Semiparametric Bootstrap Research Articles

Bootstrap Order Determination for ARMA Models: A Comparison between Different Model Selection Criteria

The present paper deals with the order selection of models of the class for autoregressive moving average. A novel method—previously designed to enhance the selection capabilities of the Akaike Information Criterion and successfully tested—is now extended to the other three popular selectors commonly used by both theoretical statisticians and practitioners. They are the final prediction error, the Bayesian information criterion, and the Hannan-Quinn information criterion which are employed in conjunction with a semiparametric bootstrap scheme of the type sieve.

Interval estimation of higher order quantiles. Analysis of accuracy of selected procedures

In the paper selected nonparametric and semiparametric estimation methods of higher orders quantiles are considered. The construction of nonparametric confidence intervals is based on order statistics of appropriate ranks from random samples or from generated bootstrap samples. Semiparametric bootstrap methods are characterized by double bootstrap simulations. The values of bootstrap sample below the prearranged threshold are generated by the empirical distribution and the values above this threshold are generated by the distribution based on the asymptotic properties of the tail of the random variable distribution. The results of the study allow one to draw conclusions about the effectiveness of the considered procedures and to compare these methods.

Interval Estimation of Higher Order Quantiles. Analysis of Accuracy of Selected Procedures

Abstract In the paper selected nonparametric and semiparametric estimation methods of higher orders quantiles are considered. The construction of nonparametric confidence intervals is based on order statistics of appropriate ranks from random samples or from generated bootstrap samples. Semiparametric bootstrap methods are characterized by double bootstrap simulations. The values of bootstrap sample below the prearranged threshold are generated by the empirical distribution and the values above this threshold are generated by the distribution based on the asymptotic properties of the tail of the random variable distribution. The results of the study allow one to draw conclusions about the effectiveness of the considered procedures and to compare these methods.

Bootstrapowe metody estymacji wartości zagrożonej ryzykiem

Interval bootstrap methods can be used to estimate Value at Risk, defined as a quantile of fixed order of random variable being the value of losses from investments. These methods are applied when there is no information about the distribution class of the variable considered, which is the advantage of bootstrap methods compared with parametric methods. Semiparametric estimation procedures are of particular importance. They can be used in the estimation of high-order quantiles. They guarantee the occurrence of large values in the generated bootstrap samples. The paper presents nonparametric and semiparametric bootstrap estimation methods and the results of simulation studies for higher-order quantiles of a heavy-tailed distribution. The application of the methods analysed provide confidence intervals with greater accuracy compared to the nonparametric classical method. The procedures under discussion are used in VaR estimation of daily returns of selected shares at Warsaw Stock Exchange.

Properties of bootstrap tests for N-of-1 studies.

N‐of‐1 study designs involve the collection and analysis of repeated measures data from an individual not using an intervention and using an intervention. This study explores the use of semi‐parametric and parametric bootstrap tests in the analysis of N‐of‐1 studies under a single time series framework in the presence of autocorrelation. When the Type I error rates of bootstrap tests are compared to Wald tests, our results show that the bootstrap tests have more desirable properties. We compare the results for normally distributed errors with those for contaminated normally distributed errors and find that, except when there is relatively large autocorrelation, there is little difference between the power of the parametric and semi‐parametric bootstrap tests. We also experiment with two intervention designs: ABAB and AB, and show the ABAB design has more power. The results provide guidelines for designing N‐of‐1 studies, in the sense of how many observations and how many intervention changes are needed to achieve a certain level of power and which test should be performed.

European Population Exposure to Airborne Pollutants Based on a Multivariate Spatio-Temporal Model

In this paper, we estimate the distribution of population by exposure to multiple airborne pollutants, taking into account the spatio-temporal variability of daily air quality and the high-resolution spatial spread of human population around Europe. In particular, we consider monitoring network data for five pollutants, namely carbon monoxide, nitrogen dioxide, ozone, coarse and fine particulate matters. The spatial information contained in the large dataset of daily continental air quality is exploited using a multivariate spatio-temporal model capable to cover cross correlation among pollutants, covariates, and missing data as well as spatial and temporal variability and correlation. At the same time, the model is simple enough to be feasible for the large dataset of daily continental air quality over three years. Maximum likelihood estimation is performed using the EM algorithm, and kriging-like spatial estimates are used to compute high-resolution exposure distribution. Moreover, a novel semi-parametric bootstrap technique is used to assess the exposure distribution uncertainty. In this way, we compare the daily population exposure of 33 European countries and three important metropolitan areas in years 2009–2011 using a single flexible model. Extensive tabulations and graphs are reported in the supplementary material.

