Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests

Standard methods for inference in cointegrating systems require all the variables to have exact unit roots and are not at all robust even to slight violations of this condition. In this article, I consider an alternative approach to inference in a cointegrating system. This involves testing the hypothesis that a cointegrating vector takes on a specified value by testing for the stationarity of the associated residual. Confidence sets for the cointegrating vector can be constructed by exploiting the equivalence between tests and confidence sets. This method has the advantage that it remains valid even if the regressors have roots that are not exactly equal to unity.     

Embodied Technological Change and Tests of the Internal-Adjustment-Cost Hypothesis

Standard unit-root and cointegration tests are sensitive to atypical events such as outliers and structural breaks. In this article, we use outlier-robust estimation techniques to examine the impact of these events on cointegration analysis. Our outlier-robust cointegration test provides a new diagnostic tool for signaling when standard cointegration results might be driven by a few aberrant observations. A main feature of our approach is that the proposed robust estimator can be used to compute weights for all observations, which in turn can be used to identify the approximate dates of atypical events. We evaluate our method using simulated data and a Monte Carlo experiment. We also present an empirical example showing the usefulness of the proposed analysis.     

Near-integration and deterministic trends

In this paper we seek to analyze the implications for estimation and inference within the Dickey-Fuller class of models when time series contain a root local to unity. We extend the results previously obtained in the literature to models with maintained deterministic components and especially the ability of conducting inference on the deterministic elements is focused. The approach undertaken also helps bridging the discontinuity in limiting distributions that usually apply when roots lie exactly on the unit circle, as opposed to roots strictly less than unity. The paper is completed by simulating some of the distributions suggested by the asymptotic theory to see how well these approximate the actual finite sample distributions.     

Linear rank tests for homogeneity against ordered alternatives in anova and anocova

A unified method of constructing rank tests for homogeneity against ordered alternatives in unbalanced analysis of variance and analysis of covariance is considered. The relationship between these tests with some of the existing methods are studied. The normal theory likelihood ratio tests are also derived and the asymptotic relative efficiency comparisons, in Pitman sense, of the rank tests with respect to the likelihood ratio tests are carried out.     

Likelihood Ratio Tests for Interval Hypotheses with Applications

In this article, we derive the likelihood ratio tests (LRTs) for simultaneously testing interval hypotheses for normal means with known and unknown variances, and also with unknown but equal variance. Special cases when the interval hypotheses boil down to a point hypothesis are also discussed. Remarks regarding comparison of the LRT with tests based on combination of p-values are made, and several applications based on real data are mentioned.     

An Approximation for the Test of the Equality of the Smallest Eigenvalues of a Covariance Matrix

A limiting distribution of the likelihood ratio statistic for the test of the equality of the q smallest eigenvalues of a covariance matrix is obtained. This distribution can be used as an alternative to the chi-squared distribution which is usually used with this test. It is shown that this new method yields reasonable significance levels for those situations in which the chi-squared approximation is inadequate.     

Retrospective Parametric Tests for Homogeneity of Data

The problem considered in this study is that of detecting a change in the unknown parameters of known distribution on the basis of a finite sequence of independent observations, assuming that if a change in the parameters of a distribution has occurred then it is unique. We examine various methods that have been suggested for this problem and suggest a uniform approach, based on likelihood ratio analysis. For tests derived this way we present approximations for levels of significance based on asymptotic analyses. The suggested tests meet the needs of specific problems (such as a one-sided alternative), for which general parametric case solutions have not been suggested explicitly before. We also find that rate of convergence of our asymptotics is fast, and provide accurate results for a level of significance of the suggested tests for sample sizes commonly observed in practice.     

A simple algorithm for the adaptation of scores and power behavior of the corresponding rank test

The purpose of this paper is twofold:On one hand we want to give a very simple algorithm for evaluating a special rank estimator of the type given in Behnen, Neuhaus, and Ruymgaart (1983) for the approximate optimal choice of the scores-generating function of a two-sample linear rank test for the general testing problem H_o:F=G versus H₁:F ≤ G, F ≠ G, in order to demonstrate that the corresponding adaptive rank statistic is simple enough for practical applications. On the other hand we prove the asymptotic normality of the adaptive rank statistic under H (leading to approximate critical values) and demonstrate the adaptive behavior of the corresponding rank test by a Monte Carlo power simulation for sample sizes as low as m=10, n=10.     

Confidence intervals based on the deviance statistic for the hyperparameters in state space models

The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.     

Some linear and nonlinear rank tests for competing risks models

Using the methods of asymptotic decision theory asymptotically optimal for translation and scale families as well as for certian nonparmetric families. Moreover, two new classes of nonlinear rank tests are introduced. These tests are designed for detecting either “ omnibus alternatives ” or “ one sided alternatives of trend ”. Under the null hypothesis of randomness all tests are distribution - free. The asymptotic distributions of the test statistics are derived under contiguous alternatives.     

