Large-Sample Theory

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honor¨¦ estimator, Hansen¡¯s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honor¨¦ estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honor¨¦ estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.

For a commonly occurring pattern of missing data, estimators of regression coefficients are derived by a non-likelihood method. The small-sample properties are investigated for the case of normality assumptions. The estimators are shown to be unbiased, exact small-sample variance formulae are derived, comparisons are made with ordinary least-squares estimators and it is demonstrated that the estimators can be more efficient than maximum-likelihood estimators in small samples.

Corrigendum to ‘Deep learning improves taphonomic resolution: high accuracy in differentiating tooth marks made by lions and jaguars'

Modeling of Social Economic Systems

Summary A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under ideal circumstances. At present, linear regression models are commonly used to analyse observational data and estimate causal effects. How do linear regression adjustments in observational studies emulate key features of randomized experiments, such as covariate balance, self-weighted sampling and study representativeness? In this paper, we provide answers to this and related questions by analysing the implied individual-level data weights of various linear regression methods. We derive new closed-form expressions of these implied weights, and examine their properties in both finite and large samples. Among others, in finite samples we characterize the implied target population of linear regression, and in large samples demonstrate the multiply robust properties of regression estimators from the perspective of their implied weights. We show that the implied weights of general regression methods can be equivalently obtained by solving a convex optimization problem. This equivalence allows us to bridge ideas from the regression modelling and causal inference literatures. As a result, we propose novel regression diagnostics for causal inference that are part of the design stage of an observational study. We implement the weights and diagnostics in the new lmw package for R.

The purpose of this study was to examine the performance of Naive Bayes, k-nearest neighborhood, neural networks, and logistic regression analysis in terms of sample size and test data rate in classifying students according to their mathematics performance. The target population was 62728 students in the 15-year-old group who were participated in the Programme for International Student Assessment (PISA) in 2012 from The Organisation for Economic Co-operation and Development (OECD) countries. The performance of each algorithm was tested by using 11%, 22%, 33%, 44% and 55% of each dataset for small (500 students), medium (1000 students) and large (5000 students) sample sizes. 100 replications were performed for each analysis. As the evaluation criteria, accuracy rates, RMSE values, and total elapsed time were used. RMSE values for each algorithm were statistically compared by using Friedman and Wilcoxon tests. The results revealed that while the classification performance of the methods increased as the sample size increased, the increase of training data ratio had different effects on the performance of the algorithms. The Naive Bayes showed high performance even in small samples, performed the analyzes very quickly, and was not affected by the change in the training data ratio. Logistic regression analysis was the most effective method in large samples but had a poor performance in small samples. While neural networks showed a similar tendency, its overall performance was lower than Naive Bayes and logistic regression. The lowest performances in all conditions were obtained by the k-nearest neighborhood algorithm.

Measurement error is a continuing concern for sociologists. A particularly nagging problem has been estimating regression coefficients of multiplicative effects when the component variables contain measurement error. Recently, Heise (1986) presented a corrected estimator for multiplicative terms containing measurement error. The research presented here extends Heise's work, and examines the use of an alternate corrected/constrained estimator proposed by Fuller (1980, 1987). The results of a Monte Carlo simulating give some support for Heise's findings, while providing further explanation for the behavior of estimators. The simulation focuses on small samples (n = 60 and n = 90), and examines the impact of different levels of measurement reliability on error correction procedures. Estimators are compared on the basis of bias, variance, root mean squared error, and singlesample inference accuracy. OLS is included as a benchmark. Results indicated only modest improvements over OLS in estimation using the corrected/constrained estimator, and some hazards in using the simpler corrected estimator in small samples. OLS is judged to be fairly robust and predictable in its inaccuracy.

Paired dichotomous data may arise in clinical trials such as pre-/post-test comparison studies and equivalence trials. Reporting parameter estimates (e.g. odds ratio, rate difference and rate ratio) along with their associated confidence interval estimates becomes a necessity in many medical journals. Various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions. Nevertheless, the performance of these asymptotic methods may have poor coverage properties in small samples. In this article, we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small-sample paired data. Specifically, we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test. The exact unconditional confidence interval guarantees the coverage probability, and it is recommended if strict control of coverage probability is required. However, the exact method tends to be overly conservative and computationally demanding. Our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small-sample designs, and yet they are relatively easy to implement computationally. We illustrate the methods using real examples from a pain management study and a cancer study.

