An empirical study of a test for polynomial relationships in randomly right censored regression models

In this paper, a test statistic is constructed to test polynomial relationships in randomly right censored regression models based on the local polynomial smoothing technique. Two bootstrap procedures, namely the residual-based bootstrap and the naive bootstrap procedures, are suggested to derive the p-value of the test. Some simulations are conducted to empirically assess the performance of the two bootstrap procedures. The results demonstrate that the residual-based bootstrap performs much better than the naive bootstrap and the test method with the residual-based bootstrap to derive the p-value works satisfactorily. Although the limiting distribution of the test statistic and the consistency of the bootstrap approximations remain to be investigated, simulation results indicate that the proposed test method may be of some practical use. As a real example, the proposed test is applied to the Stanford heart transplant data.     

Improving the reliability of bootstrap tests with the fast double bootstrap

Two procedures are proposed for estimating the rejection probabilities (RPs) of bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive (per replication) as estimating RPs for asymptotic tests. Then a new procedure is proposed for computing bootstrap P values that will often be more accurate than ordinary ones. This “fast double bootstrap” (FDB) is closely related to the double bootstrap, but it is far less computationally demanding. Simulation results for three different cases suggest that the FDB can be very useful in practice.     

Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model

The prediction of vectors of small area quantities based on a multivariate Fay-Herriot model is addressed. For this, an empirical best linear unbiased predictor (EBLUP) of the target vector is used, where the model parameters are estimated by two different methods based on moments. The mean cross product error matrix of the multidimensional EBLUP is approximated both analytically and by a wild bootstrap method that yields direct and bias-corrected bootstrap estimators. A simulation study compares the small sample properties of the bootstrap estimators and the analytical approximation, including a comparison under lack of normality. Finally, the number of replicates needed for the bootstrap procedures to get stabilized are studied.     

Tests of Random Walk: A Comparison of Bootstrap Approaches

This paper compares different versions of the multiple variance ratio test based on bootstrap techniques for the construction of empirical distributions. It also analyzes the crucial issue of selecting optimal block sizes when block bootstrap procedures are used. The comparison of the different approaches using Monte Carlo simulations leads to the conclusion that methodologies using block bootstrap methods present better performance for the construction of empirical distributions of the variance ratio test. Moreover, the results are highly sensitive to methods employed to test the null hypothesis of random walk.     

Re-sampling procedures for reducing bias of error rate estimation in multinomial classification

The bias in estimating the error rate of a multinomial classification problem is addressed. The cross-validation, jackknife and bootstrap procedures are introduced to obtain the bias-reducing estimates of error rate. The performance of these procedures is examined by Monte Carlo simulation under different population structures. It is found that all three procedures are effective in reducing bias under small sample situations.     

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

In the context of linear state space models with known parameters, the Kalman filter (KF) generates best linear unbiased predictions of the underlying states together with their corresponding Prediction Mean Square Errors (PMSE). However, in practice, when the filter is run with the parameters substituted by consistent estimates, the corresponding PMSE do not take into account the parameter uncertainty. Consequently, they underestimate their true counterparts. In this paper, we propose two new bootstrap procedures to obtain PMSE of the unobserved states designed to incorporate this latter uncertainty. We show that the new bootstrap procedures have better finite sample properties than bootstrap alternatives and than procedures based on the asymptotic approximation of the parameter distribution. The proposed procedures are implemented for estimating the PMSE of several key unobservable US macroeconomic variables as the output gap, the Non-accelerating Inflation Rate of Unemployment (NAIRU), the long-run investment rate and the core inflation. We show that taking into account the parameter uncertainty may change their prediction intervals and, consequently, the conclusions about the utility of the NAIRU as a macroeconomic indicator for expansions and recessions.     

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.     

Homogenous panel unit root tests under cross sectional dependence: Finite sample modifications and the wild bootstrap

First generation panel unit root tests are known to be invalid under cross sectional dependence. Focussing on the subclass of homogenous tests, three extensions of existing approaches are proposed. First, a test based on a generalized variance estimator is suggested for panels with small time and relatively large cross sectional dimension. Second, the application of refined residuals in variance estimators is proposed to reduce finite sample biases. Third, the wild bootstrap is proved to be an asymptotically valid method of resampling homogenous panel unit root test statistics. A Monte Carlo study shows that the wild bootstrap yields unbiased inference, even in cases where existing procedures are biased. Most accurate results under the null hypothesis are obtained by resampling robust statistics while there is no, or minor, evidence of power loss invoked by the wild bootstrap. An empirical illustration underpins that the current account to GDP ratio is likely panel stationary.     

Homogenous panel unit root tests under cross sectional dependence: Finite sample modifications and the wild bootstrap

First generation panel unit root tests are known to be invalid under cross sectional dependence. Focussing on the subclass of homogenous tests, three extensions of existing approaches are proposed. First, a test based on a generalized variance estimator is suggested for panels with small time and relatively large cross sectional dimension. Second, the application of refined residuals in variance estimators is proposed to reduce finite sample biases. Third, the wild bootstrap is proved to be an asymptotically valid method of resampling homogenous panel unit root test statistics. A Monte Carlo study shows that the wild bootstrap yields unbiased inference, even in cases where existing procedures are biased. Most accurate results under the null hypothesis are obtained by resampling robust statistics while there is no, or minor, evidence of power loss invoked by the wild bootstrap. An empirical illustration underpins that the current account to GDP ratio is likely panel stationary.     

