Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by examination of the Bayesian posterior and frequentist means of this statistic. Second-order matching conditions are shown to arise from matching of the Bayesian posterior and frequentist variances of a mean-adjusted version of the signed root statistic. ...

In case-control association studies unobserved population stratification may act as a confounder, leading to an increased number of false positive results. Methods accounting for population structure by using additional genetic markers broadly follow one of two concepts: Genomic Control (GC) and Structured Association (SA). While extending existing methods of Structured Association we show that...

Owen (1988) showed that the non-parametric empirical likelihood ratio under a linear constrain has an asymptotic chi-square distribution, same as in the paramet-ric case. This fact can be used to form (non-parametric, asymptotic) conndence intervals. We suggest here to use the non-parametric version of the Pearson's chi-square statistic instead of the likelihood ratio to form conndence interval...

This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting ...

The classical distribution theory of the log likelihood ratio test statistic does not hold for testing homogeneity (i.e., no mixture) against mixture alternatives. Asymptotic theory for this problem is developed. For some special cases, asymptotically locally minimax tests are also found. It is pointed out that the main problem is lack of identifiability of the usual parameterization even when ...

Construction of precise confidence sets of disease gene locations after initial identification of linked regions can improve the efficiency of the ensuing fine mapping effort. We took the confidence set inference, a framework proposed and implemented using the Mean test statistic (CSI-Mean) and improved the efficiency substantially by using a likelihood ratio test statistic (CSI-MLS). The CSI f...

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the leastsquares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process ...