Residual Bootstrap Research Articles

Predicting Social Inequality in Poland Using Price Dispersion on the Real Estate Market

Measuring and predicting price dispersion on the real estate market is an important issue for both investors and policymakers. Price dispersion in the housing market can be seen as an additional dimension for measuring social inequality and one of the main goals of public policies that focus on life satisfaction and the accumulation of permanent wealth. The article considers the Polish real estate market and proposes the prediction methods of four measures of dispersion. They are based on quantiles and allow overall measurement of dispersion. In the prediction of dispersion measures the plug-in predictors utylizing longitudinal mixed models are proposed. Furthermore, the ex ante prediction accuracy measure called the quantile of absolute prediction errors (QAPE) is assessed using the residual bootstrap estimators. QAPE allows for a comprehensive description of the distribution of prediction errors, thus fostering discussion of possible various market scenarios.

Estimation of Symptomatic Respiratory Syncytial Virus Infection Incidence in Adults in Multiple Countries: A Time-Series Model-Based Analysis Protocol.

Estimating respiratory syncytial virus (RSV) burden in adults is challenging because of non-specific symptoms, infrequent standard-of-care testing, resolution of viral shedding before seeking medical care, test positivity that varies by specimen site in the upper airway and lower diagnostic test sensitivity compared to children. Conducting prospective observational studies to assess RSV burden in adults is time- and resource-intensive. Thus, model-based approaches can be applied using existing data to obtain more accurate estimates of RSV burden. This protocol establishes essential elements for estimating RSV incidence rate in adults using a time series model-based approach. It can be tailored to specific databases and applied globally across countries, enabling estimation of local RSV disease burden to inform public health decision-making, including immunization policy. Data are analysed using a quasi-Poisson regression model, considering the effect of baseline trends and pathogen co-circulation, stratified by age and risk status. Pathogen co-circulation is represented by viral proxies defined based on ICD code groupings indicating RSV and influenza-specific hospitalizations, lagged 0 up to 4weeks based on the model selection. A final model is constructed in two steps: optimization of the time trend (using p-values) and selection of the viral proxy lag time (using test statistics, to prioritize the most biologically plausible option). The yearly incidence rate and percentage of events attributable to RSV are estimated from the final model. Confidence intervals are calculated using residual bootstrapping. Outcomes to be modelled are based on administrative ICD code groupings and include the number of cardiorespiratory, respiratory and cardiovascular events in a specific care setting (e.g., general practitioner visit, emergency department visit, hospitalization and death). Cardiovascular events are limited to those for which existing evidence suggests an association with RSV infection. Additional secondary outcomes are constructed as a subset of the primary outcomes based on specific ICD code groups.

A residual bootstrap for conditional Value-at-Risk

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zakoïan(2015) associated with the conditional Value-at-Risk. The bootstrap’s consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation.

Optimal Fingerprinting with Estimating Equations

Abstract Climate change detection and attribution have played a central role in establishing the influence of human activities on climate. Optimal fingerprinting, a linear regression with errors in variables (EIVs), has been widely used in detection and attribution analyses of climate change. The method regresses observed climate variables on the expected climate responses to the external forcings, which are measured with EIVs. The reliability of the method depends critically on proper point and interval estimations of the regression coefficients. The confidence intervals constructed from the prevailing method, total least squares (TLS), have been reported to be too narrow to match their nominal confidence levels. We propose a novel framework to estimate the regression coefficients based on an efficient, bias-corrected estimating equations approach. The confidence intervals are constructed with a pseudo residual bootstrap variance estimator that takes advantage of the available control runs. Our regression coefficient estimator is unbiased, with a smaller variance than the TLS estimator. Our estimation of the sampling variability of the estimator has a low bias compared to that from TLS, which is substantially negatively biased. The resulting confidence intervals for the regression coefficients have coverage rates close to the nominal level, which ensures valid inferences in detection and attribution analyses. In applications to the annual mean near-surface air temperature at the global, continental, and subcontinental scales during 1951–2020, the proposed method led to shorter confidence intervals than those based on TLS in most of the analyses. Significance Statement Optimal fingerprinting is an important statistical tool for estimating human influences on the climate and for quantifying the associated uncertainty. Nonetheless, the estimators from the prevailing practice are not as optimal as believed, and their uncertainties are underestimated, both owing to the unreliable estimation of the optimal weight matrix that is critical to the method. Here we propose an estimation method based on the theory of estimating equations; to assess the uncertainty of the resulting estimator, we propose a pseudo bootstrap procedure. Through extensive numerical studies commonly used in statistical investigations, we demonstrate that the new estimator has a smaller mean-square error, and its uncertainty is estimated much closer to the true uncertainty than the prevailing total least squares method.

