Bootstrap Bias Correction Research Articles

Bias-Correction Methods for the Unit Exponential Distribution and Applications

The bias of the maximum likelihood estimator can cause a considerable estimation error if the sample size is small. To reduce the bias of the maximum likelihood estimator under the small sample situation, the maximum likelihood and parametric bootstrap bias-correction methods are proposed in this study to obtain more reliable maximum likelihood estimators of the unit exponential distribution parameters. The procedure to implement the bias-corrected maximum likelihood estimation method is derived analytically, and the steps to obtain the bias-corrected bootstrap estimators are presented. The simulation results show that the proposed maximum likelihood bootstrap bias-correction method can significantly reduce the bias and mean squared error of the maximum likelihood estimators for most of the parameter combinations in the simulation study. A soil moisture data set and a numerical example are used for illustration.

Predicting effects of a digital stress intervention for patients with depressive symptoms: Development and validation of meta-analytic prognostic models using individual participant data.

Digital stress interventions could be helpful as an "indirect" treatment for depression, but it remains unclear for whom this is a viable option. In this study, we developed models predicting individualized benefits of a digital stress intervention on depressive symptoms at 6-month follow-up. Data of N = 1,525 patients with depressive symptoms (Center for Epidemiological Studies' Depression Scale, CES-D ≥ 16) from k = 6 randomized trials (digital stress intervention vs. waitlist) were collected. Prognostic models were developed using multilevel least absolute shrinkage and selection operator and boosting algorithms, and were validated using bootstrap bias correction and internal-external cross-validation. Subsequently, expected effects among those with and without a treatment recommendation were estimated based on clinically derived treatment assignment cut points. Performances ranged from R² = 21.0%-23.4%, decreasing only slightly after model optimism correction (R² = 17.0%-19.6%). Predictions were greatly improved by including an interim assessment of depressive symptoms (optimism-corrected R2 = 32.6%-35.6%). Using a minimally important difference of d = -0.24 as assignment cut point, approximately 84.6%-93.3% of patients are helped by this type of intervention, while the remaining 6.7%-15.4% would experience clinically negligible benefits (δ^ = -0.02 to -0.19). Using reliable change as cut point, a smaller subset (39.3%-46.2%) with substantial expected benefits (δ^ = -0.68) receives a treatment recommendation. Meta-analytic prognostic models applied to individual participant data can be used to predict differential benefits of a digital stress intervention as an indirect treatment for depression. While most patients seem to benefit, the developed models could be helpful as a screening tool to identify those for whom a more intensive depression treatment is needed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A Note on Bias Correction for the Standard Two‐Sided Power Distribution

AbstractIt is verified that the maximum likelihood (ML) estimators of the standard two‐sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are proposed. The numerical study favors a particular bootstrap estimator based on parametric resampling. Real data applications are also considered to illustrate the impact of bias correction of the usual maximum likelihood estimators of the standard two‐sided power distribution parameters when the sample size is small.

Another Warning About Median Reaction Time

Contrary to the warning of Miller (1988), Rousselet and Wilcox (2020) argued that it is better to summarize each participant's single-trial reaction times (RTs) in a given condition with the median than with the mean when comparing the central tendencies of RT distributions across experimental conditions. They acknowledged that median RTs can produce inflated Type~I error rates when conditions differ in the number of trials tested, consistent with Miller's warning, but they showed that the bias responsible for this error rate inflation could be eliminated with a bootstrap bias correction technique. The present simulations extend their analysis by examining the power of bias-corrected medians to detect true experimental effects and by comparing this power with the power of analyses using means and regular medians. Unfortunately, although bias corrected medians solve the problem of inflated Type~I error rates, their power is lower than that of means or regular medians in many realistic situations. In addition, even when conditions do not differ in the number of trials tested, the power of tests (e.g., t-tests) is generally lower using medians rather than means as the summary measures. Thus, the present simulations demonstrate that summary means will often provide the most powerful test for differences between conditions, and they show what aspects of the RT distributions determine the size of the power advantage for means.

Bias correction for eta squared in one-way ANOVA

Eta squared is a popular effect size, but contains positive bias. Bootstrapping can be used to remove the bias from eta squared. Compared to epsilon squared and omega squared, bootstrap bias correction does not make distributional assumption, and it is easy to implement. A real example and computer simulations are included to illustrate its application. The bootstrap bias-corrected eta squared shows very little bias, and it serves as a good alternative to eta squared and epsilon squared, the latter of which can turn negative in some circumstances.

