary points, and a one-sided local linear forecasting model for outside points. Specifically, under the framework of locally weighted least squares regression, we derive the asymptotic bias and variance of the proposed estimators, as well as establish their asymptotic normality. Moreover, to reduce the estimation bias for highly-oscillatory functions, we propose debiased estimators based on high-order polynomials and derive their corresponding kernel functions. A data-driven two-step procedure for simultaneous selection of the model and tuning parameters is also proposed. Finally, the usefulness of our proposed estimators is demonstrated by simulation studies and two real data examples.

Transformed Estimation for Panel Interactive Effects Models

We propose a transformed estimator for the slope coefficients of panel models with interactive effects. The transformed estimation method does not require the prior knowledge of the dimension of factor structure. It is consistent and asymptotically normally distributed under fairly general conditions when N is fixed and or T is fixed and or when both N and T are large and Moreover, because the transformation is equivalent to aggregating cross-sectional units or time units before implementing the least-square method over time or across cross-sectional units, it can bypass the issues arising from heteroscedasticity across cross-sectional units or serial correlations over time in the idiosyncratic errors. Furthermore, in the case that the idiosyncratic errors are independent over time, there is no asymptotic bias even the explanatory variables contain lagged dependent variables when as Extensive Monte Carlo simulations are also conducted to examine the finite sample performance of the transformed estimation method.

Robust and Nonrobust Linking of Two Groups for the Rasch Model with Balanced and Unbalanced Random DIF: A Comparative Simulation Study and the Simultaneous Assessment of Standard Errors and Linking Errors with Resampling Techniques

In this article, the Rasch model is used for assessing a mean difference between two groups for a test of dichotomous items. It is assumed that random differential item functioning (DIF) exists that can bias group differences. The case of balanced DIF is distinguished from the case of unbalanced DIF. In balanced DIF, DIF effects on average cancel out. In contrast, in unbalanced DIF, the expected value of DIF effects can differ from zero and on average favor a particular group. Robust linking methods (e.g., invariance alignment) aim at determining group mean differences that are robust to the presence of DIF. In contrast, group differences obtained from nonrobust linking methods (e.g., Haebara linking) can be affected by the presence of a few DIF effects. Alternative robust and nonrobust linking methods are compared in a simulation study under various simulation conditions. It turned out that robust linking methods are preferred over nonrobust alternatives in the case of unbalanced DIF effects. Moreover, the theory of M-estimation, as an important approach to robust statistical estimation suitable for data with asymmetric errors, is used to study the asymptotic behavior of linking estimators if the number of items tends to infinity. These results give insights into the asymptotic bias and the estimation of linking errors that represent the variability in estimates due to selecting items in a test. Moreover, M-estimation is also used in an analytical treatment to assess standard errors and linking errors simultaneously. Finally, double jackknife and double half sampling methods are introduced and evaluated in a simulation study to assess standard errors and linking errors simultaneously. Half sampling outperformed jackknife estimators for the assessment of variability of estimates from robust linking methods.

Two-stage instrumental variable estimation of linear panel data models with interactive effects

Summary This paper analyses the instrumental variables (IV) approach put forward by Norkute et al. (2021), in the context of static linear panel data models with interactive effects present in the error term and the regressors. Instruments are obtained from transformed regressors, thereby it is not necessary to search for external instruments. We consider a two-stage IV (2SIV) and a mean-group IV (MGIV) estimator for homogeneous and heterogeneous slope models, respectively. The asymptotic analysis reveals that: (i) the $\sqrt{\textit {NT}}$-consistent 2SIV estimator is free from asymptotic bias that may arise due to the estimation error of the interactive effects, while (ii) existing estimators can suffer from asymptotic bias; (iii) the proposed 2SIV estimator is asymptotically as efficient as existing estimators that eliminate interactive effects jointly in the regressors and the error, while (iv) the relative efficiency of the estimators that eliminate interactive effects only in the error term is indeterminate. A Monte Carlo study confirms good approximation quality of our asymptotic results.

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application.

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease.

Asymptotic properties of correlation-based principal component analysis

It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a novel jackknife-type estimator of the asymptotic variance of the integrated volatility functional estimator. This new variance estimator shows much better finite sample performances compared to other existing ones. This paper also proposes several statistical tests for some commonly tested hypotheses in the literature. Simulation results show that one will get misleading results if one uses the analytical results of the covariance case when applying PCA on the correlation matrix.

Misspecified diffusion models with high-frequency observations and an application to neural networks

We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the misspecified setting and fails to achieve an optimal rate of convergence. To address this, we consider a new quasi-likelihood function that allows constructing a maximum-likelihood-type estimator that achieves the optimal rate of convergence. Study of misspecified models enables us to apply machine-learning techniques to the maximum-likelihood approach. With these techniques, we can efficiently study the microstructure of a stock market by using rich information of high-frequency data. Neural networks have particularly good compatibility with the maximum-likelihood approach, so we will consider an example of using a neural network for simulation studies and empirical analysis of high-frequency data from the Tokyo Stock Exchange. We demonstrate that the neural network outperforms polynomial models in volatility predictions for major stocks in Tokyo Stock Exchange.