Inference for L-Estimators of Location Using a Bootstrap Warping Approach

In this note we propose a new semi-parametric bootstrap procedure for hypothesis tests about a statistical function and termed bootstrap warping. This procedure was motivated by empirical likelihood and bootstrap tilting techniques. The procedure is computationally efficient and has a fixed number of parameters. We show that the warping procedure has good type I error control and has monotone power as a function of sample size and shift alternatives.

A statistical test of the equality of latent orders

It is sometimes the case that a theory proposes that the population means on two variables should have the same rank order across a set of experimental conditions. This paper presents a test of this hypothesis. The test statistic is based on the coupled monotonic regression algorithm developed by the authors. The significance of the test statistic is determined by comparison to an empirical distribution specific to each case, obtained via non-parametric or semi-parametric bootstrap. We present an analysis of the power and Type I error control of the test based on numerical simulation. Partial order constraints placed on the variables may sometimes be theoretically justified. These constraints are easily incorporated into the computation of the test statistic and are shown to have substantial effects on power. The test can be applied to any form of data, as long as an appropriate statistical model can be specified.

Misspecified poisson regression models for large‐scale registry data: inference for ‘largenand smallp’

Poisson regression is an important tool in register-based epidemiology where it is used to study the association between exposure variables and event rates. In this paper, we will discuss the situation with 'large n and small p', where n is the sample size and p is the number of available covariates. Specifically, we are concerned with modeling options when there are time-varying covariates that can have time-varying effects. One problem is that tests of the proportional hazards assumption, of no interactions between exposure and other observed variables, or of other modeling assumptions have large power due to the large sample size and will often indicate statistical significance even for numerically small deviations that are unimportant for the subject matter. Another problem is that information on important confounders may be unavailable. In practice, this situation may lead to simple working models that are then likely misspecified. To support and improve conclusions drawn from such models, we discuss methods for sensitivity analysis, for estimation of average exposure effects using aggregated data, and a semi-parametric bootstrap method to obtain robust standard errors. The methods are illustrated using data from the Danish national registries investigating the diabetes incidence for individuals treated with antipsychotics compared with the general unexposed population.

Bootstrap hypothesis testing in generalized additive models for comparing curves of treatments in longitudinal studies

The study of the effect of a treatment may involve the evaluation of a variable at a number of moments. When assuming a smooth curve for the mean response along time, estimation can be afforded by spline regression, in the context of generalized additive models. The novelty of our work lies in the construction of hypothesis tests to compare two curves of treatments in any interval of time for several types of response variables. The within-subject correlation is not modeled but is considered to obtain valid inferences by the use of bootstrap. We propose both semiparametric and nonparametric bootstrap approaches, based on resampling vectors of residuals or responses, respectively. Simulation studies revealed a good performance of the tests, considering, for the outcome, different distribution functions in the exponential family and varying the correlation between observations along time. We show that the sizes of bootstrap tests are close to the nominal value, with tests based on a standardized statistic having slightly better size properties. The power increases as the distance between curves increases and decreases when correlation gets higher. The usefulness of these statistical tools was confirmed using real data, thus allowing to detect changes in fish behavior when exposed to the toxin microcystin-RR.

Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk

Where mortality projection is concerned, it is essential to quantify the extent of the prediction error. This is especially important in light of the aggravating risk of longevity and as a result the increasing demand for longevity-linked products. In the literature so far, only parameter error and process error have been considered jointly while the issue of model error has yet been systematically studied. In this paper, we propose a method to account for process error, parameter error and model error in an integrated manner by modifying the semi-parametric bootstrapping technique. We apply the method to two data sets from the Continuous Mortality Investigation (CMI) and use the simulated scenarios to price the q -forward contracts via the maximum entropy approach. We find that model selection has a significant impact on the risk-neutral valuation results and thus it is crucial to incorporate model error in mortality projection.