Letter to the Editor: Pulling Unmeasured Confounding Out by your Bootstraps: Too Good to be True?

Inverse probability of treatment weighting can account for confounding under a number of assumptions, including that of no unmeasured confounding. A recent simulation study proposed a bootstrap bias correction, apparently demonstrating good performance in removing bias due to unmeasured confounding. We revisited the simulations, finding no evidence of bias reduction. Journal of Statistical Research 2021, Vol. 55, No. 2, pp. 293-297

Bias Correction Method for Log-Power-Normal Distribution

The log-power-normal distribution is a generalized version of the log-normal distribution. The maximum likelihood estimation method is the most popular method to obtain the estimates of the log-power-normal distribution parameters. In this article, we investigate the performance of the maximum likelihood estimation method for point and interval inferences. Moreover, a simple method that has less impact from the subjective selection of the initial solutions to the model parameters is proposed. The bootstrap bias correction method is used to enhance the estimation performance of the maximum likelihood estimation method. The proposed bias correction method is simple for use. Monte Carlo simulations are conducted to check the quality of the proposed bias correction method. The simulation results indicate that the proposed bias correction method can improve the performance of the maximum likelihood estimation method with a smaller bias and provide a coverage probability close to the nominal confidence coefficient. Two real examples about the air pollution and cement’s concrete strength are used for illustration.

Improving the causal treatment effect estimation with propensity scores by the bootstrap

When observational studies are used to establish the causal effects of treatments, the estimated effect is affected by treatment selection bias. The inverse propensity score weight (IPSW) is often used to deal with such bias. However, IPSW requires strong assumptions whose misspecifications and strategies to correct the misspecifications were rarely studied. We present a bootstrap bias correction of IPSW (BC-IPSW) to improve the performance of propensity score in dealing with treatment selection bias in the presence of failure to the ignorability and overlap assumptions. The approach was motivated by a real observational study to explore the potential of anticoagulant treatment for reducing mortality in patients with end-stage renal disease. The benefit of the treatment to enhance survival was demonstrated; the suggested BC-IPSW method indicated a statistically significant reduction in mortality for patients receiving the treatment. Using extensive simulations, we show that BC-IPSW substantially reduced the bias due to the misspecification of the ignorability and overlap assumptions. Further, we showed that IPSW is still useful to account for the lack of treatment randomization, but its advantages are stringently linked to the satisfaction of ignorability, indicating that the existence of relevant though unmeasured or unused covariates can worsen the selection bias.

Methods of Estimation and Bias Corrected Maximum Likelihood Estimators of Unit Burr III Distribution

In this article, various classical estimation methods are employed to estimate the parameters of unit Burr III distribution. Further, the associated second-order bias corrections of the MLEs of its parameters are obtained by using a modified bias-corrected approach. In addition, another parametric bootstrap bias correction method is also considered for model parameters. Extensive Monte-Carlo simulation studies are performed to evaluate different estimation methods in terms of their average biases and mean squared error, and the performance of these estimators are compared as well. Our results reveal that the bias corrections improve the accuracy of maximum likelihood estimates. Finally, one real data example is discussed to illustrate the applicability of the unit Burr III distribution.

Improved maximum likelihood estimation of the parameters of the Gamma-Uniform distribution with bias-corrections

A two-parameter Gamma-Uniform distribution was recently introduced as a prominent alternative in modeling bounded phenomena. Unfortunately, however, its maximum likelihood estimators (MLEs) are found to be highly biased in finite samples, a limitation that might effect this model’s application in data modeling. In this article, we construct nearly unbiased estimators for the unknown parameters of this distribution by deriving analytical bias-corrected maximum likelihood estimators applying the Cox and Snell methodology, the Firth’s method and also via the parametric Bootstrap bias correction approach. Our extensive simulation clearly revealed that the three bias reduction methods yield very good estimates which are nearly unbiased and exhibit comparable efficiency. Finally, we consider a real data set where the variable under enquiry is the proportion of unemployed labor force reported across some 158 nations in 2018 to show case the positive gain of incorporating the bias correction in the model fitting.

