Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model

In this paper, we investigate a partially single-index varying-coefficient model, and suggest two empirical log-likelihood ratio statistics for the unknown parameters in the model. The first statistic is asymptotically distributed as a weighted sum of independent chi-square variables under some mild conditions. It is proved that another statistic, with adjustment factor, is asymptotically standard chi-square under some suitable conditions. These useful statistics could be used to construct the confidence regions of the parameters. A simulation study indicates that, with the increase of sample size, the coverage probability of the confidence region constructed by us gradually approaches the theoretical value.

PERFORMANCE ANALYSIS AND ROBUSTNESS EVALUATION OF A SEQUENTIAL PROBABILITY RATIO TEST FOR NON-IDENTICALLY DISTRIBUTED OBSERVATIONS

In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.

Tests of exponentiality against some parametric over/under-dispersed life time models

We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (S1, L1), (S2, L2), and (S3, L3) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics S3 and L3 have best overall performance, in terms of both, level and power. However, the statistic L3 can be liberal in some instances and it needs the maximum likelihood estimates of the parameters of the Weibull distribution as opposed to the statistic S3 which is very simple to use. So, our recommendation is to use the statistic S3 to test the fit of an exponential distribution over any over/under-dispersed exponential distribution.

ASYMMETRIES IN BUSINESS CYCLES AND THE ROLE OF OIL PRICES

We estimate asymmetries in innovations to Solow residuals for 11 Organization for Economic Co-operation and Development (OECD) countries using stochastic frontier analysis. Likelihood ratio statistics and variance ratios imply that all countries with net energy imports have significant negative asymmetries, whereas other countries do not. We construct a simple theoretical model in which the measured Solow residual combines effects from technology, factor utilization, and the terms of trade. For oil importers, the model implies an asymmetric response of measured total factor productivity to oil price increases and decreases. When we condition Solow residuals separately on positive and negative oil price changes to allow asymmetric responses, evidence for remaining negative asymmetric innovations to the Solow residuals vanishes for all countries except Switzerland. Switzerland's relatively dominant financial sector suggests that their asymmetries could be due to a financial crisis, a hypothesis that we test and fail to reject.

Near-Exact Distributions for Likelihood Ratio Statistics Used in the Simultaneous Test of Conditions on Mean Vectors and Patterns of Covariance Matrices

The authors address likelihood ratio statistics used to test simultaneously conditions on mean vectors and patterns on covariance matrices. Tests for conditions on mean vectors, assuming or not a given structure for the covariance matrix, are quite common, since they may be easily implemented. But, on the other hand, the practical use of simultaneous tests for conditions on the mean vectors and a given pattern for the covariance matrix is usually hindered by the nonmanageability of the expressions for their exact distribution functions. The authors show the importance of being able to adequately factorize the c.f. of the logarithm of likelihood ratio statistics in order to obtain sharp and highly manageable near-exact distributions, or even the exact distribution in a highly manageable form. The tests considered are the simultaneous tests of equality or nullity of means and circularity, compound symmetry, or sphericity of the covariance matrix. Numerical studies show the high accuracy of the near-exact distributions and their adequacy for cases with very small samples and/or large number of variables. The exact and near-exact quantiles computed show how the common chi-square asymptotic approximation is highly inadequate for situations with small samples or large number of variables.