Testing the parametric form of the conditional variance in regressions based on distance covariance

A new test based on distance covariance is proposed for testing the parametric form of the conditional variance in parametric and nonparametric regression models. Inherit from the nice properties of distance covariance, the new test is very easy to implement in practice and less effected by the dimensionality of covariates. The asymptotic properties of the test statistic are investigated under the null and alternative hypotheses. The proposed test is consistent against any alternative hypothesis and can detect some classes of local alternative hypotheses converging to the null hypothesis at the parametric rate in both the parametric and nonparametric settings. As the limiting null distribution of the test statistic is intractable, a smooth residual bootstrap is proposed to approximate the limiting null distribution. Simulation studies are conducted to assess the finite sample performance of the proposed test. A real data set is also analyzed for illustration.

Zeeman Doppler imaging ofξBoo A and B

Aims.We present a magnetic-field surface map for both stellar components of the young visual binaryξBoo AB (A: G8V, B: K5V).Methods.We employed high-resolution Stokes-Vspectra obtained with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) at the Large Binocular Telescope (LBT). We inverted StokesVline profiles with ouriMAP software and compared them with previous inversions. We employed an iterative regularization scheme without the need for a penalty function and incorporated a three-component description of the surface magnetic-field vector. The spectral resolution of our data is 130 000 (0.040–0.055 Å) and we obtain a signal-to-noise ratio (S/N) of up to 3000 per pixel depending on wavelength. We used a singular-value decomposition (SVD) of a total of 1811 spectral lines to average Stokes-Vprofiles. Our mapping is accompanied by a residual bootstrap error analysis.Results.We constructed magnetic flux densities of the radial field component forξBoo A andξBoo B of up to plus or −115±5 G and 55±3 G, respectively. The magnetic morphology ofξBoo A is characterized by a very high latitude, nearly polar spot of negative polarity and three low-to-mid-latitude spots of positive polarity, while that ofξBoo B is characterized by four low-to-mid-latitude spots of mixed polarity. No polar magnetic field is reconstructed for the coolerξBoo B star. Both our maps are dominated by the radial field component, containing 86% and 89% of the magnetic energy ofξBoo A and B, respectively. We find only weak azimuthal and meridional field densities on both stars (plus or −15–30 G), about a factor two weaker than what was seen previously forξBoo A. The phase averaged longitudinal field component and dispersion is +4.5±1.5 G for ξ Boo A and −5.0±3.0 G forξBoo B.

A robust and fast two-sample test of equal correlations withan application to differential co-expression.

A robust and fast two-sample test for equal Pearson correlation coefficients (PCCs) is important in solving many biological problems, including, for example, analysis of differential co-expression. However, few existing methods for this test can achieve robustness against deviation from normal distributions, accuracy under small sample sizes, and computational efficiency simultaneously. Here, we propose a new method for testing differential correlation using a saddlepoint approximation of the residual bootstrap (DICOSAR). To achieve robustness, accuracy, and efficiency, DICOSAR combines the ideas underlying the pooled residual bootstrap, the signed root of a likelihood ratio statistic, and a multivariate saddlepoint approximation. Through a comprehensive simulation study and a real data analysis of gene co-expression, we demonstrate that DICOSAR is accurate and robust in controlling the type I error rate for detecting differential correlation and provides a faster alternative to the bootstrap and permutation methods. We further show that DICOSAR can also be used for testing differential correlation matrices. These results suggest that DICOSAR provides an analytical approach to facilitate rapid testing for the equality of PCCs in large-scale analysis.

A Glimpse of Nonparametric Single and Double Residual Bootstrap Method with Outliers

A Glimpse of Nonparametric Single and Double Residual Bootstrap Method with Outliers

Bootstrapping tests for breaks in mean or variance based on U-statistics

Bootstrapping tests are implemented for the tests U by Schmidt [Detecting changes in the trend function of heteroscedastic time series; 2021. Preprint: arXiv:2108.09206 [math.ST]] for mean break and Schmidt et al. [An asymptotic test for constancy of the variance under short-range dependence. Ann Stat. 2021;49:3460–3481.] for variance break based on U-statistics. The tests U have good powers against epidemic breaks that are common in practice. The test U for variance break is proved to have the nice property of consistency against a general class of alternatives. However, the tests U have non-ignorable finite sample size distortion under serial correlation and/or conditional heteroscedasticity. Our implementation based on autoregressive residual bootstrapping and moving block bootstrapping are shown to remedy the size distortion problems of U for mean break and for variance break, respectively, in a Monte-Carlo experiment. The experiment also demonstrates the power advantages of bootstrapping tests over the original tests and other standard break tests against epidemic breaks, which, however, are accompanied by disadvantages against simple single breaks. The proposed bootstrapping tests are well illustrated by break analyses of means and variances of the log-return and realized the volatility of the US S&P 500.

