Bootstrap Methodology Research Articles

Measuring Heterogeneous Price Effects for Home Acquisition Programs in At‐Risk Regions

Any entity offering flood insurance, whether it is private or government‐administered such as the National Flood Insurance Program (NFIP), faces the challenge of solvency. This is especially true for the NFIP, where homeowner affordability criteria limit the opportunity to charge fully risk‐based premiums. One solution is to remove the highest flood risk properties from the insurer's book of business. Acquisition (buyout) of flood‐prone structures is a potentially permanent solution that eliminates the highest risk properties while providing homeowners with financial assistance to relocate in a less risky location. To encourage participation, homeowners are offered a preflood fair market value of their damaged (or at risk of damage) structures. Although many factors have been shown to affect a homeowner's decision to accept an acquisition offer, very little research has been devoted to the influence of price or monetary incentive offered on homeowners' willingness to participate in acquisition programs. We estimate a pooled probit model and employ a bootstrap methodology to determine the effects of hypothetical home price offers on homeowners' acquisition decisions. We do so while controlling for environmental factors, property characteristics, and homeowner sociodemographic characteristics. Results show that price indeed has a positive effect on likelihood of accepting an acquisition contract. Furthermore, estimated homeowner supply curves differ significantly based on the damage status of the acquisition offer, as well as homeowner and property characteristics.

Microarray Data Normalization and Robust Detection of Rhythmic Features.

Data derived from microarray technologies are generally subject to various sources of noise and accordingly the raw data are pre-processed before formally analysed. Data normalization is a key pre-processing step when dealing with microarray experiments, such as circadian gene-expressions, since it removes systematic variations across arrays. A wide variety of normalization methods are available in the literature. However, from our experience in the study of rhythmic expression patterns in oscillatory systems (e.g. cell-cycle, circadian clock), the choice of the normalization method may substantially impair the identification of rhythmic genes. Hence, the identification of a gene as rhythmic could be just as an artefact of how the data were normalized. Yet, gene rhythmicity detection is crucial in modern toxicological and pharmacological studies, thus a procedure to truly identify rhythmic genes that are robust to the choice of a normalization method is required.To perform the task of detecting rhythmic features, we propose a rhythmicity measure based on bootstrap methodology to robustly identify rhythmic genes in oscillatory systems. Although our methodology can be extended to any high-throughput experiment, in this chapter, we illustrate how to apply it to a publicly available circadian clock microarray gene-expression data and give full details (both statistical and computational) so that the methodology can be used in an easy way. We will show that the choice of normalization method has very little effect on the proposed methodology since the results derived from the bootstrap-based rhythmicity measure are highly rank correlated for any pair of normalization methods considered. This suggests, on the one hand, that the rhythmicity measure proposed is robust to the choice of the normalization method, and on the other hand, that gene rhythmicity detected using this measure is potentially not a mere artefact of the normalization method used. In this way the researcher using this methodology will be protected against the possible effect of different normalizations, as the conclusions obtained will not depend so strongly on them. Additionally, the described bootstrap methodology can also be employed as a tool to simulate gene-expression participating in an oscillatory system from a reference data set.

Estimation of Cost Efficiency in Non-parametric Frontier Models

The paper proposes a bootstrap methodology for estimating cost efficiency in data envelopment analysis. We consider the conventional concept of Fare, Grosskopf and Lovellcost efficiency, for which our algorithm re-samples “naive” input-oriented efficiency scores, rescales original inputs to bring them to the frontier, and then re-estimates cost efficiency scores for the rescaled inputs. Next, we examine Tone cost efficiency, where input prices vary across producers. Here we show that the direct modification on bootstrap algorithms by Simar and Wilson are applicable. We consider cases both with the absence and presence of environmental variables (i.e. input variables not directly controlled by firms). The bootstrap methodology exploits these assumptions: 1) the sample are i.i.d. random variables with the continuous joint probability density function with support over production set; 2) the frontier is smooth; and 3) the probability of observing firms on the frontier approaches unity with an increase in sample. The results of simulations for a multi-input, multi-output Cobb–Douglas production function with correlated outputs, and correlated technical and cost efficiency, show consistency of our proposed algorithm, even for small samples. Finally, we offer real data estimates for the Japanese banking industry in 2013. Our package “rDEA,” developed in the R language, is available from the GitHub and CRAN repository.

