Robust Bootstrap Method Research Articles

Robust multipe imputation with GAM

Multiple imputation of missing values is a key step in data analytics and a standard process in data science. Nonlinear imputation methods come into play whenever the linear relationship between a response and predictors cannot be linearized by transformations of variables, adding interactions, or using, e.g., quadratic terms. Generalized additive models (GAM) and its extension, GAMLSS—where each parameter of the distribution, such as mean, variance, skewness, and kurtosis, can be represented as a function of predictors, are widely used nonlinear methods. However, non-robust methods such as standard GAM’s and GAMLSS’s can be swayed by outliers, leading to outlier-driven imputations. This can apply concerning both representative outliers—those true yet unusual values of your population—and non-representative outliers, which are mere measurement errors. Robust (imputation) methods effectively manage outliers and exhibit resistance to their influence, providing a more reliable approach to dealing with missing data. The innovative solution of the proposed new imputation algorithm tackles three major challenges related to robustness. (1) A robust bootstrap method is employed to handle model uncertainty during the imputation of a random sample. (2) The approach incorporates robust fitting techniques to enhance accuracy. (3) It effectively considers imputation uncertainty in a resilient manner. Furthermore, any complex model for any variable with missingness can be considered and run through the algorithm. For the real-world data sets used and the simulation study conducted, the novel algorithm imputeRobust which includes robust methods for imputation with GAM’s demonstrates superior performance compared to existing imputation methods using GAMLSS. Limitations pertain to the imputation of categorical variables using robust techniques.

Research on the Relationship between Lifestyle and Sleep Health

Insomnia, a widespread concern among the populace, frequently prompts questions about the determinants of sleep quality. Addressing these queries, the study meticulously examines the impact of various lifestyle factors on sleep. This paper utilizes a comprehensive dataset from Kaggle, encompassing an array of lifestyle habits and their corresponding sleep quality metrics. Through the application of a linear regression model and the robust bootstrap method, the analysis has brought to light a substantial scientific link between lifestyle choices and the quality of sleep. The findings are revealing: key factors such as age, the extent of physical activity, and the number of steps taken daily exhibit a positive correlation with enhanced sleep quality. In stark contrast, this paper observes that elevated stress levels and increased systolic blood pressure negatively impinge upon sleep. Intriguingly, the study further reveals that sleep quality is not uniform across the board; it varies significantly with gender differences and Body Mass Index (BMI) levels. These insights underscore the multifaceted nature of sleep quality, influenced by a tapestry of lifestyle elements. The research contributes to a deeper understanding of sleep dynamics, offering valuable perspectives for improving sleep health in the society.

Perceived eWallet security: impact of COVID-19 pandemic

Purpose Coronavirus (COVID-19) pandemic forced nationwide lockdown in India. During the period of lockdown usage of eWallet increased by 44%. With the increased usage of digital transactions, cyber-crime attacks also increased as much as by 86%. The socio-economic environment and the peoples’ mindset in the country yet not ready for this kind of rise in digital transactions. The purpose of this study is to capture “security concern” and “comfortability” in regard to using eWallet during the COVID-19 pandemic situation. The study further investigated the influence of demographics such as gender and income on “security concern” and “comfortability” in using eWallet. Design/methodology/approach This was an empirical study. The respondents were selected using a purposive sampling method. Only those people who had been using eWallet were included in the survey. The questionnaire was circulated to 100 respondents who agreed to participate in the survey. After scrutiny total of 43 questionnaires were found to be completely filled in all aspects, and thus used for analysis. This study used an innovative multi-method approach for analysis. The hypotheses were tested using two methods: the conventional p-value method and the robust BCa bootstrap method. The effect size was also reported. Findings The findings suggest that female users are more concerned about eWallet security than male users. This study showed that people from the middle-income group are more concerned about the security of digital payments than the people from the lower-income group. Research limitations/implications This study covered the influence of two demographic variables “gender” and “income” on security and comfort in using eWallets. Other demographic variables such as age, education, occupation and area of residence (rural or urban) need to be investigated with the inclusion of rural populations. From the findings of this study, this paper argues that the middle-income group in India is more risk intolerant than the lower-income group while higher and lower-income groups are indifferent. A separate detailed study is recommended for additional support. This study used an innovative multi-method approach of analysis and use of bootstrapping. This may encourage other researchers to adopt such approaches. Practical implications This study showed that irrespective of the forceful adoption; security concerns are prevailing and on the rise. This is an alarm to developers and service providers that, although the use of eWallets increased exponentially during this COVID-19 pandemic, it is a forceful adoption and not willful. They should not get deceived by rise in eWallet users and must endeavor to improve the security of eWallets otherwise, there may be a sharp decline in eWallet users once the COVID-19 pandemic is over. Originality/value This study attempted to capture the comfortability and security concerns of eWallet users during the COVID-19 pandemic. This study used an innovative multi-method approach of analysis and used bootstrapping in addition to the conventional p-value method to test the significance. This study showed that irrespective of the forceful adoption of eWallets owing to the COVID-19 pandemic, security concerns are prevailing and on the rise. The study confirms that gender has an influence on eWallet security. The findings of this study are in partial conformity with the findings of previous researchers.

