On finite sample properties of the tests of robinson (1994) for fractional integration

This article proposes a bootstrap version of the tests of Robinson (1994) for testing unit and/or fractional roots. The finite-sample behaviour of the tests, based on these bootstrap critical values is compared with those based on asymptotic and on finite-sample results and with a number of leading unit-root tests. The Monte-Carlo simulations indicate that the bootstrap version of the tests of Robinson (1994) outperforms the other tests, including the one using finite-sample critical values. The improvement in the size and the power is particularly important under AR(1) alternatives. A small empirical application is also carried out with inflation for a panel of 16 European countries. The results show that the differences across countries depend on the critical values used: whereas the I (1) property of inflation is unclear with the asymptotic tests in some countries, the bootstrap version of Robinson's (1994) tests cannot reject the presence of a unit-root in inflation.     

A comment on “testing the lucas critique: A review ”

We derive general distribution tests based on the method of maximum entropy (ME) density. The proposed tests are derived from maximizing the differential entropy subject to given moment constraints. By exploiting the equivalence between the ME and maximum likelihood (ML) estimates for the general exponential family, we can use the conventional likelihood ratio (LR), Wald, and Lagrange multiplier (LM) testing principles in the maximum entropy framework. In particular, we use the LM approach to derive tests for normality. Monte Carlo evidence suggests that the proposed tests are compatible with and sometimes outperform some commonly used normality tests. We show that the proposed tests can be extended to tests based on regression residuals and non-i.i.d. data in a straightforward manner. An empirical example on production function estimation is presented.     

Reconsidering LM unit root testing

Non-rejection of a unit root hypothesis by usual Dickey & Fuller (1979) (DF, hereafter) or Phillips & Perron (1988) (hereafter PP) tests should not be taken as strong evidence in favour of unit root presence. There are less popular, but more powerful, unit root tests that should be employed instead of DF-PP tests. A prime example of an alternative test is the LM unit root test developed by Schmidt & Phillips (1992) (hereafter SP) and Schmidt & Lee (1991) (hereafter SL). LM unit root tests are easy to calculate and invariant (similar); they employ optimal detrending and are more powerful than usual DF-PP tests. Asymptotic theory and finite sample critical values (with inaccuracies that we correct in this paper) are available for SP-SL tests. However, the usefulness of LM tests is not fully understood, due to ambiguity over test type recommendation, as well as potentially inefficient derivation of the test that might confuse applied researchers. In this paper, we reconsider LM unit root testing in a model with linear trend. We derive asymptotic distribution theory (in a new fashion), as well as accurate appropriate critical values. We undertake Monte Carlo investigation of finite sample properties of SP-SL LM tests, along with applications to the Nelson & Plosser (1982) time series and real quarterly UK GDP.     

Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.     

Likelihood ratio test for testing order of continuous time finite markov chains

Anderson and Goodman ( 1957) have obtained the likelihood ratio tests and chi-square tests for testing the hypothesis about the order of discrete time finite Markov chains, On the similar lines we have obtained likeli¬hood ratio tests and chi-square tests (asymptotic) for testing hypotheses about the order of continuous time Markov chains (MC) with finite state space.     

Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.     

A monte carlo study of the wald,lm, and lr tests in a heteroscedastic linear model

In this paper, we examine by Monte Carlo experiments the small sample properties of the W (Wald), LM (Lagrange Multiplier) and LR (Likelihood Ratio) tests for equality between sets of coefficients in two linear regressions under heteroscedasticity. The small sample properties of the size-corrected W, LM and LR tests proposed by Rothenberg (1984) are also examined and it is shown that the performances of the size-corrected W and LM tests are very good. Further, we examine the two-stage test which consists of a test for homoscedasticity followed by the Chow (1960) test if homoscedasticity is indicated or one of the W, LM or LR tests if heteroscedasticity should be assumed. It is shown that the pretest does not reduce much the bias in the size when the sizecorrected citical values are used in the W, LM and LR tests.     