Event-study volatility and bootstrapping: an international study

This paper examines the impact of terrorism on volatility of stock returns over 17 market indices between 1994 and 2005. Using a volatility event study approach methodology, we find that terrorism has a significant impact on the stock market volatility. We also propose a new semi-parametric bootstrap technique which consists in re-sampling the rescaled residuals obtained from the estimations of GARCH equations before the event and using a moving block approach where the residuals are chosen in a chronologically consecutive manner each time we generate a bootstrap sample. This technique provides a better way to perform inference that is more reliable on finite samples than inference based on conventional asymptotic theory.

꼬리가 두꺼운 분포의 고분위수에 대한 신뢰구간

꼬리가 두꺼운 분포의 고분위수에 대한 신뢰구간을 연구하였다. 통계량의 극한 분포에 근거한 점근적 방법과 붓스트랩 방법을 같이 고려하였다. 이 두 방법에 모수적, 비모수적, 준모수적 기법을 각각 적용할 수 있는데, 전체 11가지 신뢰구간의 성능을 실제신뢰수준과 길이로 비교하였다. 모의실험 결과 준모수적이면서 점근적인 신뢰구간과 축량을 이용하는 준모수적 붓스트랩 신뢰구간이 실제신뢰수준의 기준에서 안정된 성능을 보인다는 것을 알 수 있었다. We consider condence intervals for high quantiles of heavy-tailed distribution. The asymptotic condence intervals based on the limiting distribution of estimators are considered together with bootstrap condence intervals. We can also apply a non-parametric, parametric and semi-parametric approach to each of these two kinds of condence intervals. We considered 11 condence intervals and compared their performance in actual coverage probability and the length of condence intervals. Simulation study shows that two condence intervals (the semi-parametric asymptotic condence interval and the semi-parametric bootstrap condence interval using pivotal quantity) are relatively more stable under the criterion of actual coverage probability.

Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events

Analysis of extreme rainfall events can be performed using two main approaches; fitting Generalized Extreme Value distribution to the yearly peaks of events in the observation period or the annual maximum series, and fitting Generalized Pareto distribution to the peaks of events that exceed a given threshold or the partial duration series. Even though partial duration series are able to reduce sampling uncertainty and are useful for analyzing extreme values and tail asymmetries, the series require an optimal threshold. The objective of this study is to compare and determine the best method for selecting the optimal threshold of partial duration series using hourly, 12-hour and 24-hour data of rainfall time series in Peninsular Malaysia. Nine semi-parametric second order reduced-bias estimators are applied to estimate extreme value index and six estimators are used for the external estimation of the second order parameter. A semi-parametric bootstrap is used to estimate mean square error of the estimator at each threshold and the optimal threshold is then selected based on the smallest mean square error. Based on the plots of extreme value index and mean square error, several second order reduced-bias estimators behave reasonably well compared to Hill estimator, as indicated by their stable sample paths and flatter mean square errors.

The effect of market structure, regulation, and risk on banks efficiency

Purpose – The purpose of this paper is to analyze the efficiency performance of the Gulf Cooperation Countries (GCC) banking sector. The primary focus is to assess whether market power, risk taking activities, and regulations have significant effects on GCC banks’ efficiency performance. Design/methodology/approach – The estimation and inference has been implemented using a double bootstrap procedure that simultaneously corrects for bias and validates inference on the influence of covariates. In the first stage, efficiency scores are estimated with data envelopment analysis (DEA). In the second stage, variation in the resulting efficiency scores is explained using a truncated regression model with inference based on a semi-parametric bootstrap routine. Findings – The authors found compelling evidence that efficiency is not independent of the market structure, the bank's risk taking activities, and the regulatory environment. In particular, the Lerner Index provides evidence that market power decreases efficiency. The capital adequacy, the supervisory power and the market discipline were all found to improve efficiency. Additionally, when the risk is measured by the Z-Score or even by the ratio of non-performing loans to total loans, it adversely affects efficiency. Research limitations/implications – The results of the current study have important implications for regulators and supervisors. Promoting banks’ competitive environment in the GCC countries through reducing the information barriers to entry, encouraging bank privatization, and lowering the activities restrictions can potentially improve operational efficiency of banks. Also enhancing banks’ diversification activities and risk management techniques may have the advantage of increasing operational efficiency. Furthermore, improvements in the regulatory conditions that enhance banking supervision and monitoring would also improve efficiency. Originality/value – The main contributions of the paper are threefold: first, to the knowledge, this study is the first to employ by far the most comprehensive data set of GCC banks investigated to date. Second, the analysis focusses on the influence of a wide set of factors, most of them was not covered before in related economic literature on bank efficiency of the GCC countries. Third, the methodological innovation involves applying a double bootstrap procedure proposed by Simar and Wilson (2007).