WEAK-IDENTIFICATION ROBUST WILD BOOTSTRAP APPLIED TO A CONSISTENT MODEL SPECIFICATION TEST

We present a new robust bootstrap method for a test when there is a nuisance parameter under the alternative, and some parameters are possibly weakly or nonidentified. We focus on a Bierens (1990, Econometrica 58, 1443–1458)-type conditional moment test of omitted nonlinearity for convenience. Existing methods include the supremum p-value which promotes a conservative test that is generally not consistent, and test statistic transforms like the supremum and average for which bootstrap methods are not valid under weak identification. We propose a new wild bootstrap method for p-value computation by targeting specific identification cases. We then combine bootstrapped p-values across polar identification cases to form an asymptotically valid p-value approximation that is robust to any identification case. Our wild bootstrap procedure does not require knowledge of the covariance structure of the bootstrapped processes, whereas Andrews and Cheng’s (2012a, Econometrica 80, 2153–2211; 2013, Journal of Econometrics 173, 36–56; 2014, Econometric Theory 30, 287–333) simulation approach generally does. Our method allows for robust bootstrap critical value computation as well. Our bootstrap method (like conventional ones) does not lead to a consistent p-value approximation for test statistic functions like the supremum and average. Therefore, we smooth over the robust bootstrapped p-value as the basis for several tests which achieve the correct asymptotic level, and are consistent, for any degree of identification. They also achieve uniform size control. A simulation study reveals possibly large empirical size distortions in nonrobust tests when weak or nonidentification arises. One of our smoothed p-value tests, however, dominates all other tests by delivering accurate empirical size and comparatively high power.

Statistical inference of random field auto-correlation structure from multiple sets of incomplete and sparse measurements using Bayesian compressive sampling-based bootstrapping

Abstract Bootstrapping is a simulation-based method to provide statistical inference, or to measure accuracy, on estimators of interest, such as random field parameters, i.e., mean and variance of a physical quantity at each location within a random field, and auto-correlation coefficient of the quantities among any two different locations of the field. Statistical inference may be performed using analytical methods together with multiple sets of complete measurement data. However, measurement data may be incomplete sometimes, due to, for examples, sensor failure, storage capacity in collecting measurement data, or cost/difficulty in increasing measurement density. In such a case, it is challenging to perform statistical inference of auto-correlation coefficients, particularly between locations where no data are measured directly. This study aims to develop an innovative and robust bootstrap method to perform statistical inference on auto-correlation coefficient in one dimensional random fields, e.g., time series or variations of a quantity along a spatial direction such as depth, from multiple sets of incomplete and sparse measurements. The proposed approach is based on a Bayesian compressive sampling (BCS)-Karhunen–Loeve (KL) expansion random field generator, which has been used to generate random field samples from sparse measurement data. The proposed bootstrap method is illustrated and validated through both numerical examples and real measurement data. The results obtained from the proposed bootstrap method using multiples sets of incomplete measurement data are consistent with those obtained from analytical methods using multiple sets of complete measurement data.

