Improved point estimation for the Kumaraswamy distribution

We develop nearly unbiased estimators for the Kumaraswamy distribution proposed by Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 46 (1980), pp. 79–88], which has considerable attention in hydrology and related areas. We derive modified maximum-likelihood estimators that are bias-free to second order. As an alternative to the analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. We conduct Monte Carlo simulations in order to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates.     

Bootstrap-based bias corrections for INAR count time series

Integer-valued autoregressive (INAR) processes form a very useful class of processes suitable to model time series of counts. Several practically relevant estimators based on INAR data are known to be systematically biased away from their population values, e.g. sample autocovariances, sample autocorrelations, or the dispersion index. We propose to do bias correction for such estimators by using a recently proposed INAR-type bootstrap scheme that is tailor-made for INAR processes, and which has been proven to be asymptotically consistent under general conditions. This INAR bootstrap allows an implementation with and without parametrically specifying the innovations' distribution. To judge the potential of corresponding bias correction, we compare these bootstraps in simulations to several competitors that include the AR bootstrap and block bootstrap. Finally, we conclude with an illustrative data application.     

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A.G. Patriota and A.J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655–1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.     

A package of four edited books on structural equations modeling

We consider two analytical and a bootstrap bias correction scheme existing in the literature for maximum likelihood estimators (MLEs) in the special case of a particular biparametric exponential family, the estimators being obtained from i.i.d. samples. We assess the performances of the estimators through numerical simulations for three particular cases of the family explored here. We observe that the two analytical proposals display very similar behavior for these distributions and that all proposed estimators are effective in reducing bias and mean square error of the MLEs.     

带异质线性趋势的动态二元选择面板模型估计

本文提出了带异质线性趋势的动态二元面板模型的极大似然偏误纠正估计量和近似条件Logit估计量。我们给出了通常极大似然估计量偏误的解析形式,并提供了相应的估计方法。小样本实验表明近似条件似然函数可以很好的消除异质性参数的影响,而偏误纠正估计量可以显著的修正极大似然估计量的偏误。最后我们将本文提出的方法应用到现金红利支付模型。     

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this performance is very similar to that of a parametric bootstrap correction based on a linear bias function. Three examples with actual data illustrate the application of our bias correction.     

Iterative Bias Correction of the Cross‐Validation Criterion

Abstract. The cross‐validation (CV) criterion is known to be asecond‐order unbiased estimator of the risk function measuring the discrepancy between the candidate model and the true model, as well as the generalized information criterion (GIC) and the extended information criterion (EIC). In the present article, we show that the 2kth‐order unbiased estimator can be obtained using a linear combination from the leave‐one‐out CV criterion to the leave‐k‐out CV criterion. The proposed scheme is unique in that a bias smaller than that of a jackknife method can be obtained without any analytic calculation, that is, it is not necessary to obtain the explicit form of several terms in an asymptotic expansion of the bias. Furthermore, the proposed criterion can be regarded as a finite correction of a bias‐corrected CV criterion by using scalar coefficients in a bias‐corrected EIC obtained by the bootstrap iteration.     

Statistical inference for the extreme value distribution under adaptive Type-II progressive censoring schemes

Adaptive Type-II progressive censoring schemes have been shown to be useful in striking a balance between statistical estimation efficiency and the time spent on a life-testing experiment. In this article, some general statistical properties of an adaptive Type-II progressive censoring scheme are first investigated. A bias correction procedure is proposed to reduce the bias of the maximum likelihood estimators (MLEs). We then focus on the extreme value distributed lifetimes and derive the Fisher information matrix for the MLEs based on these properties. Four different approaches are proposed to construct confidence intervals for the parameters of the extreme value distribution. Performance of these methods is compared through an extensive Monte Carlo simulation.     

Reducing Bias and Mean Squared Error Associated With Regression-Based Odds Ratio Estimators

Ratio estimators of effect are ordinarily obtained by exponentiating maximum-likelihood estimators (MLEs) of log-linear or logistic regression coefficients. These estimators can display marked positive finite-sample bias, however. We propose a simple correction that removes a substantial portion of the bias due to exponentiation. By combining this correction with bias correction on the log scale, we demonstrate that one achieves complete removal of second-order bias in odds ratio estimators in important special cases. We show how this approach extends to address bias in odds or risk ratio estimators in many common regression settings. We also propose a class of estimators that provide reduced mean bias and squared error, while allowing the investigator to control the risk of underestimating the true ratio parameter. We present simulation studies in which the proposed estimators are shown to exhibit considerable reduction in bias, variance, and mean squared error compared to MLEs. Bootstrapping provides further improvement, including narrower confidence intervals without sacrificing coverage.     