Wild bootstrap inference for penalized quantile regression for longitudinal data

The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator. The model puts no restrictions on individual effects, and the estimator achieves consistency by letting the shrinkage decay in importance asymptotically. The new method is easy to implement and simulation studies show that it has accurate small sample behavior in comparison with existing procedures. Finally, we illustrate the new approach using U.S. Census data to estimate a model that includes more than eighty thousand parameters.

Percentile Bootstrap Interval on Univariate Local Polynomial Regression Prediction

This study offers a new technique for constructing percentile bootstrap intervals to predict the regression of univariate local polynomials. Bootstrap regression uses resampling derived from paired and residual bootstrap methods. The main objective of this study is to perform a comparative analysis between the two resampling methods by considering the nominal coverage probability. Resampling uses a nonparametric bootstrap technique with the return method, where each sample point has an equal chance of being selected. The principle of nonparametric bootstrapping uses the original sample data as a source of diversity in contrast to parametric bootstrapping, where the variety comes from generating a particular distribution. The simulation results show that the paired and residual bootstrap interval coverage probabilities are close to nominal coverage. The results showed no significant difference between paired bootstrap interval and percentile residual. Increasing the bootstrap sample size sufficiently large gives the scatterplot smoothness of the confidence interval. Applying the smoothing parameter by choice gives a second-order polynomial regression with a smoother distribution than the first-order polynomial regression. The scatterplot shows that the second-degree polynomial regression can capture the data curvature feature compared to the first-degree polynomial. The bands made from second-degree polynomials give a narrower width than first-degree polynomials. In contrast, applying optimal smoothing parameters to the model provides different conclusions by using smoothing parameters based on choice. In addition to the differences based on the scatterplot, the bootstrap estimates of the coverage probability are also other. Selecting smoothing parameters based on a particular value provides probability coverage with the paired bootstrap method for the first-degree local polynomial regression is 0.93, while the second-degree local polynomial is 0.96. The probability of coverage based on the residual bootstrap method for the first-degree local polynomial regression is 0.95, while the second-degree local polynomial is 0.96. The probability coverage based on the optimal parameters of the paired bootstrap method for the first-degree local polynomial regression is 0.945, while the second-degree local polynomial is 0.93. The residual bootstrap method gives the first-degree local polynomial regression of 0.95, while the second-degree local polynomial is 0.93. In general, both bootstrap methods work well for estimating prediction confidence intervals.

Bootstrap-t Confidence Interval on Local Polynomial Regression Prediction

In local polynomial regression, prediction confidence interval estimation using standard theory will give coverage probability close to exact coverage probability. However, if the normality assumption is not met, the bootstrap method makes it possible to apply it. The working principle of the bootstrap method uses the resampling method where the sample data becomes a population and there is no need to know the distribution of the sample data is normal or not. Indiscriminate selection of smoothing parameters allows scatterplot results from local polynomial regressions to be rough and can even lead to misleading statistical conclusions. It is necessary to consider the optimal smoothing parameters to get local polynomial regression predictions that are not overfitting or underfitting. We offer two new algorithms based on the nested bootstrap resampling method to determine the bootstrap-t confidence interval in predicting local polynomial regression. Both algorithms consider the search for optimal smoothing parameters. The first algorithm performs paired and residual bootstrap samples, and the second algorithm performs based on residuals with residuals. The first algorithm provides a scatterplot and reasonable coverage probability on relatively large sample data. In contrast, the second algorithm is more powerful for each data size, including for relatively small sample data sizes. The mean of the bootstrap-t confidence interval coverage probability shows that the second algorithm for second-degree local polynomial regression is better than the other three. However, the larger the sample data size gives, the closer the closer the average coverage probability of the two algorithms is to the nominal coverage probability.