Inference When There is a Nuisance Parameter under the Alternative and Some Parameters are Possibly Weakly Identified

We present a new robust bootstrap method for a test when there is a nuisance parameter under the alternative, and some parameters are possibly weakly or non-identified. We focus on a Bierens (1990)-type conditional moment test of omitted nonlinearity for convenience, and because of difficulties that have been ignored to date. Existing methods include the supremum p-value which promotes a conservative test that is generally not consistent, and test statistic transforms like the supremum and average for which bootstrap methods are not valid under weak identification. We propose a new wild bootstrap method for p-value computation by targeting specific identification cases. We then combine bootstrapped p-values across polar identification cases to form an asymptotically valid p-value approximation that is robust to any identification case. The wild bootstrap does not require knowledge of the covariance structure of the bootstrapped processes, whereas Andrews and Cheng's (2012, 2013, 2014) simulation approach generally does. Our method allows for robust bootstrap critical value computation as well. Our bootstrap method (like conventional ones) does not lead to a consistent p-value approximation for test statistic functions like the supremum and average. We therefore smooth over the robust bootstrapped p-value as the basis for several tests which achieve the correct asymptotic level, and are consistent, for any degree of identification. A simulation study reveals possibly large empirical size distortions in non-robust tests when weak or non-identification arises. One of our smoothed p-value tests, however, dominates all other tests by delivering accurate empirical size and comparatively high power.

Basic Psychological Needs Satisfaction Mediates the Association between Self-Control Skills and Subjective Well-Being.

Although studies have shown that self-control skills (SCSs) are positively linked to both personal and interpersonal outcomes in adolescent students, studies on the putative mechanisms underlying this relationship are scarce. Drawing on Self-Determination Theory and previous studies, we theorized that the association between students’ SCSs and their subjective well-being (SWB) in school may be mediated by students’ perceived satisfaction of their basic psychological needs for competence, relatedness, and autonomy. The sample consisted of 1576 Israeli adolescent students (54% girls) in grades 10–12 (mean age 16) enrolled in 20 schools. A mediation model was tested with structural equation modeling and a robust bootstrap method for testing indirect effects, controlling for school-level variance. The findings supported the hypothesized model and a post hoc multi-group comparison analysis yielded gender invariance in the model. The findings suggest that both girls and boys with high SCSs may perceive themselves as having greater needs satisfaction in school and consequently higher school-related SWB. Implications for policy and practice are discussed.

Enhanced bootstrap method for statistical inference in the ICA model

In this paper, we develop low complexity and stable bootstrap procedures for FastICA estimators. Our bootstrapping techniques allow for performing cost efficient and reliable bootstrap-based statistical inference in the ICA model. Performing statistical inference is needed to quantitatively assess the quality of the estimators and testing hypotheses on mixing coefficients in the ICA model. The developed bootstrap procedures stem from the fast and robust bootstrap (FRB) method [1], which is applicable for estimators that may be found as solutions to fixed-point (FP) equations. We first establish analytical results on the structure of the weighted covariance matrix involved in the FRB formulation. Then, we exploit our analytical results to compute the FRB replicas at drastically reduced cost. The developed enhanced FRB method (EFRB) for FastICA permits using bootstrap-based statistical inference in a variety of applications (e.g., EEG, fMRI) in which ICA is commonly applied. Such an approach has not been possible earlier due to incurred substantial computational efforts of the conventional bootstrap. Our simulation studies compare the complexity and numerical stability of the proposed methods with the conventional bootstrap method. We also provide an example of utilizing the developed bootstrapping techniques in identifying equipotential lines of the brain dipoles from electroencephalogram (EEG) recordings.

Weighted Split Sample Bootstrap for Regression Models with High Dimensional Data

Bootstrapping is a statistical resampling technique that can be used in the estimation of statistical measures. This computer-based method has great application in many statistical areas, including regression analysis. Numerous bootstrap methods have been introduced in regression analysis; but, methods that deliberately addressing regression models for high dimensional data are scarcely found. Many classical bootstrap methods cannot provide good estimates when outliers are present in data set. Hence, this study introduces a robust bootstrap method that is specially designed for regression models with high dimensional data (i.e., Partial Least Squares (PLS) regression). This proposed method is called Weighted Split Sample Bootstrap (WSSB). Its performance was compared to the Split Sample Bootstrap (SSB) method by means of standard errors, biases and confidence intervals of parameter estimates through simulation studies. Results indicate that WSSB outperforms SSB.

Foreign exchange rate moments and FDI in Ghana

In this paper, we estimate the effect of exchange rate moments on foreign direct investment (FDI). Using data from a developing country (specifically Ghana) during the years 1990–2012 and robust regression and bootstrap method, the study finds that FDI increases as a result of the depreciation of the local currency. Secondly, using standard deviation as a measure of volatility, we find positive relationship between exchange rate volatility and FDI. Skewness did not show any significant relationship with FDI, which is straight to the heart of the mean reverting principle of the exchange rate. We find the political atmosphere as one of the main factors of drawing FDI into Ghana. These results are robust in the presence of all the standard control variables having significant coefficients under the various methodologies.