Two-Dimensional Numerical Model of the Fracture Process in Steel Fibre Reinforced Concrete with the Continuum Strong Discontinuity Approach and Functional Data Analysis

Abstract This paper presents the formulation of a two-dimensional numeri-cal model able to describe the fracture process in structural mem-bers of steel fibre reinforced concrete (SFRC) from the volume ratio of the fibres and the mechanical properties of the compo-nents: a concrete matrix and a set of steel fibres with a random orientation. The relationship between the stress and the strain fields of the composite material is obtained using the mixture theory with a compatibility strain of its component materials. The concrete matrix is represented with a scalar damage constitutive model with a softening strain and a different strength in tension and compression. The mechanical strain of an insulated fibre and the slip between the fibre and the matrix are simultaneously de-scribed with a one-dimensional plasticity constitutive model. The cracking of the composite material indicates a jump in the dis-placement field and non-bounded values of the strain field, which are represented by the Continuum Strong Discontinuity Ap-proach. The model has been implemented in the framework of the nonlinear analysis with the Finite Element Method, using con-stant strain triangular elements. Moreover, the fibres distribution and orientation change randomly in each finite element and each simulation or observation. The structural responses of the simula-tions are treated as curves and analysed by tools from the Func-tional Data Analysis. Confidence intervals for the structural re-sponse are built using bootstrap methodology. Finally, experi-mental tests of SFRC members subjected to tension and bending are simulated. The structural response and the cracking patterns obtained from the numerical simulation are satisfactory.

A PRELIMINARY QUANTITATIVE ANALYSIS OF RURALITY IN ROMANIA AND THE IMPACT OF COMMON AGRICULTURAL POLICY SUBSIDIES

In the literature, many studies have sought to assess through a quantitative approach the principle relationships between quantitative variables correlated to rurality. The impediment to such studies arises from the impossibility of quantitatively assessing cause-effect relationships between variables. The core purpose of this research was to assess by a quantitative approach the main cause-effect relationships in counties of Romania over the years 2007 to 2016, in order to identify variables affecting the rurality index. The study used Partial Least Squares Structural Equation Modelling following the bootstrap methodology. The research outcomes highlighted the notable and positive role of financial subsidies allocated by the second pillar of the Common Agricultural Policy and specifically, the payments in favour of disadvantaged rural areas in relation to the rurality index across all regions of Romania. Some decoupled payments allocated within the framework of the first pillar of the CAP were found to have had no effect on crop farming. Drawing conclusions from this research, the financial support disbursed by the rural development programme is a fundamental stimulus to the reduction of socioeconomic marginalisation in Romanian farms and farming areas.

Price signatures

Price signatures are statistical measurements that aim to detect systematic patterns in price dynamics localised around the point of trade execution. They are particularly useful in electronic trading because they uncover market dynamics, strategy characteristics, implicit execution costs, or counter-party trading behaviours that are often hard to identify, in part due to the vast amounts of data involved and the typically low signal to noise ratio. Because the signature summarises price dynamics over a specified time interval, it constitutes a curve (rather than a point estimate) and because of potential overlap in the price paths it has a non-trivial dependence structure which complicates statistical inference. In this paper, I show how recent advances in functional data analysis can be applied to study the properties of these signatures. To account for data dependence, I analyse and develop resampling-based bootstrap methodologies that enable reliable statistical inference and hypothesis testing. I illustrate the power of this approach using a number of case studies taken from a live trading environment in the over-the-counter currency market. I demonstrate that functional data analysis of price signatures can be used to distinguish between internalising and externalising liquidity providers in a highly effective data driven manner. This in turn can help traders to selectively engage with liquidity providers whose risk management style best aligns with their execution objectives.

Bootstrap-based testing approaches for the assessment of the diagnostic accuracy of biomarkers subject to a limit of detection.

Assessment of the diagnostic accuracy of biomarkers through receiver operating characteristic curve analysis frequently involves a limit of detection imposed by the laboratory analytical system precision. As a consequence, measurements below a certain level are undetectable and ignoring these is known to lead to negatively biased estimates of the area under the receiver operating characteristic curve. In this article, we introduce two receiver operating characteristic curve-based parametric approaches that tackle the issue of correct assessment of diagnostic markers in the presence of a limit of detection. Proposed approaches are simulation-based utilising bootstrap methodology. Non-parametric alternatives that are naively used in the literature do not solve the inherent problem of limit of detection values which are treated as censored observations. However, the latter seems to perform adequately well in our simulation study. Nonparametric bootstrap was consistently used throughout, while other bootstrap alternatives performed similarly in our pilot simulation study. The simulation study involves the comparison of parametric and non-parametric options described here versus alternative strategies that are routinely used in the literature. We apply all methods to a study-setting resembling a chemical quasi-standard situation, where compound tumour biomarkers were searched within a multi-variable set of measurements to discriminate between two groups, namely colorectal cancer and controls. We focus in the assessment of glutamine and methionine.