Stochastic smoothing of point processes for wildlife-vehicle collisions on road networks

Wildlife-vehicle collisions on road networks represent a natural problem between human populations and the environment, that affects wildlife management and raise a risk to the life and safety of car drivers. We propose a statistically principled method for kernel smoothing of point pattern data on a linear network when the first-order intensity depends on covariates. In particular, we present a consistent kernel estimator for the first-order intensity function that uses a convenient relationship between the intensity and the density of events location over the network, which also exploits the theoretical relationship between the original point process on the network and its transformed process through the covariate. We derive the asymptotic bias and variance of the estimator, and adapt some data-driven bandwidth selectors to estimate the optimal bandwidth. The performance of the estimator is analysed through a simulation study under inhomogeneous scenarios. We present a real data analysis on wildlife-vehicle collisions in a region of North-East of Spain.

Taylor Rule Estimation by OLS

Ordinary Least Squares (OLS) estimation of monetary policy rules produces potentially inconsistent estimates of policy parameters. The reason is that central banks react to variables, such as inflation and the output gap, that are endogenous to monetary policy shocks. Endogeneity implies a correlation between regressors and the error term – hence, an asymptotic bias. In principle, Instrumental Variables (IV) estimation can solve this endogeneity problem. In practice, however, IV estimation poses challenges, as the validity of potential instruments depends on various unobserved features of the economic environment. We argue in favor of OLS estimation of monetary policy rules. To that end, we show analytically in the three-equation New Keynesian model that the asymptotic OLS bias is proportional to the fraction of the variance of regressors due to monetary policy shocks. Using Monte Carlo simulations, we then show that this relationship also holds in a quantitative model of the U.S. economy. Since monetary policy shocks explain only a small fraction of the variance of regressors typically included in monetary policy rules, the endogeneity bias tends to be small. For realistic sample sizes, OLS outperforms IV. Finally, we estimate a standard Taylor rule on different subsamples of U.S. data and find that OLS and IV estimates are quite similar.

Bayesian seismic inversion: a fast sampling Langevin dynamics Markov chain Monte Carlo method

SUMMARY In this study, we aim to solve the seismic inversion in the Bayesian framework by generating samples from the posterior distribution. This distribution incorporates the uncertainties in the seismic data, forward model, and prior information about the subsurface model parameters; thus, we obtain more information through sampling than through a point estimate (e.g. maximum a posteriori method). Based on the numerical cost of solving the forward problem and the dimensions of the subsurface model parameters and observed data, sampling with Markov chain Monte Carlo (MCMC) algorithms can be prohibitively expensive. Herein, we consider the promising Langevin dynamics MCMC algorithm. However, this algorithm has two central challenges: (1) the step size requires prior tuning to achieve optimal performance and (2) the Metropolis–Hastings acceptance step is computationally demanding. We approach these challenges by proposing an adaptive step-size rule and considering the suppression of the Metropolis–Hastings acceptance step. We highlight the proposed method’s potential through several numerical examples and rigorously validate it via qualitative and quantitative evaluation of the sample quality based on the kernelized Stein discrepancy (KSD) and other MCMC diagnostics such as trace and autocorrelation function plots. We conclude that, by suppressing the Metropolis–Hastings step, the proposed method provides fast sampling at efficient computational costs for large-scale seismic Bayesian inference; however, this inflates the second statistical moment (variance) due to asymptotic bias. Nevertheless, the proposed method reliably recovers important aspects of the posterior, including means, variances, skewness and 1-D and 2-D marginals. With larger computational budget, exact MCMC methods (i.e. with a Metropolis–Hastings step) should be favoured. The results thus obtained can be considered a feasibility study for promoting the approximate Langevin dynamics MCMC method for Bayesian seismic inversion on limited computational resources.

Maker Breaker on digraphs

AbstractWe study two biased Maker–Breaker games played on the complete digraph . In the strong connectivity game, Maker wants to build a strongly connected subgraph. We determine the asymptotic optimal bias for this game viz. . In the Hamiltonian game, Maker wants to build a Hamiltonian subgraph. We determine the asymptotic optimal bias for this game up to a constant factor.