Robust, Scalable, and Fast Bootstrap Method for Analyzing Large Scale Data

In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We propose a scalable, statistically robust and computationally efficient bootstrap method, compatible with distributed processing and storage systems. Bootstrap resamples are constructed with smaller number of distinct data points on multiple disjoint subsets of data, similarly to the bag of little bootstrap method (BLB) [1]. Then significant savings in computation is achieved by avoiding the re-computation of the estimator for each bootstrap sample. Instead, a computationally efficient fixed-point estimation equation is analytically solved via a smart approximation following the Fast and Robust Bootstrap method (FRB) [2]. Our proposed bootstrap method facilitates the use of highly robust statistical methods in analyzing large scale data sets. The favorable statistical properties of the method are established analytically. Numerical examples demonstrate scalability, low complexity and robust statistical performance of the method in analyzing large data sets.

Robust and Efficient One-Way MANOVA Tests

We propose robust tests as alternatives to the classical Wilks’ Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multisample multivariate S-estimators or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis. We show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples. We also investigate the power of the new tests, as well as their robustness against outliers. Finally, we illustrate the use of these robust test statistics on a real data example. Some additional results are provided as supplemental material.

Robust Value at Risk Prediction

This paper proposes a robust semiparametric bootstrap method to estimate predictive distributions of GARCH-type models. The method is based on a robust estimation of parametric GARCH models and a robustified resampling scheme for GARCH residuals that controls bootstrap instability due to outlying observations. A Monte Carlo simulation shows that our robust method provides more accurate Value at Risk (VaR) forecasts than classical methods, often by a large extent, especially for several days ahead horizons and/or in presence of outlying observations. An empirical application confirms the simulation results. The robust procedure outperforms in backtesting several other VaR prediction methods, such as RiskMetrics, CAViaR, historical simulation, and classical filtered historical simulation methods. We show empirically that robust estimation reduces tail estimation risk, providing more accurate and more stable VaR prediction intervals over time.

BCR ®-701: A review of 10-years of sequential extraction analyses

A detailed quantitative analysis was performed on data presented in the literature that focused on the sequential extraction of cadmium (Cd), chromium (Cr), copper (Cu), nickel (Ni), lead (Pb) and zinc (Zn) from the certified reference material BCR-701 (lake sediment) using the three-step harmonized BCR ® procedure. The accuracy of data reported in the literature, including precision and different measures of trueness, was assessed relative to the certified values for BCR-701. Forty data sets were accepted following extreme outlier removal, and statistically summarized with measures of central tendency, dispersion, and distribution form. In general, literature data were similar in their measurement precision to the expert laboratories used to certify the trace element contents in BCR-701. The overall median precision for literature reported data was 10% (range 6–19%), compared to certifying laboratories of 9% (range 4–33%). One measure of literature data trueness was assessed via a confirmatory approach using a robust bootstrap method. Only 22% of the comparisons indicated significantly different (all were lower) concentrations reported in the literature compared to certified values. The question of whether the differences are practically significant for environmental studies is raised. Bias was computed as a measure of trueness, and literature data were more frequently negatively biased, indicating lower concentrations reported in the literature for the six trace elements for the three-step sequential procedure compared to the certified values. However, 95% confidence intervals about the average bias for the 18 comparisons indicated only four instances when a mean bias of 0 (i.e., measured = certified) was not incorporated—suggesting statistical difference. Finally, Z-scores incorporating a Horwitz-type function were used to assess the general trueness of laboratory data. Of the 468 laboratory Z-score values computed, 92% were considered to be satisfactory, 5% were questionable, and 3% were unsatisfactory. A detailed examination of the methodology sections of the various studies showed that despite claiming adherence to the harmonized BCR sequential extraction protocol, significant deviations were commonly observed; particularly in moisture correction, sample mass, centrifugation specifics, shaking specifics, and incorporation of filtration. It is likely that failure to strictly adhere to the protocol adversely impacted accuracy, by increasing the degree of imprecision and resulting in more discrepant trueness values.

