A bootstrap test for symmetry based on ranked set samples

To test the hypothesis of symmetry about an unknown median we propose the maximum of a partial sum process based on ranked set samples. We discuss the properties of the test statistic and investigate a modified bootstrap ranked set sample bootstrap procedure to obtain its sampling distribution. The power of the new test statistic is compared with two existing tests in a simulation study.     

Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models

An approximate F-form of the Lagrange multiplier (LM) test for serial correlation in dynamic regression models is compared with three bootstrap tests. In one bootstrap procedure, residuals from restricted estimation under the null hypothesis are resampled. The other two bootstrap tests use residuals from unrestricted estimation under an alternative hypothesis. A fixed autocorrelation alternative is assumed in one of the two unrestricted bootstrap tests and the other is based upon a Pitman-type sequence of local alternatives. Monte Carlo experiments are used to estimate rejection probabilities under the null hypothesis and in the presence of serial correlation.     

The Size and Power of Bootstrap Tests for Spatial Dependence in a Linear Regression Model

In this paper, we define the spatial bootstrap test as a residual-based bootstrap method for hypothesis testing of spatial dependence in a linear regression model. Based on Moran’s I statistic, the empirical size and power of bootstrap and asymptotic tests for spatial dependence are evaluated and compared. Under classical normality assumption of the model, the performance of the spatial bootstrap test is equivalent to that of the asymptotic test in terms of size and power. For more realistic heterogeneous non-normal distributional models, the applicability of asymptotic normal tests is questionable. Instead, spatial bootstrap tests have shown superiority in smaller size distortion and higher power when compared to asymptotic counterparts, especially for cases with a small sample and dense spatial contiguity. Our Monte Carlo experiments indicate that the spatial bootstrap test is an effective alternative to the theoretical asymptotic approach when the classical distributional assumption is violated.     

Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties

The construction of bootstrap hypothesis tests can differ from that of bootstrap confidence intervals because of the need to generate the bootstrap distribution of test statistics under a specific null hypothesis. Similarly, bootstrap power calculations rely on resampling being carried out under specific alternatives. We describe and develop null and alternative resampling schemes for common scenarios, constructing bootstrap tests for the correlation coefficient, variance, and regression/ANOVA models. Bootstrap power calculations for these scenarios are described. In some cases, null-resampling bootstrap tests are equivalent to tests based on appropriately constructed bootstrap confidence intervals. In other cases, particularly those for which simple percentile-method bootstrap intervals are in routine use such as the correlation coefficient, null-resampling tests differ from interval-based tests. We critically assess the performance of bootstrap tests, examining size and power properties of the tests numerically using both real and simulated data. Where they differ from tests based on bootstrap confidence intervals, null-resampling tests have reasonable size properties, outperforming tests based on bootstrapping without regard to the null hypothesis. The bootstrap tests also have reasonable power properties.     

Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties

The construction of bootstrap hypothesis tests can differ from that of bootstrap confidence intervals because of the need to generate the bootstrap distribution of test statistics under a specific null hypothesis. Similarly, bootstrap power calculations rely on resampling being carried out under specific alternatives. We describe and develop null and alternative resampling schemes for common scenarios, constructing bootstrap tests for the correlation coefficient, variance, and regression/ANOVA models. Bootstrap power calculations for these scenarios are described. In some cases, null-resampling bootstrap tests are equivalent to tests based on appropriately constructed bootstrap confidence intervals. In other cases, particularly those for which simple percentile-method bootstrap intervals are in routine use such as the correlation coefficient, null-resampling tests differ from interval-based tests. We critically assess the performance of bootstrap tests, examining size and power properties of the tests numerically using both real and simulated data. Where they differ from tests based on bootstrap confidence intervals, null-resampling tests have reasonable size properties, outperforming tests based on bootstrapping without regard to the null hypothesis. The bootstrap tests also have reasonable power properties.     

A bootstrap panel unit root test under cross-sectional dependence, with an application to PPP

A bootstrap methodology for dealing with cross-sectional dependence in panel unit root tests of real exchange rates is suggested. Monte Carlo simulations are employed to investigate the size distortion and the power of the bootstrap test-statistic. It is shown that the statistic has good power and no size distortions for moderate and large samples. The panel unit root test procedure is then applied to the long-run purchasing power parity (PPP) hypothesis, using a panel of 20 OECD countries over the recent float period, and the results are compared to those obtained by other tests.     

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.     

Finite-Sample Adjustments for Homogeneity and Symmetry Tests in Systems of Demand Equations: A Monte Carlo Evaluation

This paper gives simulation results comparing the finite-sample performance of three commonly used homogeneity and symmetry asymptotic tests, and some size-corrected tests that can be used when the sample size is small. The results suggest that such finite-sample corrections can be effective in bringing the empirical sizes of the tests closer to their nominal levels. They also suggest that the likelihood ratio test is, in general, more reliable than the Wald and Lagrange multiplier tests. Finally, it is shown that size-corrections of homogeneity tests tend to introduce reductions in power, which can be very large when bootstrap corrections are used. An application to a well known data set is also presented.     

Bowker's test for symmetry and modifications within the algebraic framework

Categorical data occur in a wide range of statistical applications. If the data are observed in matched pairs, it is often of interest to examine the differences between the responses. The focus is on tests of axial symmetry in two-way tables. A commonly used procedure is the Bowker test which is a generalization of the McNemar test. The test decision is based on a chi-squared approximation which might not be adequate, for example if the table is sparse. Therefore, modifications of the test statistic have been discussed. A test of symmetry based on Bowker's test and Markov Chain Monte Carlo methods is proposed. A simulation study is carried out to determine and compare the performances of the simulation test, the Bowker test and two modifications.     

Goodness-of-fit tests based on empirical characteristic functions

A class of goodness-of-fit tests based on the empirical characteristic function is studied. They can be applied to continuous as well as to discrete or mixed data with any arbitrary fixed dimension. The tests are consistent against any fixed alternative for suitable choices of the weight function involved in the definition of the test statistic. The bootstrap can be employed to estimate consistently the null distribution of the test statistic. The goodness of the bootstrap approximation and the power of some tests in this class for finite sample sizes are investigated by simulation.