Objectives Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML). TMLE is often argued or suggested to be better than DML estimators and several other estimators in small to moderate samples – even if they share the same large-sample properties – because TMLE is a plug-in estimator and respects the known bounds on the parameter, while other estimators might fall outside the known bounds and yield absurd estimates. However, this argument is not a rigorously proven result and may fail in certain cases. Methods In a carefully chosen simulation setting, I compare the performance of several versions of TMLE and DML estimators of the average treatment effect among treated in small to moderate samples. Results In this simulation setting, DML estimators outperforms some versions of TMLE in small samples. TMLE fluctuations are unstable, and hence empirically checking the magnitude of the TMLE fluctuation might alert cases where TMLE might perform poorly. Conclusions As a plug-in estimator, TMLE is not guaranteed to outperform non-plug-in counterparts such as DML estimators in small samples. Checking the fluctuation magnitude might be a useful diagnosis for TMLE. More rigorous theoretical justification is needed to understand and compare the finite-sample performance of these highly flexible estimators in general.

Time-Series Estimation of Structural Import Demand Equations: A Cross-Country Analysis

Asymptotic goodness-of-fit tests based on large sample theory have been shown to be unreliable in small sample designs and sparse data structures. In these situations, it is widely believed that exact version tests are dependable. However, exact goodness-of-fit tests that are based on discrete probabilities are conservative and the calculation of the exact distribution may be computationally intractable. In this article, we present a method, which is based on recursive polynomial multiplication, for performing exact analysis of goodness-of-fit tests. This method has been shown to be more efficient and accurate than an existing fast Fourier transform method. To overcome the conservativeness problem, we suggest the use of mid–P version goodness–of–fit tests. The small sample properties of the asymptotic, the exact, and the mid–P version goodness–of–fit tests are examined via the recursive polynomial multiplication method. Four commonly used power divergence statistics and six null hypotheses ranging from the equiprobable to the extremely skew are considered. The actual significance level behaviors under various null hypotheses suggest that as an anti–conservative test, the mid–P version tests behave fairly well. Nevertheless, it is not the case for the asymptotic and the exact tests. Among the four statistics considered, the exact power comparisons under a specific alternative to various null hypotheses show that the power divergence statistic with λ= 2/3 and the Pearson’s chi–squared statistic (λ = 1) are generally the most preferable.

A DCC-type approach for realized covariance modeling with score-driven dynamics

The aim of this paper is to demonstrate the impact of high leverage observations on the performances of prominent and popular Heteroskedasticity-Consistent Covariance Matrix Estimators (HCCMEs) with the help of computer simulation. Firstly, we figure out high leverage observations, then remove them and recalculate the HCCMEs without these observations in order to compare the HCCME performances with and without high leverage points. We identify high leverage observations with the Minimum Covariance Determinant (MCD). We select from among different covariates and disturbance term variances from the related literature in simulation runs in order to compare the percentage difference between the expected value of the HCCME and true covariance matrix as well as the symmetric loss function. Our results revealed that the elimination of high leverage (high MCD distance) observations had improved the HCCME performances considerably and under some settings substantially, depending on the degree of leverage. We hope our theoretical findings will be benefited for practical purposes in applications.

Predictive Regressions: A Reduced-Bias Estimation Method

Available methods for dealing with autocorrelated disturbanecs are unsatisfactory. They are computationally cumbersome and lead to estimators that have only weak asymptotic properties. Maximum likelihood estimation of all parameters is theoretically preferable, but has been unpopular due to the practical difficulties of numerical optimization in a multidimensional space. In this paper it is shown that the computational aspect of maximum likelihood estimation can be greatly simplified. The numerical search is confined to the interval (— 1, 1) of the autocorrelation parameter. The method is applicable to a single static equation as well as to autoregressive models with one or more equations. Some sampling experiments demonstrate the superiority of the maximum likelihood estimator over ordinary least squares, generalized least squares, and one other estimator in small samples.