Assessing accuracy of a continuous screening test in the presence of verification bias

Summary.  In studies to assess the accuracy of a screening test, often definitive disease assessment is too invasive or expensive to be ascertained on all the study subjects. Although it may be more ethical or cost effective to ascertain the true disease status with a higher rate in study subjects where the screening test or additional information is suggestive of disease, estimates of accuracy can be biased in a study with such a design. This bias is known as verification bias. Verification bias correction methods that accommodate screening tests with binary or ordinal responses have been developed; however, no verification bias correction methods exist for tests with continuous results. We propose and compare imputation and reweighting bias-corrected estimators of true and false positive rates, receiver operating characteristic curves and area under the receiver operating characteristic curve for continuous tests. Distribution theory and simulation studies are used to compare the proposed estimators with respect to bias, relative efficiency and robustness to model misspecification. The bias correction estimators proposed are applied to data from a study of screening tests for neonatal hearing loss.     

Bootstrap methods for bias correction and confidence interval estimation for nonlinear quantile regression of longitudinal data

This paper examines the use of bootstrapping for bias correction and calculation of confidence intervals (CIs) for a weighted nonlinear quantile regression estimator adjusted to the case of longitudinal data. Different weights and types of CIs are used and compared by computer simulation using a logistic growth function and error terms following an AR(1) model. The results indicate that bias correction reduces the bias of a point estimator but fails for CI calculations. A bootstrap percentile method and a normal approximation method perform well for two weights when used without bias correction. Taking both coverage and lengths of CIs into consideration, a non-bias-corrected percentile method with an unweighted estimator performs best.     

Bayesian analysis of semiparametric Bernstein polynomial regression models for data with sample selection

In regression analysis, a sample selection scheme often applies to the response variable, which results in missing not at random observations on the variable. In this case, a regression analysis using only the selected cases would lead to biased results. This paper proposes a Bayesian methodology to correct this bias based on a semiparametric Bernstein polynomial regression model that incorporates the sample selection scheme into a stochastic monotone trend constraint, variable selection, and robustness against departures from the normality assumption. We present the basic theoretical properties of the proposed model that include its stochastic representation, sample selection bias quantification, and hierarchical model specification to deal with the stochastic monotone trend constraint in the nonparametric component, simple bias corrected estimation, and variable selection for the linear components. We then develop computationally feasible Markov chain Monte Carlo methods for semiparametric Bernstein polynomial functions with stochastically constrained parameter estimation and variable selection procedures. We demonstrate the finite-sample performance of the proposed model compared to existing methods using simulation studies and illustrate its use based on two real data applications.     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.     

A Fast Iterated Bootstrap Procedure for Approximating the Small-Sample Bias

This article proposes a fast approximation for the small sample bias correction of the iterated bootstrap. The approximation adapts existing fast approximation techniques of the bootstrap p-value and quantile functions to the problem of estimating the bias function. We show an optimality result which holds under general conditions not requiring an asymptotic pivot. Monte Carlo evidence, from the linear instrumental variable model and the nonlinear GMM, suggest that in addition to its computational appeal and success in reducing the mean and median bias in identified models, the fast approximation provides scope for bias reduction in weakly identified configurations.     

Bootstrap bias corrections for ensemble methods

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning. We demonstrate empirically that the proposed bootstrap bias correction can lead to substantial improvements in both bias and predictive accuracy. In the context of ensembles of trees, we show that this correction can be approximated at only double the cost of training the original ensemble. Our method is shown to improve test set accuracy over random forests by up to 70% on example problems from the UCI repository.     

Bias correction for parameter estimates of spatial point process models

When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best.     

Testing for error cross-sectional uncorrelatedness in a two-way error components panel data model

This paper proposes a new test for the error cross-sectional uncorrelatedness in a two-way error components panel data model based on large panel data sets. By virtue of an existing statistic under the raw data circumstance, an analogous test statistic using the within residuals of the model is constructed. We show that the resulting statistic needs bias correction to make valid inference, and then propose a method to implement feasible correction. Simulation shows that the test based on the feasible bias-corrected statistic performs well. Additionally, we employ a real data set to illustrate the use of the new test.     

A Monte Carlo study of bias corrections for panel probit models

We examine bias corrections which have been proposed for the fixed effects panel probit model with exogenous regressors, using several different data generating processes to evaluate the performance of the estimators in different situations. We find a best estimator across all cases for coefficient estimates, but when the marginal effects are the quantity of interest no analytical correction is able to outperform the uncorrected maximum-likelihood estimator.     

Boundary and Bias Correction in Kernel Hazard Estimation

A new class of local linear hazard estimators based on weighted least square kernel estimation is considered. The class includes the kernel hazard estimator of Ramlau-Hansen (1983), which has the same boundary correction property as the local linear regression estimator (see Fan & Gijbels, 1996). It is shown that all the local linear estimators in the class have the same pointwise asymptotic properties. We derive the multiplicative bias correction of the local linear estimator. In addition we propose a new bias correction technique based on bootstrap estimation of additive bias. This latter method has excellent theoretical properties. Based on an extensive simulation study where we compare the performance of competing estimators, we also recommend the use of the additive bias correction in applied work.     

The Third-Order Bias of Nonlinear Estimators

The third-order bias of nonlinear estimators is derived and illustrated using a variety of estimators popular in applied econometrics. A simulation using the exponential regression model indicates that the third-order analytical correction reduces bias substantially compared to higher-order bootstrap and Jackknife corrections, particularly in very small samples.