Comparisons between Resampling Techniques in Linear Regression: A Simulation Study

The classic methods used in estimating the parameters in linear regression need to fulfill some assumptions. If the assumptions are not fulfilled, the conclusion is questionable. Resampling is one of the ways to avoid such problems. The study aims to compare resampling techniques in linear regression. The original data used in the study is clean, without any influential observations, outliers and leverage points. The ordinary least square method was used as the primary method to estimate the parameters and then compared with resampling techniques. The variance, p-value, bias, and standard error are used as a scale to estimate the best method among random bootstrap, residual bootstrap and delete-one Jackknife. After all the analysis took place, it was found that random bootstrap did not perform well while residual and delete-one Jackknife works quite well. Random bootstrap, residual bootstrap, and Jackknife estimate better than ordinary least square. Is was found that residual bootstrap works well in estimating the parameter in the small sample. At the same time, it is suggested to use Jackknife when the sample size is big because Jackknife is more accessible to apply than residual bootstrap and Jackknife works well when the sample size is big.

Analytical and Residual Bootstrap Methods for Parameter Uncertainty Assessment in Tidal Analysis with Temporally Correlated Noise

Abstract Reconstructing tidal signals is indispensable for verifying altimetry products, forecasting water levels, and evaluating long-term trends. Uncertainties in the estimated tidal parameters must be carefully assessed to adequately select the relevant tidal constituents and evaluate the accuracy of the reconstructed water levels. Customary harmonic analysis uses ordinary least squares (OLS) regressions for their simplicity. However, the OLS may lead to incorrect estimations of the regression coefficient uncertainty due to the neglect of the residual autocorrelation. This study introduces two residual resamplings (moving-block and semiparametric bootstraps) for estimating the variability of tidal regression parameters and shows that they are powerful methods to assess the effects of regression errors with nontrivial autocorrelation structures. A Monte Carlo experiment compares their performance to four analytical procedures selected from those provided by the RT_Tide, UTide, and NS_Tide packages and the robustfit.m MATLAB function. In the Monte Carlo experiment, an iteratively reweighted least squares (IRLS) regression is used to estimate the tidal parameters for hourly simulations of one-dimensional water levels. Generally, robustfit.m and the considered RT_Tide method overestimate the tidal amplitude variability, while the selected UTide and NS_Tide approaches underestimate it. After some substantial methodological corrections the selected NS_Tide method shows adequate performance. As a result, estimating the regression variance–covariance with the considered RT_Tide, UTide, and NS_Tide methods may lead to the erroneous selection of constituents and underestimation of water level uncertainty, compromising the validity of their results in some applications. Significance Statement At many locations, the production of reliable water level predictions for marine navigation, emergency response, and adaptation to extreme weather relies on the precise modeling of tides. However, the complicated interaction between tides, weather, and other climatological processes may generate large uncertainties in tidal predictions. In this study, we investigate how different statistical methods may lead to different quantification of tidal model uncertainty when using data with completely known properties (e.g., knowing the tidal signal, as well as the amount and structure of noise). The main finding is that most commonly used statistical methods may estimate incorrectly the uncertainty in tidal parameters and predictions. This inconsistency is due to some specific simplifying assumptions underlying the analysis and may be reduced using statistical techniques based on data resampling.

Two-Stage Bootstrap Sampling for Probabilistic Load Forecasting

The integration of distributed renewable energy and the implementation of the demand response complicate the change patterns of load profiles and present great uncertainties. Probabilistic load forecasting, an effective method for capturing the future load uncertainty, has been a hot issue. This article proposes a two-stage bootstrap sampling method for probabilistic load forecasting. In the first stage, alpha-bootstrap, which is a modification of traditional bootstrap methods, is applied to characterize the uncertainties from multiple forecasting models; in the second stage, the residual bootstrap method is used to formulate the regression errors. Finally, the probabilistic load forecasts can be obtained by integrating the uncertainties in both stages. Various off-the-shelf point load forecasting methods such as random forest (RF) and gradient boosting regression tree (GBRT) can be integrated into the proposed framework. We illustrate the effectiveness of our proposed method and superiority over direct quantile regression methods such as quantile RF and quantile GBRT using the case studies on open load datasets of eight zones in ISO New-England.