Finding confidence bound using two-stage data

ABSTRACTMultistage sampling schemes for statistical inference are widespread. In particular, computing one or two sided confidence limits from two-stage samples has many applications. Typically, in a two stage sampling scheme, at the end of the first stage, the investigator carries out a statistical testing procedure to decide whether to move on to the second stage or to stop sampling. If the investigator decides to go to the second stage, then more samples are taken and a final decision is reached. Since the cost of sampling is sometimes very high, it is desired to use all the samples from both the stages to make a terminal decision. Bias considerations usually make it improper to simply combine the samples and treat them as one sample. In this paper, we consider computing confidence bounds for a mean using data from two stages. Let n1 sample points be taken in the first stage and a standard level-α t-test performed for testing the hypothesis If H0 is rejected, then a second sample of size n2 is taken. Now the goal is to compute a lower confidence bound for the true mean μ using all (n1 + n2) sample points. Here we propose three different methods to compute the lower confidence bound using bootstrap methodology. The procedures differ in their demands of computational power which is reflected in their accuracy of coverage probability. Performance of the procedures is evaluated by simulation. It is noteworthy that in almost all the research mentioned above, the values of n1 and n2 considered are relatively small. Hence we focus on small sample behavior of two stage confidence bound.

A Bootstrap Based Measure Robust to the Choice of Normalization Methods for Detecting Rhythmic Features in High Dimensional Data.

Motivation: Gene-expression data obtained from high throughput technologies are subject to various sources of noise and accordingly the raw data are pre-processed before formally analyzed. Normalization of the data is a key pre-processing step, since it removes systematic variations across arrays. There are numerous normalization methods available in the literature. Based on our experience, in the context of oscillatory systems, such as cell-cycle, circadian clock, etc., the choice of the normalization method may substantially impact the determination of a gene to be rhythmic. Thus rhythmicity of a gene can purely be an artifact of how the data were normalized. Since the determination of rhythmic genes is an important component of modern toxicological and pharmacological studies, it is important to determine truly rhythmic genes that are robust to the choice of a normalization method.Results: In this paper we introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes in an oscillatory system. Although the proposed methodology can be used for any high-throughput gene expression data, in this paper we illustrate the proposed methodology using several publicly available circadian clock microarray gene-expression datasets. We demonstrate that the choice of normalization method has very little effect on the proposed methodology. Specifically, for any pair of normalization methods considered in this paper, the resulting values of the rhythmicity measure are highly correlated. Thus it suggests that the proposed measure is robust to the choice of a normalization method. Consequently, the rhythmicity of a gene is potentially not a mere artifact of the normalization method used. Lastly, as demonstrated in the paper, the proposed bootstrap methodology can also be used for simulating data for genes participating in an oscillatory system using a reference dataset.Availability: A user friendly code implemented in R language can be downloaded from http://www.eio.uva.es/~miguel/robustdetectionprocedure.html

Empirical evolution equations

Evolution equations comprise a broad framework for describing the dynamics of a system in a general state space: when the state space is finite-dimensional, they give rise to systems of ordinary differential equations; for infinite-dimensional state spaces, they give rise to partial differential equations. Several modern statistical and machine learning methods concern the estimation of objects that can be formalized as solutions to evolution equations, in some appropriate state space, even if not stated as such. The corresponding equations, however, are seldom known exactly, and are empirically derived from data, often by means of non-parametric estimation. This induces uncertainties on the equations and their solutions that are challenging to quantify, and moreover the diversity and the specifics of each particular setting may obscure the path for a general approach. In this paper, we address the problem of constructing general yet tractable methods for quantifying such uncertainties, by means of asymptotic theory combined with bootstrap methodology. We demonstrates these procedures in important examples including gradient line estimation, diffusion tensor imaging tractography, and local principal component analysis. The bootstrap perspective is particularly appealing as it circumvents the need to simulate from stochastic (partial) differential equations that depend on (infinite-dimensional) unknowns. We assess the performance of the bootstrap procedure via simulations and find that it demonstrates good finite-sample coverage.