Predicting Individual Effects in Fixed Effects Panel Probit Models

Abstract Many applied settings in empirical economics require estimation of a large number of individual effects, like teacher effects or location effects; in health economics, prominent examples include patient effects, doctor effects or hospital effects. Increasingly, these effects are the object of interest of the estimation, and predicted effects are often used for further descriptive and regression analyses. To avoid imposing distributional assumptions on these effects, they are typically estimated via fixed effects methods. In short panels, the conventional maximum likelihood estimator for fixed effects binary response models provides poor estimates of these individual effects since the finite sample bias is typically substantial. We present a bias-reduced fixed effects estimator that provides better estimates of the individual effects in these models by removing the first-order asymptotic bias. An additional, practical advantage of the estimator is that it provides finite predictions for all individual effects in the sample, including those for which the corresponding dependent variable has identical outcomes in all time periods over time (either all zeros or ones); for these, the maximum likelihood prediction is infinite. We illustrate the approach in simulation experiments and in an application to health care utilization.

On Genetic Correlation Estimation With Summary Statistics From Genome-Wide Association Studies

Cross-trait polygenic risk score (PRS) method has gained popularity for assessing genetic correlation of complex traits using summary statistics from biobank-scale genome-wide association studies (GWAS). However, empirical evidence has shown a common bias phenomenon that highly significant cross-trait PRS can only account for a very small amount of genetic variance (R 2 can be ) in independent testing GWAS. The aim of this paper is to investigate and address the bias phenomenon of cross-trait PRS in numerous GWAS applications. We show that the estimated genetic correlation can be asymptotically biased toward zero. A consistent cross-trait PRS estimator is then proposed to correct such asymptotic bias. In addition, we investigate whether or not SNP screening by GWAS p-values can lead to improved estimation and show the effect of overlapping samples among GWAS. We analyze GWAS summary statistics of reaction time and brain structural magnetic resonance imaging-based features measured in the Pediatric Imaging, Neurocognition, and Genetics study. We find that the raw cross-trait PRS estimators heavily underestimate the genetic similarity between cognitive function and human brain structures (mean ), whereas the bias-corrected estimators uncover the moderate degree of genetic overlap between these closely related heritable traits (mean ). Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Double smoothing local linear estimation in nonlinear time series

We generalize the double smoothing local linear regression method to nonparametric regression of time series. Under a strong mixing condition for the dependence of the time series, we show that after another round of smoothing based on the local linear regression estimates, the double smoothing local linear estimate will have reduced asymptotic bias, while keeping the variance at the same asymptotic order. The asymptotic bias reduces from the order of h 2 for the local linear estimates to h 4 for the double smoothing local linear estimates, where h is the bandwidth. Hence the double smoothing local linear method produces more optimal estimates in terms of mean squared error. Simulation studies and real time series data analysis confirm the advantages of the double smoothing method compared to the local linear method.

Using shrinkage strategies to estimate fixed effects in zero-inflated negative binomial mixed model

In this paper, we address the estimation of fixed effects parameters in the zero-inflated negative binomial mixed model based on shrinkage estimators, namely linear shrinkage, pretest, shrinkage pretest, shrinkage, and positive-shrinkage estimators when the random effects are considered as nuisance parameters. We compare the performance of the shrinkage estimators to unrestricted and restricted estimators when certain prior subspace information is available. The asymptotic distributional biases and risks of the proposed estimators are obtained. We also conduct a Monte Carlo simulation study to compare the performance of each estimator in the sense of simulated relative efficiency. The results of simulation study show that the proposed estimation strategies perform strongly better than the maximum likelihood method. Finally, proposed methodologies are applied to a real dataset to appraise their performances.

Semiparametric recurrent event vs time-to-first-event analyses in randomized trials: Estimands and model misspecification.

Insights regarding the merits of recurrent event and time-to-first-event analyses are needed to provide guidance on strategies for analyzing intervention effects in randomized trials involving recurrent event responses. Using established asymptotic results we introduce a framework for studying the large sample properties of estimators arising from semiparametric proportional rate function models and Cox regression under model misspecification. The asymptotic biases and power implications are investigated for different data generating models, and we study the impact of dependent censoring on these findings. Illustrative applications are given involving data from a cystic fibrosis trial and a carcinogenicity experiment, following which we summarize findings and discuss implications for clinical trial design.

Asymptotic linear expansion of regularized M-estimators

Parametric high-dimensional regression requires regularization terms to get interpretable models. The respective estimators correspond to regularized M-functionals which are naturally highly nonlinear. Their Gâteaux derivative, i.e., their influence curve linearizes the asymptotic bias of the estimator, but only up to a remainder term which is not guaranteed to tend (sufficiently fast) to zero uniformly on suitable tangent sets without profound arguments. We fill this gap by studying, in a unified framework, under which conditions the M-functionals corresponding to convex penalties as regularization are compactly differentiable, so that the estimators admit an asymptotically linear expansion. This key ingredient allows influence curves to reasonably enter model diagnosis and enable a fast, valid update formula, just requiring an evaluation of the corresponding influence curve at new data points. Moreover, this paves the way for optimally-robust estimators, bounding the influence curves in a suitable way.