Inference on the dynamics of COVID-19 in the United States

The evolution of the COVID-19 pandemic is described through a time-dependent stochastic dynamic model in discrete time. The proposed multi-compartment model is expressed through a system of difference equations. Information on the social distancing measures and diagnostic testing rates are incorporated to characterize the dynamics of the various compartments of the model. In contrast with conventional epidemiological models, the proposed model involves interpretable temporally static and dynamic epidemiological rate parameters. A model fitting strategy built upon nonparametric smoothing is employed for estimating the time-varying parameters, while profiling over the time-independent parameters. Confidence bands of the parameters are obtained through a residual bootstrap procedure. A key feature of the methodology is its ability to estimate latent unobservable compartments such as the number of asymptomatic but infected individuals who are known to be the key vectors of COVID-19 spread. The nature of the disease dynamics is further quantified by relevant epidemiological markers that make use of the estimates of latent compartments. The methodology is applied to understand the true extent and dynamics of the pandemic in various states within the United States (US).

Improvement of Extreme Value Modeling for Extreme Rainfall Using Large-Scale Climate Modes and Considering Model Uncertainty

Extreme value modeling for extreme rainfall is one of the most important processes in the field of hydrology. For the improvement of extreme value modeling and its physical meaning, large-scale climate modes have been widely used as covariates of distribution parameters, as they can physically account for climate variability. This study proposes a novel procedure for extreme value modeling of rainfall based on the significant relationship between the long-term trend of the annual maximum (AM) daily rainfall and large-scale climate indices. This procedure is characterized by two main steps: (a) identifying significant seasonal climate indices (SCIs), which impact the long-term trend of AM daily rainfall using statistical approaches, such as ensemble empirical mode decomposition, and (b) selecting an appropriate generalized extreme value (GEV) distribution among the stationary GEV and nonstationary GEV (NS-GEV) using time and SCIs as covariates by comparing their model fit and uncertainty. Our findings showed significant relationships between the long-term trend of AM daily rainfall over South Korea and SCIs (i.e., the Atlantic Meridional Mode, Atlantic Multidecadal Oscillation in the fall season, and North Atlantic Oscillation in the summer season). In addition, we proposed a model selection procedure considering both the Akaike information criterion and residual bootstrap method to select an appropriate GEV distribution among a total of 59 GEV candidates. As a result, the NS-GEV with SCI covariates generally showed the best performance over South Korea. We expect that this study can contribute to estimating more reliable extreme rainfall quantiles using climate covariates.

An Empirical Study on Relationship between Residents’ Disposable Income and CPI Based on TVECM: Application of Bootstrap SupLM Testing for Threshold Cointegration

Based on the fluctuation characteristics of residents’ disposable income and CPI (Consumer Price Index) in different periods, this article introduces a nonlinear threshold cointegration theory, establishes a TVECM (Threshold Vector Error Correction Model) of the residents’ disposable income and CPI. We propose an algorithm to obtain maximum likelihood estimation under the condition of cointegration vector and threshold value which are unknown and then propose a SupLM test for the presence of a threshold. The asymptotic distribution of the SupLM statistic is analyzed, and it appears to depend on the moment functionals, so tabulated critical values are unavailable. We discuss how the residual bootstrap can be used to calculate asymptotic critical values and p values, investigate the size and power of the SupLM test using Monte Carlo simulation, and find that the test works quite well. In the empirical section, we apply our methods to test and estimate the TVECM of residents’ disposable income and CPI. According to the experimental results, the causal relationship between residents’ disposable income and CPI under different mechanisms is tested and compared with the test results under the linear cointegration hypothesis. The empirical results show that the disposable income of residents and CPI belong to a two‐mechanism nonlinear threshold cointegration system. When the deviation from the equilibrium state exceeds the threshold value, the system may adjust to the equilibrium state, and the adjustment speed of CPI shall be faster than that of the residents’ disposable income.

A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

A Weighted Residual Bootstrap Method for Multilevel Modeling with Sampling Weights

Multilevel modeling is often used to analyze survey data collected with a multistage sampling design. When the selection is informative, sampling weights need to be incorporated in the estimation. We propose a weighted residual bootstrap method as an alternative to the multilevel pseudo-maximum likelihood (MPML) estimators. In a Monte Carlo simulation using two-level linear mixed effects models, the bootstrap method showed advantages over MPML for the estimates and the statistical inferences of the intercept, the slope of the level-2 predictor, and the variance components at level-2. The impact of sample size, selection mechanism, intraclass correlation (ICC), and distributional assumptions on the performance of the methods were examined. The performance of MPML was suboptimal when sample size and ICC were small and when the normality assumption was violated. The bootstrap estimates performed generally well across all the simulation conditions, but had notably suboptimal performance in estimating the covariance component in a random slopes model when sample size and ICCs were large. As an illustration, the bootstrap method is applied to the American data of the OECD’s Program for International Students Assessment (PISA) survey on math achievement using the R package bootmlm.