Measuring the Impact of Extreme Weather Phenomena on Total Factor Productivity of General Cropping Farms in East Anglia

One of the main challenges of climate change on agriculture in UK is how to adapt to the potential changes to the availability of water. Changes in rainfall distribution may potentially lead to an increase in drought frequency, magnitude and duration. In this research a Data Envelopment Analysis (DEA) and a Malmquist Index (MI) are combined with a double bootstrap methodology to measure changes in Total Factor Productivity of general cropping farms in East Anglia. More specifically, the DEA technique was used to measure the year by year efficiency score for the farms in the sample and the MI and its components used to derive information on productivity over time. Data for the input – output models was obtained from the Farm Business Survey. Climate change is taken into consideration by using data for water cost as a proxy indicator of water consumption per farm. Results reveal changes in total, technical and scale efficiency and provide information on how the 2011 drought affect the TFP of the farms in the sample.

Bootstrap testing of trading strategies in emerging balkan stock markets

Most lately, the attention of technical trading analysis has shifted to emerging stock markets which collectively bring a signifi cant alternative source of opportunities to international investors. Accordingly, the aim of this paper is to investigate the effectiveness of four technical trading rules (moving average, fi lter, trading range breakout and channel breakout rule) in six stock market indices of the Balkan States. Also, the paper is providing resume evidence on the predictive power of four mentioned trading rules. We apply the Reality Check and the Superior Predictive Ability test using bootstrap methodology to evaluate the relative performance of those rules. Furthermore, presented tests provide an answer to data snooping problems, which is essential to obtain unbiased outcomes. The original time series is resampled with random draw in two ways: a parametric residual-based method from the AR(1)-GARCH(1,1) model, and a nonparametric, the moving block bootstrap. After including data snooping biases, this study fi nds that the null hypothesis that trading rules do not outperform the benchmark can be rejected at the 5 percent signifi cance level for fi ve separate stock indices, excluding the MBI10 index. Similarly, such results show the rejection of the weak-form market effi ciency hypothesis in case of mentioned stock markets. Applied technical trading rule algorithms in all six stock market indices mainly generate more losing trades then wining trades. Finally, transaction costs have relatively small effect on the overall performance of selected technical trading rules in case of indices BELEX15, CROBEX, SBITOP and MONEX20, but with some changes in choice of the best technical trading rule considering the effects of trading frequencies.

Testing normality for unconditionally heteroscedastic macroeconomic variables

In this paper the testing of normality for unconditionally heteroscedastic macroeconomic time series is studied. It is underlined that the classical Jarque-Bera test (JB hereafter) for normality is inadequate in our framework. On the other hand it is found that the approach which consists in correcting the heteroscedasticity by kernel smoothing for testing normality is justified asymptotically. Nevertheless it appears from Monte Carlo experiments that such a methodology can noticeably suffer from size distortion for samples that are typical for macroeconomic variables. As a consequence a parametric bootstrap methodology for correcting the problem is proposed. The innovations distribution of a set of inflation measures for the U.S., Korea and Australia are analyzed.

New association schemes for mono-ethylene glycol: Cubic-Plus-Association parameterization and uncertainty analysis

Accurate thermodynamic predictions for systems containing glycols are essential for the design and commissioning of novel subsea natural gas dehydration units. Previously it has been shown that the Cubic-Plus-Association (CPA) equation of state can be used to model VLE, SLE and LLE for mixtures of interest to this application. Recent developments for association schemes have shown that the use of a binary association site provided improved modelling of 1-alkanols. In this work, we implement the binary association site for mono-ethylene glycol (MEG) by proposing three new association schemes (3C, 4E & 4F). New parameter sets have been regressed and uncertainty analysis, using the bootstrap methodology, was performed to obtain 95% confidence intervals for each parameter. An improved parameter set for the literature 4C scheme was also determined.The four association schemes were tested against eight data types, with single parameter sensitivity analysis showing that new parameter sets are near optimal. The 3C scheme provides the best results for pure component properties and the liquid phase of MEG-H2O, while new 4C parameters provide the best results for the MEG-H2O (vapour phase) and MEG-nC7 LLE. For the limited ternary (MEG-H2O-CH4) data and MEG-nC6 LLE, the best results are achieved using the 4F scheme. Ternary modelling performance was further improved by using binary interaction parameters fitted to binary vapour phase data.While each of the new parameter sets provided an improvement over the literature parameters, it was found that no specific scheme was universally the best option. Given the uncertainty ranges and inconsistency between literature data, additional experimental data are required.Despite the lack of sufficient data, the value of the bootstrap method has been highlighted, both for finding improved parameter sets and transferring uncertainty from experimental data through to thermodynamic and process models.

