Fast Double Bootstrap Research Articles

Research on the Validity of Bootstrap LM-Error Test in Spatial Random Effect Models

Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.

CLUSTER FAST DOUBLE BOOTSTRAP APPROACH WITH RANDOM EFFECT SPATIAL MODELING

Panel data is a combination of cross-sectional and time series data. Spatial panel analysis is an analysis to obtain information based on observations affected by the space or location effects. The effect of location effects on spatial analysis is presented in the form of weighting. The use of panel data in spatial regression provides a number of advantages, however, the spatial dependence test and parameter estimators generated in the spatial regression of data panel will be inaccurate when applied to areas with a small number of spatial units. One method to overcome the problem of small spatial unit size is the bootstrap method. This study used the fast double bootstrap (FDB) method by modeling the poverty rate in the Flores islands. The data used in the study was sourced from the BPS NTT Province website. The results of Hausman test show that the right model is Random effect. The spatial dependence test concludes that there is a spatial dependence and the poverty modeling in the Flores islands tends to use the SAR model. SAR random effect model R2 shows the value of 77.38 percent and it does not meet the assumption of normality. Spatial Autoregressive Random effect model with the Fast Double Bootstrap approach is able to explain the diversity of poverty rate in the Flores Island by 99.83 percent and fulfilling the assumption of residual normality. The results of the analysis using the FDB approach on the spatial panel show better results than the common spatial panel.

Spatial Modeling of Fixed Effect and Random Effect with Fast Double Bootstrap Approach

Spatial Modeling of Fixed Effect and Random Effect with Fast Double Bootstrap Approach

The fast iterated bootstrap

The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suffers from less size distortion under the null with no accompanying loss of power.

Bootstrap-based testing inference in beta regressions

We address the issue of performing testing inference in small samples in the class of beta regression models. We consider the likelihood ratio test and its standard bootstrap version. We also consider two alternative resampling-based tests. One of them uses the bootstrap test statistic replicates to numerically estimate a Bartlett correction factor that can be applied to the likelihood ratio test statistic. By doing so, we avoid estimation of quantities located in the tail of the likelihood ratio test statistic null distribution. The second alternative resampling-based test uses a fast double bootstrap scheme in which a single second level bootstrapping resample is performed for each first level bootstrap replication. It delivers accurate testing inferences at a computational cost that is considerably smaller than that of a standard double bootstrapping scheme. The Monte Carlo results we provide show that the standard likelihood ratio test tends to be quite liberal in small samples. They also show that the bootstrap tests deliver accurate testing inferences even when the sample size is quite small. An empirical application is also presented and discussed.

Bootstrap LM Tests for Spatial Dependence in Panel Data Models with Fixed Effects

AbstractThis paper applies bootstrap methods to LM tests (including LM-lag test and LM-error test) for spatial dependence in panel data models with fixed effects, and removes fixed effects based on orthogonal transformation method proposed by Lee and Yu (2010). The consistencies of LM tests and their bootstrap versions are proved, and then some asymptotic refinements of bootstrap LM tests are obtained. It shows that the convergence rate of bootstrap LM tests isO((NT)−2) and that of fast double bootstrap LM tests isO((NT)−5/2). Extensive Monte Carlo experiments suggest that, compared to aysmptotic LM tests, the size of bootstrap LM tests gets closer to the nominal level of signifiance, and the power of bootstrap LM tests is higher, especially in the cases with small spatial correlation. Moreover, when the error is not normal or with heteroskedastic, asymptotic LM tests suffer from severe size distortion, but the size of bootstrap LM tests is close to the nominal significance level. Bootstrap LM tests are superior to aysmptotic LM tests in terms of size and power.

A new test for the significance of neural network inputs

This paper introduces a new formal test of the significance of neural network inputs. It is simple, accurate, and powerful and is based on a linear relationship between the output of a neural network when all of the input variables are fixed at their mean values—other than the input variable, which is subject to significance testing—and the target values of the network. Simulation results show that as the number of observations increases, the power of the test tends to 1 in all cases, and that the empirical size approaches the nominal size in some cases. The results, based on the ordinary least squares (OLS) estimation of parameters, are very encouraging, but using a heteroscedasticity and autocorrelation consistent covariance matrix and fast double bootstrap improves the speed of the convergence to the nominal size. The test can also be used for nonlinear models with nuisance parameters.