A multi-marker molecular signature approach for treatment-specific subgroup identification with survival outcomes

Delivering on the promise of personalized medicine has become a focus of the pharmaceutical industry as the era of the blockbuster drug is fading. Central to realizing this promise is the need for improved analytical strategies for effectively integrating information across various biological assays (for example, copy number variation and targeted protein expression) toward identification of a treatment-specific subgroup-identifying the right patients. We propose a novel combination of elastic net followed by a maximal χ(2) and semiparametric bootstrap. The combined approaches are presented in a two-stage strategy that estimates patient-specific multi-marker molecular signatures (MMMS) to identify and directly test for a biomarker-driven subgroup with enhanced treatment effect. This flexible strategy provides for incorporation of business-specific needs, such as confining the search space to a subgroup size that is commercially viable, ultimately resulting in actionable information for use in empirically based decision making.

Bootstrap Power of Time Series Goodness of fit tests

In this article, we looked at power of various versions of Box and Pierce statistic and Cramer von Mises test. An extensive simulation study has been conducted to compare the power of these tests. Algorithms have been provided for the power calculations and comparison has also been made between the semi parametric bootstrap methods used for time series. Results show that Box-Pierce statistic and its various versions have good power against linear time series models but poor power against non linear models while situation reverses for Cramer von Mises test. Moreover, we found that dynamic bootstrap method is better than xed design bootstrap method.

Asymptotic and bootstrap inference for top income shares

We analyse statistical inference for top income shares in finite samples. The asymptotic inference performs poorly even in large samples. The standard bootstrap tests give some improvement, but can be unreliable. The semi-parametric bootstrap approach is accurate in moderate and larger samples.

Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events

The two primary approaches of extreme events analysis are annual maximum series (AMS), which fits Generalized Extreme Value (GEV) distribution to the yearly peaks of events in the observation period, and partial duration series (PDS), which fits Generalized Pareto (GP) distribution to the peaks of events that exceed a given threshold. The PDS is able to reduce sampling uncertainty and is more useful in dealing with extreme values and asymmetries in the tails, but the optimal threshold is required. The objective of this study is to compare and determine the best method for selecting the optimal threshold of PDS using the hourly, 12-h and 24-h aggregated data of rainfall time series in Peninsular Malaysia. The choice of the threshold, or the number of largest order statistics, can be estimated by the parameters of extreme events. In this study, thirteen semi-parametric estimators are considered and applied to estimate the shape parameter or extreme value index (EVI). A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. Based on the smallest MSE, the majority of stations and data durations favor the Adapted Hill estimator, followed by the QQ, Hill and Moment Ratio 1 estimators. Therefore, this study proves that the application of different estimators on real data may result in different optimal values of threshold and the choice of the best method is very much data-dependent.

Bootstrap Point Optimal Unit Root Tests

In this article, we investigate and compare the behaviour of some bootstrap unit root tests in finite ARMA models with a constant and/or a trend and use them to obtain asymptotic results for the point optimal (hereafter PO) test, in terms of both size and power. We demonstrate the asymptotic validity of bootstrapping the PO test. We provide a feasible method for obtaining approximate critical values for the PO unit root test. Through simulations, we investigate how effective the bootstrap is in different sample sizes, correlative coefficients and close unity autoregressive roots in two different models. Our main objective is to show that the bootstrap PO test can be used in regression models with AR and MA errors and trending regressors. The results reported here provide an analytical investigation of the use of the bootstrap for PO tests with dependent data.The main contribution of this article has two features. First, we choose the PO test and make this powerful but unfeasible procedure both powerful and feasible, by plugging in a consistent estimation of the coefficient structure, and we show that the bootstrap PO test provides asymptotically valid critical values. Second, through simulation, our numerical results suggest that the bootstrap PO test performs well in having the correct size properties and retaining good power in the parametric (and semi-parametric) bootstrap procedure.