Modified fast double sieve bootstraps for ADF tests

This paper studies the finite sample performance of the sieve bootstrap augmented Dickey-Fuller (ADF) unit root test. It is well known that this test’s accuracy in terms of rejection probability under the null depends greatly on the underlying DGP. Through extensive simulations, we find that it also depends on the number of lags employed in the bootstrap DGP and in the bootstrap ADF regression. Based on this finding and using some well established theoretical results, we propose a simple modification that significantly improves the test’s accuracy. We also introduce different versions of the fast double bootstrap, each modified according to the same theoretical basis. According to our simulations, these new testing procedures have lower error in rejection probability under the null while retaining good power.     

On properties of predictors derived with a two-step bootstrap model averaging approach—A simulation study in the linear regression model

In many applications of model selection there is a large number of explanatory variables and thus a large set of candidate models. Selecting one single model for further inference ignores model selection uncertainty. Often several models fit the data equally well. However, these models may differ in terms of the variables included and might lead to different predictions. To account for model selection uncertainty, model averaging procedures have been proposed. Recently, an extended two-step bootstrap model averaging approach has been proposed. The first step of this approach is a screening step. It aims to eliminate variables with negligible effect on the outcome. In the second step the remaining variables are considered in bootstrap model averaging. A large simulation study is performed to compare the MSE and coverage rate of models derived with bootstrap model averaging, the full model, backward elimination using Akaike and Bayes information criterion and the model with the highest selection probability in bootstrap samples. In a data example, these approaches are also compared with Bayesian model averaging. Finally, some recommendations for the development of predictive models are given.     

Multiple forecasts with autoregressive time series models: case studies

It is indisputable that accurate forecasts of economic activities are vital to successful business and government policies. In many circumstances, instead of a single forecast, simultaneous prediction intervals for multiple forecasts are more useful to decision-makers. For example, based on previous monthly sales records, a production manager would be interested in the next 12 interval forecasts of the monthly sales using for the annual inventory and manpower planning. For Gaussian autoregressive time series processes, several procedures for constructing simultaneous prediction intervals have been proposed in the literature. These methods assume a normal error distribution and can be adversely affected by departures from normality which are commonly encountered in business and economic time series. In this article, we explore the bootstrap methods for the construction of simultaneous multiple interval forecasts. To understand the mechanisms and characteristics of the proposed bootstrap procedures, several macro-economic time series are selected for illustrative purposes. The selected series are fitted reasonably well with autoregressive models which form an important class in time series. As a matter of fact, the major ideas discussed in this paper with autoregressive processes can be extended to other more complicated time series models.     

Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables

Multiple imputation is a popular way to handle missing data. Automated procedures are widely available in standard software. However, such automated procedures may hide many assumptions and possible difficulties from the view of the data analyst. Imputation procedures such as monotone imputation and imputation by chained equations often involve the fitting of a regression model for a categorical outcome. If perfect prediction occurs in such a model, then automated procedures may give severely biased results. This is a problem in some standard software, but it may be avoided by bootstrap methods, penalised regression methods, or a new augmentation procedure.     

Using the bootstrap for finite sample confidence intervals of the log periodogram regression

Log periodogram regression is widely applied in empirical applications to estimate the memory parameter, d, of long memory time series. This estimator is consistent for d<1 and pivotal asymptotically normal for d<3/4. However, the asymptotic distribution is a poor approximation of the (unknown) finite sample distribution if the sample size is small. Finite sample improvements in the construction of confidence intervals can be achieved by different nonparametric bootstrap procedures based on the residuals of log periodogram regression. In addition to the basic residual bootstrap, the local and block bootstraps seem adequate for replicating the structure that may arise in the errors of the regression when the series shows weak dependence in addition to long memory. The performances of different bias correcting bootstrap techniques and a bias reduced log periodogram regression are also analyzed with a view to adjusting the bias caused by that structure. Finally, an application to the Nelson and Plosser US macroeconomic data is included.     

A transportable extendable compiler

This report describes the development of a transportable extendable self-compiler for the language SIMPL-T. SIMPL-T is designed as the base language for a family of languages. The structure of the SIMPL-T compiler and its transportable bootstrap are described. In addition, the procedures for generating a compiler for a new machine and for boot-strapping the new compiler on to the new machine are demonstrated.     

Distributed learning with bagging-like performance

Bagging forms a committee of classifiers by bootstrap aggregation of training sets from a pool of training data. A simple alternative to bagging is to partition the data into disjoint subsets. Experiments with decision tree and neural network classifiers on various datasets show that, given the same size partitions and bags, disjoint partitions result in performance equivalent to, or better than, bootstrap aggregates (bags). Many applications (e.g., protein structure prediction) involve use of datasets that are too large to handle in the memory of the typical computer. Hence, bagging with samples the size of the data is impractical. Our results indicate that, in such applications, the simple approach of creating a committee of n classifiers from disjoint partitions each of size 1/n (which will be memory resident during learning) in a distributed way results in a classifier which has a bagging-like performance gain. The use of distributed disjoint partitions in learning is significantly less complex and faster than bagging.     

The missing censoring indicator model and the smoothed bootstrap

For right censored data with missing censoring indicators, sub-density function kernel estimators play a significant role for estimating a survival function. Data-driven bandwidths for computing these kernel estimators are proposed. The bandwidths are obtained as minimizers of certain estimates of the mean integrated squared error (MISE). It is shown that the smoothed bootstrap offers a motivation for choosing the proposed MISE estimates for minimization. The efficacy of the proposed procedures is investigated through simulation studies and some illustrations are provided.     

The missing censoring indicator model and the smoothed bootstrap

For right censored data with missing censoring indicators, sub-density function kernel estimators play a significant role for estimating a survival function. Data-driven bandwidths for computing these kernel estimators are proposed. The bandwidths are obtained as minimizers of certain estimates of the mean integrated squared error (MISE). It is shown that the smoothed bootstrap offers a motivation for choosing the proposed MISE estimates for minimization. The efficacy of the proposed procedures is investigated through simulation studies and some illustrations are provided.