Diagnostics for the bootstrap and fast double bootstrap

ABSTRACTThe bootstrap is typically less reliable in the context of time-series models with serial correlation of unknown form than when regularity conditions for the conventional IID bootstrap apply. It is, therefore, useful to have diagnostic techniques capable of evaluating bootstrap performance in specific cases. Those suggested in this paper are closely related to the fast double bootstrap (FDB) and are not computationally intensive. They can also be used to gauge the performance of the FDB itself. Examples of bootstrapping time series are presented, which illustrate the diagnostic procedures, and show how the results can cast light on bootstrap performance.

A Subsampled Double Bootstrap for Massive Data

ABSTRACTThe bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little sacrifice of statistical accuracy. Building on BLB and the idea of fast double bootstrap, we propose a new resampling method, the subsampled double bootstrap, for both independent data and time series data. We establish consistency of the subsampled double bootstrap under mild conditions for both independent and dependent cases. Methodologically, the subsampled double bootstrap is superior to BLB in terms of running time, more sample coverage, and automatic implementation with less tuning parameters for a given time budget. Its advantage relative to BLB and bootstrap is also demonstrated in numerical simulations and a data illustration. Supplementary materials for this article are available online.

Moran's I test of spatial panel data model — Based on bootstrap method

Under the condition of the finite sample or the unknown distributed error term, testing for spatial dependence in panel data models is an unresolved problem in spatial econometrics. In this paper, a fast double bootstrap (FDB) method is used to construct bootstrap Moran's I tests for Moran's I test in spatial panel data models, and Monte Carlo simulation experiments are used to prove the effectiveness from two aspects including size distortion and power. The experiment results show that, in asymptotic Moran's I test, there is serious size distortion, which could be rectified in bootstrap Moran's I test.

The Iterated Bootstrap

The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suers from less size distortion under the null with no accompanying loss of power.

Forage Response to Swine Effluent: A Cox Nonnested Test of Alternative Functional Forms Using a Fast Double Bootstrap

A Cox nonnested test is conducted using a fast double bootstrap (FDB) method to select among three competing functional forms (linear response plateau, quadratic, and Mitscherlich-Baule) to model forage yield response to nitrogen applied with swine effluent. The quadratic is rejected in favor of one of the other functional forms in all cases. The FDBpvalues differed slightly from the single bootstrappvalues. Buffalograss was slightly more profitable than bermudagrass and has the ability to use almost as much nitrogen as bermudagrass.

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.

Bootstrap and fast double bootstrap tests of cointegration rank with financial time series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. Bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test are introduced and evaluated by Monte Carlo simulation experiments. It is found that the performance of the ordinary (single) bootstrap test is in most cases good in terms of the size of the test. The FDB produces a further improvement in cases where the performance of the asymptotic test is unsatisfactory and the single bootstrap test overrejects noticeably. The FDB is shown to be a useful supplement to the single bootstrap as a tool for determining the cointegration rank. The tests are applied to US interest rates and international stock prices series. By simulating the data assuming that the cointegration rank is known, it is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

The Size and Power of Bootstrap and Bartlett-Corrected Tests of Hypotheses on the Cointegrating Vectors

In this paper we compare Bartlett-corrected, bootstrap, and fast double bootstrap tests on maximum likelihood estimates of cointegration parameters. The key result is that both the bootstrap and the Bartlett-corrected tests must be based on the unrestricted estimates of the cointegrating vectors: procedures based on the restricted estimates have almost no power. The small sample size bias of the asymptotic test appears so severe as to advise strongly against its use with the sample sizes commonly available; the fast double bootstrap test minimizes size bias, while the Bartlett-corrected test is somehow more powerful.

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.

FAST DOUBLE BOOTSTRAP TESTS OF NONNESTED LINEAR REGRESSION MODELS

ABSTRACT It has been shown in previous work that bootstrapping the J test for nonnested linear regression models dramatically improves its finite-sample performance. We provide evidence that a more sophisticated bootstrap procedure, which we call the fast double bootstrap, produces a very substantial further improvement in cases where the ordinary bootstrap does not work as well as it might. This FDB procedure is only about twice as expensive as the usual single bootstrap.

Fast and Accurate Approximate Double Bootstrap Confidence Intervals

Fast and Accurate Approximate Double Bootstrap Confidence Intervals

Fast and accurate approximate double bootstrap confidence intervals

We propose two new methods for the construction of approximate iterated bootstrap confidence intervals. Our methods follow a saddlepoint approach, but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique. The main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small- to moderately-sized samples and that they achieve this accuracy with very substantial reductions in computation time compared to other methods