The power of the tests of robinson (1994) in the context of fractionall[y integrated moving average models

We examine in this article the power of the tests of Robinson (1994) for testing I(d) statistical models in the presence of moving average (MA) disturbances. The results show that the tests behave relatively well if we correctly assume that the disturbances are MA. However, assuming white noise or autoregressive disturbances, the power of the tests against one-sided alternatives is very low.     

New Tests of Spatial Segregation Based on Nearest Neighbour Contingency Tables

Abstract.  The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause segregation or association, which are two major types of spatial patterns between the classes. These patterns can be studied using a nearest neighbour contingency table (NNCT) which is constructed using the frequencies of nearest neighbour types. Three new multivariate clustering tests are proposed based on NNCTs using the appropriate sampling distribution of the cell counts in a NNCT. The null patterns considered are random labelling (RL) and complete spatial randomness (CSR) of points from two or more classes. The finite sample performance of these tests are compared with other tests in terms of empirical size and power. It is demonstrated that the newly proposed NNCT tests perform relatively well compared with their competitors and the tests are illustrated using two example data sets.     

Lack of fit tests based on sums of ordered residuals for linear models

Christensen & Lin ( 2015 ) suggested two lack of fit tests to assess the adequacy of a linear model based on partial sums of residuals. In particular, their tests evaluated the adequacy of the mean function. Their tests relied on asymptotic results without requiring small sample normality. We propose four new tests, find their asymptotic distributions, and propose an alternative simulation method for defining tests that is remarkably robust to the distribution of the errors. To assess their strengths and weaknesses, the Christensen & Lin ( 2015 ) tests and the new tests were compared in different scenarios by simulation. In particular, the new tests include two based on partial sums of absolute residuals. Previous partial sums of residuals tests have used signed residuals whose values when summed can cancel each other out. The use of absolute residuals requires small sample normality, but allows detection of lack of fit that was previously not possible with partial sums of residuals.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.     

Comparison of tests for bivariate symmetry versus location and/or scale alternatives

This paper studies the performance of tests which use a null hypothesis of bivariate symmetry and detect the broad class of location and/or scale alternatives . The conditionally distribution-free tests of Sen (1967) and Hollander (1971) and parametric tests related to those of Bell and Haller (1969) are compared in a Monte Carlo study which also includes a new conditionally distribution-free test.     

Shapiro–Francia test compared to other normality test using expected p-value

The Shapiro–Francia (SF) normality test is an important test in statistical modelling. However, little has been done by researchers to compare the performance of this test to other normality tests. This paper therefore measures the performance of the SF and other normality tests by studying the distribution of their p-values. For the purpose of this study, we selected eight well-known normality tests to compare with the SF test: (i) Kolmogorov–Smirnov (KS), (ii) Anderson–Darling (AD), (iii) Cramer von Mises (CM), (iv) Lilliefors (LF), (v) Shapiro–Wilk (SW), (vi) Pearson chi-square (PC), (vii) Jarque– Bera (JB) and (viii) D'Agostino (DA). The distribution of p-values of these normality tests were obtained by generating data from normal distribution and well-known symmetric non-normal distribution at various sample sizes (small, medium and large). Our simulation results showed that the SF normality test was the best test statistic in detecting deviation from normality among the nine tests considered at all sample sizes.     

On testing the skew normal hypothesis

In this work two goodness-of-fit tests are proposed for the skew normal distribution, based on properties of this family of distributions and the sample correlation coefficient. The critical values for the tests are obtained by using Monte Carlo simulation for several sample sizes and levels of significance. The power of the proposed tests are compared with that of the tests studied by Mateu et al. (2007) and the one studied by Meintanis (2007) for several sample sizes and considering diverse alternatives. The results show that the proposed tests have greater power than those studied by Mateu et al. (2007) and Meintanis (2007) against some alternative distributions.     