On the estimation bias in first‐order bifurcating autoregressive models

In this paper, we study the bias of the least squares (LS) estimation for the stationary first‐order bifurcating autoregressive (BAR(1)) model which is commonly used to model binary tree‐structured data that appear in many applications, most famously cell‐lineage applications. We first show that the LS estimator can have large bias for both small and moderate sized samples and that this bias is dependent on the values of both the autoregressive parameter (the target parameter) and the correlation between model errors. We also provide a first‐order approximation to the bias of the LS estimator and show, empirically, that this approximation can accurately describe the bias as a function of the autoregressive parameter and the errors correlation over wide combinations of their values. Then we study two approaches for correcting the bias of the LS estimator, namely, bootstrap bias correction and bias correction through linear bias functions. Both single and double bootstrap bias‐corrected versions of the LS estimator are defined and studied empirically in comparison with a linear‐bias‐correcting estimator as well as the standard LS estimator. The empirical results, based on both simulated and real data, demonstrate that both the linear‐bias‐correcting estimator and the bootstrap bias‐correcting estimators can be quite effective in reducing the bias of the LS estimator and that the bootstrap estimators are more effective near the boundaries of the range of the autoregressive parameter. We also discuss the extension of these methods to higher order BAR models.

Bias Correction With Jackknife, Bootstrap, and Taylor Series

We analyze bias correction methods using jackknife, bootstrap, and Taylor series. We focus on the binomial model, and consider the problem of bias correction for estimating $f(p)$ , where $f \in C[{0,1}]$ is arbitrary. We characterize the supremum norm of the bias of general jackknife and bootstrap estimators for any continuous functions, and demonstrate the in delete- $d$ jackknife, different values of $d$ may lead to drastically different behaviors in jackknife. We show that in the binomial model, iterating the bootstrap bias correction infinitely many times may lead to divergence of bias and variance, and demonstrate that the bias properties of the bootstrap bias corrected estimator after $r-1$ rounds are of the same order as that of the $r$ -jackknife estimator if a bounded coefficients condition is satisfied.

Reaction Times and other Skewed Distributions


 
 
 
 To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that "sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions". Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised for several reasons. First, the median's bias can be corrected using a percentile bootstrap bias correction. Second, a careful examination of the sampling distributions reveals that the sample median is median unbiased, whereas the mean is median biased when dealing with skewed distributions. That is, on average the sample mean estimates the population mean, but typically this is not the case. In addition, simulations of false and true positives in various situations show that no method dominates. Crucially, neither the mean nor the median are sufficient or even necessary to compare skewed distributions. Different questions require different methods and it would be unwise to use the mean or the median in all situations. Better tools are available to get a deeper understanding of how distributions differ: we illustrate the hierarchical shift function, a powerful alternative that relies on quantile estimation. All the code and data to reproduce the figures and analyses in the article are available online.
 
 
 

Inference on mean quality-adjusted lifetime using joint models for continuous quality of life process and time to event

The estimated average treatment effect in observational studies is biased if the assumptions of ignorability and overlap are not satisfied. To deal with this potential problem when propensity score weights are used in the estimation of the treatment effects, in this paper we propose a bootstrap bias correction estimator for the average treatment effect (ATE) obtained with the inverse propensity score (BBC-IPS) estimator. We show in simulations that the BBC-IPC performs well when we have misspecifications of the propensity score (PS) due to: omitted variables (ignorability property may not be satisfied), overlap (imbalances in distribution between treatment and control groups) and confounding effects between observables and unobservables (endogeneity). Further refinements in bias reductions of the ATE estimates in smaller samples are attained by iterating the BBC-IPS estimator.

A bootstrap bias correction of long run fourth order moment estimation in the CUSUM of squares test

ABSTRACTThe aim of this paper is to propose a bias correction of the estimation of the long run fourth order moment in the CUSUM of squares test proposed in Sansó et al. [Testing for change in the unconditional variance of financial time series. Rev Econ Financ. 2004;4(1):32–53] for the detection of structural breaks in financial data. The correction is made by using the stationary bootstrap. The choice of this resampling technique is justified by the stationarity and weak dependence of the time series under the assumptions which ensure the existence of the limiting distribution of the test statistic, under the null hypothesis. Monte Carlo experiments have been implemented to evaluate the effect of the proposed bias correction considering two particular data generating processes, the GARCH(1,1) and the log-Normal Stochastic Volatility. The effectiveness of the bias correction has been evaluated also on real data sets.