Inference for robust canonical variate analysis

We consider the problem of optimally separating two multivariate populations. Robust linear discriminant rules can be obtained by replacing the empirical means and covariance in the classical discriminant rules by S or MM-estimates of location and scatter. We propose to use a fast and robust bootstrap method to obtain inference for such a robust discriminant analysis. This is useful since classical bootstrap methods may be unstable as well as extremely time-consuming when robust estimates such as S or MM-estimates are involved. In particular, fast and robust bootstrap can be used to investigate which variables contribute significantly to the canonical variate, and thus the discrimination of the classes. Through bootstrap, we can also examine the stability of the canonical variate. We illustrate the method on some real data examples.

Robust Value at Risk Prediction

This paper proposes a robust semiparametric bootstrap method to estimate predictive distributions of GARCH-type models. The method is based on a robust estimation of parametric GARCH models and a robustified resampling scheme for GARCH residuals that controls bootstrap instability due to outlying observations. A Monte Carlo simulation shows that our robust method provides more accurate VaR forecasts than classical methods, often by a large extent, especially for several days ahead horizons and/or in presence of outlying observations. An empirical application confirms the simulation results. The robust procedure outperforms in backtesting several other VaR prediction methods, such as RiskMetrics, CAViaR, Historical Simulation, and classical Filtered Historical Simulation methods. We show empirically that robust estimation reduces tail estimation risk, providing more accurate and more stable VaR prediction intervals over time.

Linear Regression Model Selection Based on Robust Bootstrapping Technique

Problem statement: Bootstrap approach had introduced new advancement in modeling and model evaluation. It was a computer intensive method that can replace theoretical formulation with extensive use of computer. The Ordinary Least Squares (OLS) method often used to estimate the parameters of the regression models in the bootstrap procedure. Unfortunately, many statistics practitioners are not aware of the fact that the OLS method can be adversely affected by the existence of outliers. As an alternative, a robust method was put forward to overcome this problem. The existence of outliers in the original sample may create problem to the classical bootstrapping estimates. There was possibility that the bootstrap samples may contain more outliers than the original dataset, since the bootstrap re-sampling is with replacement. Consequently, the outliers will have an unduly effect on the classical bootstrap mean and standard deviation. Approach: In this study, we proposed to use a robust bootstrapping method which was less sensitive to outliers. In the robust bootstrapping procedure, we proposed to replace the classical bootstrap mean and standard deviation with robust location and robust scale estimates. A number of numerical examples were carried out to assess the performance of the proposed method. Results: The results suggested that the robust bootstrap method was more efficient than the classical bootstrap. Conclusion/Recommendations: In the presence of outliers in the dataset, we recommend using the robust bootstrap procedure as its estimates are more reliable.

Robust model selection using fast and robust bootstrap

Robust model selection procedures control the undue influence that outliers can have on the selection criteria by using both robust point estimators and a bounded loss function when measuring either the goodness-of-fit or the expected prediction error of each model. Furthermore, to avoid favoring over-fitting models, these two measures can be combined with a penalty term for the size of the model. The expected prediction error conditional on the observed data may be estimated using the bootstrap. However, bootstrapping robust estimators becomes extremely time consuming on moderate to high dimensional data sets. It is shown that the expected prediction error can be estimated using a very fast and robust bootstrap method, and that this approach yields a consistent model selection method that is computationally feasible even for a relatively large number of covariates. Moreover, as opposed to other bootstrap methods, this proposal avoids the numerical problems associated with the small bootstrap samples required to obtain consistent model selection criteria. The finite-sample performance of the fast and robust bootstrap model selection method is investigated through a simulation study while its feasibility and good performance on moderately large regression models are illustrated on several real data examples.

Fast and robust bootstrap

In this paper we review recent developments on a bootstrap method for robust estimators which is computationally faster and more resistant to outliers than the classical bootstrap. This fast and robust bootstrap method is, under reasonable regularity conditions, asymptotically consistent. We describe the method in general and then consider its application to perform inference based on robust estimators for the linear regression and multivariate location-scatter models. In particular, we study confidence and prediction intervals and tests of hypotheses for linear regression models, inference for location-scatter parameters and principal components, and classification error estimation for discriminant analysis.

Robust combined estimation of states and parameters of bilinear systems

A robust bootstrap method is presented for estimating the states and parameters of bilinear systems. Based on Huber's minimax principle ( Robust Statistics, Wiley, New York (1981)), the robust bootstrap algorithm is derived from the feasible canonical forms for the state-space of bilinear systems. A convergence theorem for the proposed algorithm is presented. Results of simulation provide a comparison with non-robust bootstrap methods. These show the advantages of the algorithm developed in this paper.