This paper is concerned with the null distribution of the likelihood ratio statistic for testing the equality of variances of q nonnormal populations. It is known that the null distribution of this statistic converges to w q 1 under normality. We extend this result by obtaining an asymptotic expansion under general conditions. Numerical accuracies are studied for some approximations of the perc...

Olson's conditional-logistic model retains the nice property of the LOD score formulation and has advantages over other methods that make it an appropriate choice for complex trait linkage mapping. However, the asymptotic distribution of the conditional-logistic likelihood-ratio (CL-LR) statistic with genetic constraints on the model parameters is unknown for some analysis models, even in the c...

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution ...

Consider likelihood ratio test of a simple null hypothesis in a multiparameter exponential family. We study the asymptotic expansion of the null distribution of log likelihood ratio statistic to an arbitrary order. Bartlett correctability of the O(n ) term is well known. We show that higher order terms exhibit a similar simplicity. Moreover we give a combinatorially explicit expression for all ...

We consider the comparison of mean vectors for k groups when k is large and sample size per group is fixed. The asymptotic null and non-null distributions of the normal theory Likelihood Ratio, Lawley-Hotelling and Bartlett-Nanda-Pillai statistics are derived under general conditions. We extend the results to tests on the profiles of the mean vectors, tests for additional information (provided ...

This paper considers the construction of prediction intervals for future observations in high dimensional regression models. We propose a new approach to evaluate the uncertainty for estimating the mean parameter based on the widely-used penalization/regularization methods. The proposed method is then applied to construct prediction intervals for sparse linear models as well as sparse additive ...

ii c 2013 Yi Liu ALL RIGHTS RESERVED iii ABSTRACT YI LIU. Generalized Quasi-Likelihood Ratio Statistics for Multivariate Time-varying Coefficient Regression Models. (Under the direction of DR. JIANCHENG JIANG) Generalized likelihood ratio statistics have been a generally applicable method for testing nonparametric hypotheses about nonparametric functions.It has been widely used in many research...

Trend breaks appear to be prevalent in macroeconomic time series. Consequently, to avoid the catastrophic impact that unmodelled trend breaks have on power it is standard empirical practice to employ unit root tests which allow for such effects. A popularly applied approach is the infimum ADF-type test. Its appeal has endured with practitioners despite results which show that the infimum ADF st...

In this paper we investigate the properties of the Lagrange Multiplier LM test for autoregressive conditional heteroskedasticity ARCH and generalized ARCH GARCH in the presence of additive outliers AO s We show an alytically that both the asymptotic size and power are adversely a ected if AO s are neglected the test rejects the null hypothesis of homoskedasticity too often when it is in fact tr...

In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AO's). We show analytically that both the asymptotic size and power are adversely aaected if AO's are neglected: the test rejects the null hypothesis of homoskedasticity too often when it is i...