Confidence intervals and hypothesis testing for the Permutation Entropy with an application to epilepsy

In nonlinear dynamics, and to a lesser extent in other fields, a widely used measure of complexity is the Permutation Entropy. But there is still no known method to determine the accuracy of this measure. There has been little research on the statistical properties of this quantity that characterize time series. The literature describes some resampling methods of quantities used in nonlinear dynamics - as the largest Lyapunov exponent - but these seems to fail. In this contribution, we propose a parametric bootstrap methodology using a symbolic representation of the time series to obtain the distribution of the Permutation Entropy estimator. We perform several time series simulations given by well-known stochastic processes: the 1/fα noise family, and show in each case that the proposed accuracy measure is as efficient as the one obtained by the frequentist approach of repeating the experiment. The complexity of brain electrical activity, measured by the Permutation Entropy, has been extensively used in epilepsy research for detection in dynamical changes in electroencephalogram (EEG) signal with no consideration of the variability of this complexity measure. An application of the parametric bootstrap methodology is used to compare normal and pre-ictal EEG signals.

High-dimensional simultaneous inference with the bootstrap

We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous inference for parameters in groups G, where $$p \gg n$$ , $$s_0 = o(n^{1/2}/\{\log (p) \log (|G|)^{1/2}\})$$ and $$\log (|G|) = o(n^{1/7})$$ , with p the number of variables, n the sample size and $$s_0$$ the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi (Meier et al. hdi: high-dimensional inference. R package version 0.1-6, 2016).

Comments on: High-dimensional simultaneous inference with the bootstrap

The authors should be congratulated on their insightful article proposing forms of residual and paired bootstrap methodologies in the context of simultaneous testing in sparse and high-dimensional linear models. We appreciate the clear exposition of their work, and the effectiveness of the proposed method. The authors advocate for the bootstrap of a complete high-dimensional estimate rather than the linearized part of the test statistic. We appreciate the opportunity to comment on several aspects of this article.

Bootstrap in semi-functional partial linear regression under dependence

This paper deals with the semi-functional partial linear regression model $$Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon $$ under $$\alpha $$ -mixing conditions. $${\varvec{\beta }} \in \mathbb {R}^{p}$$ and $$m(\cdot )$$ denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates $${{\varvec{X}}}$$ and $${\varvec{\chi }}$$ are valued in $$\mathbb {R}^{p}$$ and some infinite-dimensional space, respectively, and the random error $$\varepsilon $$ verifies $$\mathbb {E}(\varepsilon |{{\varvec{X}}},{\varvec{\chi }})=0$$ . Naive and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of $${\varvec{\beta }}$$ and $$m(\chi )$$ , and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.

Bootstrap quantification of estimation uncertainties in network degree distributions

We propose a new method of nonparametric bootstrap to quantify estimation uncertainties in functions of network degree distribution in large ultra sparse networks. Both network degree distribution and network order are assumed to be unknown. The key idea is based on adaptation of the “blocking” argument, developed for bootstrapping of time series and re-tiling of spatial data, to random networks. We first sample a set of multiple ego networks of varying orders that form a patch, or a network block analogue, and then resample the data within patches. To select an optimal patch size, we develop a new computationally efficient and data-driven cross-validation algorithm. The proposed fast patchwork bootstrap (FPB) methodology further extends the ideas for a case of network mean degree, to inference on a degree distribution. In addition, the FPB is substantially less computationally expensive, requires less information on a graph, and is free from nuisance parameters. In our simulation study, we show that the new bootstrap method outperforms competing approaches by providing sharper and better-calibrated confidence intervals for functions of a network degree distribution than other available approaches, including the cases of networks in an ultra sparse regime. We illustrate the FPB in application to collaboration networks in statistics and computer science and to Wikipedia networks.

Generalised block bootstrap and its use in meteorology

Abstract. In an earlier paper, Rakonczai et al.(2014) emphasised the importance of investigating the effective sample size in case of autocorrelated data. The simulations were based on the block bootstrap methodology. However, the discreteness of the usual block size did not allow for exact calculations. In this paper we propose a new generalisation of the block bootstrap methodology, which allows for any positive real number as expected block size. We relate it to the existing optimisation procedures and apply it to a temperature data set. Our other focus is on statistical tests, where quite often the actual sample size plays an important role, even in the case of relatively large samples. This is especially the case for copulas. These are used for investigating the dependencies among data sets. As in quite a few real applications the time dependence cannot be neglected, we investigated the effect of this phenomenon on the used test statistic. The critical value can be computed by the proposed new block bootstrap simulation, where the block size is determined by fitting a VAR model to the observations. The results are illustrated for models of the used temperature data.