Maximin clusters for nonreplicated multiresponse lack of fit tests

Khuri (Technometrics 27 (1985) 213) and Levy and Neill (Comm. Statist. A 19 (1990) 1987) presented regression lack of fit tests for multiresponse data with replicated observations available at points in the experimental region, thereby extending the classical univariate lack of fit test given by Fisher (J. Roy. Statist. Soc. 85 (1922) 597). In this paper, multivariate tests for lack of fit in a linear multiresponse model are derived for the common circumstance in which replicated observations are not obtained. The tests are based on the union–intersection principle, and provide multiresponse extensions of the univariate tests for between- and within-cluster lack of fit introduced by Christensen (Ann. of Statist. 17 (1989) 673; J. Amer. Statist. Assoc. 86 (1991) 752). Since the properties of these tests depend on the choice of multivariate clusters of the observations, a multiresponse generalization of the maximin power clustering criterion given by Miller, Neill and Sherfey (Ann. of Statist. 26 (1998) 1411; J. Amer. Statist. Assoc. 94 (1999) 610) is also developed.     

Testing homogeneity of control and treatment populations — local optimality and related issues

Durairajan and Raman (1996 a, b) studied the robustness of Locally most powerful invariant (LMPI) tests for compound normal model in control and treatment populations. In the present paper, the Locally most powerful (LMP) tests are constructed for no contamination in normal mixture model through testing the parameter of mixture of distributions and the mixing proportion. The expected performance of LMP tests are compared using Efron's Statistical Curvature on the lines of Sen Gupta and Pal (1991). The Locally most powerful similar (LMPS) tests for the equality of control and treatment populations in the presence of nuisance parameters are also constructed. Further, the null and non-null distributions of the test statistics are derived and some power computations are made. Received: September 1, 1999; revised version: August 31, 2000     

Maximal invariant likelihood based testing of semi-linear models

In this paper, we use a maximal invariant likelihood (MIL) to construct two likelihood ratio (LR) tests in the context of a semi-linear regression model. The first involves testing for the inclusion of a non-linear regressor and the second involves testing a linear regressor against the alternative of a non-linear regressor. We report the results of a Monte Carlo experiment that compares the size and power properties of the traditional LR tests with those of our proposed MIL based LR tests. Our simulation results show that in both cases, the MIL based tests have more accurate asymptotic critical values and better behaved (i.e., better centred) power curves than their classical counterparts.     

Generalized Likelihood Ratio Tests and Uniformly Most Powerful Tests

For testing a one-sided hypothesis in a one-parameter family of distributions, it is shown that the generalized likelihood ratio (GLR) test coincides with the uniformly most powerful (UMP) test, assuming certain monotonicity properties for the likelihood function. In particular, the equivalence of GLR tests and UMP tests holds for one-parameter exponential families. In addition, the relationship between GLR and UMPU (UMP unbiased) tests is considered when testing two-sided hypotheses.     

A K-SAMPLE EXTENSION TO FLIGNER'S CLASS OF TESTS FOR SCALE

The parameteric tests for equality of variance are well known. The classical F-test is typically used to test the hypothesis of equality of two variances, while tests such as those developed by Bartlett (1937) are commonly used for the k-sample hypothesis. These tests assume an underlying normal distribution and are quite sensitive to departures from normality (Box, 1953). Thus, when considering data that are from non-normal distributions, alternative nonparametric tests must be employed.
Fligner (1979) has proposed a class of two-sample distribution-free tests which possess very desirable properties and are attractive alternatives to other nonparametric tests for scale. The present paper extends the Fligner class of tests to the more general k-sample case.     

Small-sample properties of covariance-adjusted survivorship data tests for treatment effect

Monte Carlo methods are used to examine the small-sample properties of 11 test statistics that can be used for comparing several treatments with respect to their mortality experiences while adjusting for covariables. The test statistics are investigated from three distinct models: the parametric, semiparametric and rank analysis of covariance (Quade, 1967) models. Four tests (likelihood ratio, Wald, conditional and unconditional score tests) from each of the first two models and three tests (based on rank scores) from the last model are discussed. The empirical size and power of the tests are investigated under a proportional hazards model in three situations: (1) the baseline hazard is correctly assumed to be Exponential, (2) the baseline hazard is incorrectly assumed to be Exponential, and (3) a treatment-covariate interaction is omitted from the analysis.