Tests for the umbrella alternative under normality

Consider a one-way layout of the analysis of variance assuming independence, normality, and homogeneity of variance. Test the null hypothesis H_o that the means, j., of each of Amp; columns, i = 1,…, k are equal versus the alternative that they follow an umbrella pattern. That is, the alternative is H₁-H₀ where H₁: μ₁> μ₂>… > μk, and m is known. We derive a class of tests which are unbiased and lie in a nontrivial complete class. We recommend specific tests within the class. A simulation of the power functions of some tests is contrasted with the simulated power function of the likelihood ratio test.     

Robust cointegration testing in the presence of weak trends,with an application to the human origin of global warming

Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009 Demetrescu, M., Lütkepohl, H., Saikkonen, P. (2009). Testing for the cointegrating rank of a vector autoregressive process with an uncertain deterministic trend term. Econometrics Journal 12:414–35.[Crossref], [Web of Science ®] , [Google Scholar]) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be always detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality.     

Sample Tests for Detection of Size-Biased Sampling Mechanism

The aim of this article is to present a new test for the detection of size-bias in a sample with or without censored observations. The test is simple in the form and demands only the knowledge of consistent estimators of any nuisance parameters appeared in the model. With the use of simulated samples from the Weibull distribution, we show the advantages of the new test compared to the Likelihood Ratio and the Wald test.     

End-Point Estimation for Decreasing Densities: Asymptotic Behaviour of the Penalized Likelihood Ratio

Abstract.  We consider the problem of estimating the modal value of a decreasing density on the positive real line. This has application in several interesting phenomena arising, for example, in renewal theory, and in biased and distance samplings. We use a penalized likelihood ratio-based approach for inference and derive the scale-free universal large sample null distribution of the log-likelihood ratio, using a suitably chosen penalty parameter. We present simulation results and a real data analysis to corroborate our findings, and compare the performance of the confidence sets with the existing results.     

Familles of confidence bands for the survival function under the general random censorship model and the Koziol-Green model

Familles of asymptotic 100(1 – α)% level confidence bands for the survival function under the general random right-censorship (GRC) model and the proportional-hazards model of random right-censorship, also known as the Koziol-Green (KG) model, are developed. The family of bands under the GRC model is based on the well-known product-limit estimator (PLE), and this family is rich in that it contains as special cases the bands of Hall and Wellner (1980) and Gillespie and Fisher (1979), and more generally, the GF-type and HW-type bands of Csörg? and Horváth (1986), as well as new bands not previously studied. The familles of bands under the KG model are based on the maximum-likelihood estimator of F under this particular model. We compare the PLE-based bands and the MLE-based bands under the KG model. This enables us to study the loss in efficiency of the former bands when used in a setting where they are not optimal. The notion of asymptotic relative width efficiency (ARWE), defined to be the limiting ratio of the sample sizes needed by the bands to achieve the same asymptotic widths, is employed to compare two bands. Through this efficiency measure it is shown that if the censoring parameter β is known, then the PLE-based bands are highly inefficient relative to the MLE-based bands when β is large. When β is not known, the MLE-based bands are asymptotically conservative. Despite their conservatism, they still dominate the PLE-based bands when β is not too small or equivalently when the degree of censoring is not too light. We also compare the various PLE-based bands under the GRC model. The resulting information is valuable for evaluating competing PLE-based bands. We illustrate the confidence bands by utilizing the well-known Channing House data.     

Tests for Equality of Inflation Parameters of Two Zero-Inflated Power Series Distributions

In this article, we consider two independent zero-inflated power series distributions and provide likelihood ratio test for equality of inflation parameters of the same. As an illustration, testing equality of inflation parameters of two zero inflated Poisson distributions is provided. Further, simulation study to investigate power of likelihood ratio tests has been carried out.     

The power of the modified Wilcoxon rank-sum test for the one-sided alternative

When testing hypotheses in two-sample problems, the Wilcoxon rank-sum test is often used to test the location parameter, and this test has been discussed by many authors over the years. One modification of the Wilcoxon rank-sum test was proposed by Tamura [On a modification of certain rank tests. Ann Math Stat. 1963;34:1101–1103]. Deriving the exact critical value of the statistic is difficult when the sample sizes are increased. The normal approximation, the Edgeworth expansion, the saddlepoint approximation, and the permutation test were used to evaluate the upper tail probability for the modified Wilcoxon rank-sum test given finite sample sizes. The accuracy of various approximations to the probability of the modified Wilcoxon statistic was investigated. Simulations were used to investigate the power of the modified Wilcoxon rank-sum test for the one-sided alternative with various population distributions for small sample sizes. The method was illustrated by the analysis of real data.     

Tests for the equality of multinomial parameters

In this paper we face the problem of testing the equality of two or more parameters of a multinomial distribution. We develop a likelihood ratio test and we consider an asymptotically equivalent Pearson's statistic. Moreover we develop an exact and a randomized test. Relationships between these tests are then discussed. The behaviour of these tests is studied by simulations. Results from two known tests developed for less general situations are compared to ours.