Corrections for measurement error due to delayed onset of illness for case-crossover designs.

Epidemiologic studies of the short-term effects of ambient particulate matter (PM) on the risk of acute cardiovascular or cerebrovascular events often use data from administrative databases in which only the date of hospitalization is known. A common study design for analyzing such data is the case-crossover design, in which exposure at a time when a patient experiences an event is compared to exposure at times when the patient did not experience an event within a case-control paradigm. However, the time of true event onset may precede hospitalization by hours or days, which can yield attenuated effect estimates. In this article, we consider a marginal likelihood estimator, a regression calibration estimator, and a conditional score estimator, as well as parametric bootstrap versions of each, to correct for this bias. All considered approaches require validation data on the distribution of the delay times. We compare the performance of the approaches in realistic scenarios via simulation, and apply the methods to analyze data from a Boston-area study of the association between ambient air pollution and acute stroke onset. Based on both simulation and the case study, we conclude that a two-stage regression calibration estimator with a parametric bootstrap bias correction is an effective method for correcting bias in health effect estimates arising from delayed onset in a case-crossoverstudy.

Bootstrap bias correction for average treatment effects with inverse propensity weights

The estimated average treatment effect in observational studies is biased if the assumptions of ignorability and overlap are not satisfied. To deal with this potential problem when propensity score weights are used in the estimation of the treatment effects, in this paper we propose a bootstrap bias correction estimator for the average treatment effect (ATE) obtained with the inverse propensity score (BBC-IPS) estimator. We show in simulations that the BBC-IPC performs well when we have misspecifications of the propensity score (PS) due to: omitted variables (ignorability property may not be satisfied), overlap (imbalances in distribution between treatment and control groups) and confounding effects between observables and unobservables (endogeneity). Further refinements in bias reductions of the ATE estimates in smaller samples are attained by iterating the BBC-IPS estimator.

Small sample properties of ML estimator in Vasicek and CIR models: a simulation experiment

In this paper we analyze small sample properties of the ML estimation procedure in Vasicek and CIR models. In particular, we consider short time series, with a length between 20 and 200, typically values observed in the field of survival data. We perform a simulation study in order to investigate which properties of the parameter estimators still remain valid and to evaluate the effect of a bootstrap bias correction method. The results show that the bias of the estimators can be really strong for small samples and the relative bias seems to be worse when the true parameters of the models are near to the nonstationarity case. The bootstrap bias correction is enough efficient in correcting the bias also for very small sample sizes, but the increase in RMSE of the estimator is greater as much as smaller is the bias in the ML estimator. Moreover, the bootstrap correction does not improve the performance of the tests on the parameters.

Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence

In this study, different frequentist estimation procedures for the parameters of the exponential-Poisson distribution are considered, such as the maximum likelihood, method of moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramér-von Mises and Anderson-Darling maximum goodness-of-fit estimators. We compare them using extensive numerical simulations, which show that using a nested expectation-maximization algorithm in the maximum likelihood estimators with bootstrap bias correction does not require numerical procedures to solve nonlinear equations and returns accurate parameter estimates. Finally, our proposed methodology is fully illustrated using two real data sets (rainfall and aircraft data) with the occurrence of zero values.

Optimal intraday power trading with a Gaussian additive process

Trading activity in intraday (ID) electricity markets has increased significantly over the last few years. We study the problem of a financial agent wishing to maximize a constant relative risk-aversion expected utility of their terminal wealth while operating in an ID market. Assuming that the price of traded hours follows an additive Ornstein– Uhlenbeck process, we derive the optimal strategy via the Hamilton–Jacobi–Bellman equation. The optimal portfolio in the log case is totally myopic with respect to time to maturity, while in the power case it becomes more and more risky as final maturity approaches. In order to implement our strategy, it is necessary to estimate the model parameters. One cannot resort to known results, as it is typical for time series to be unevenly time spaced, with more and more transactions as maturity approaches. Thus, we present an estimation procedure for unevenly spaced observations, based on maximum likelihood estimation and a bootstrap bias correction, in order to compensate for having few observations at the beginning of the observation frame. Finally, we backtest our method and conclude.