Power Of Likelihood Ratio Test Research Articles

A two-way flexible generalized gamma transformation cure rate model.

We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.

Directional monitoring and diagnosis for covariance matrices

Statistical surveillance for covariance matrices has attracted increasing attention recently. Many approaches have been developed for monitoring general shifts that are arbitrary deviations, as well as sparse shifts occurring in only a few elements. This paper considers directional shifts that occur in only one independent parameter, which is common if the process is relatively stable. A directional covariance matrix control chart is proposed, which fully exploits directional shift information and borrows the strong power of likelihood ratio test. Therefore, this chart provides a powerful tool for monitoring covariance matrices. In addition, the proposed chart does not require specifying the regularisation parameter, and it enjoys a concise quadratic form, thereby easy to implement. Furthermore, this chart naturally leads to a diagnostic prescription for identifying the shifting element in the covariance matrix. Simulation results have demonstrated the efficiency of the suggested control chart and its accompanying diagnostic scheme.

Asymptotic power of likelihood ratio tests for high dimensional data

Abstract This paper studies the asymptotic power of the likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n . The asymptotic distribution under local alternatives is derived and a simulation study is carried out to compare LRT with other tests. All these studies show that LRT is a powerful test to detect small eigenvalues.

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.

Detecting Two-Locus Gene-Gene Effects Using Monotonisation of the Penetrance Matrix

As more genetic loci are genotyped simultaneously and as the interest in effects of combinations of loci increases, the need for more powerful analysis methods is increased. In the present paper we present a method aimed at increasing the power of likelihood ratio tests for case-control studies investigating possible two-locus effects. The method is based on the notion that the expected effect pattern of one locus, as well as the expected pattern of a penetrance matrix representing the effect of two loci, is a monotone one. By using an algorithm for making the estimated penetrance matrix monotone, the alternative hypothesis is restricted to monotone penetrance matrices only. The evaluation of the likelihood ratio tests for several underlying monotone models shows that the power is substantially increased by using a monotone alternative as compared to when an unrestricted alternative is used.

An Extension of a Convolution Inequality forG-Monotone Functions and an Approach to Bartholomew's Conjectures

A variety of convolution inequalities have been obtained since Anderson's theorem. ?In this paper, we extend a convolution theorem for G -monotone functions by weakening the symmetry condition of G -monotone functions. Our inequalities are described in terms of several orderings obtained from a cone. It is noteworthy that the orderings detect differences in directions. A special case of the orderings induces a majorization-like relation on spheres. Applying our inequality, Bartholomew's conjectures, which concern directions yielding the maximum power and the minimum power of likelihood ratio tests for order-restricted alternatives, are partly settled.

Power of Likelihood Ratio Tests for Heterogeneity of Intraclass Correlation and Variance in Balanced Half-Sib Designs

Statistical power of likelihood ratio tests was investigated for detection of heterogeneous variances and intraclass correlation in balanced half-sib designs. Powers of likelihood ratio tests were obtained from simulations. For half-sib designs of sires nested within herds, true intraclass correlations and phenotypic variances, and estimates thereof, were repeatedly sampled, and likelihood ratio tests were conducted. The power for detecting heterogeneity of intraclass correlations was low, but the power for detecting heterogeneous phenotypic variances was nearly always 100%. For balanced cross-classified designs, sires had progeny in all herds, and data were simulated by assuming that heterogeneity of between- and within-sire components was the result of a herd-dependent scale effect. Using this model, the power to detect heterogeneous between-sire components was substantially higher than the corresponding power to detect heterogeneous intraclass correlations in the nested design. It seems unlikely that reliable inference about heterogeneity of genetic variances or heritabilities between individual herds from daily cattle field data can be made.

Optimal Input Design for Autoregressive Model Discrimination with Output Amplitude Constraints

The optimal input design problem is considered for discriminating two autoregressive models when the amplitude of the system output has to be regulated within a certain tolerance limit with high probability. This constraint is more meaningful than power constraint in case where extremely large system output may cause troubles in the system. Methods are presented to construct a Ds-optimal input which maximizes the power of likelihood ratio test discriminating the models. It is exemplified by digital simulation studies the applicability of the proposed Ds-optimal input for discrimination of autoregressive models.

Bounds for the Power of Likelihood Ratio Tests and Their Asymptotic Properties

Let $P_0$ and $P_1$ be two probability distributions on a measurable space $(\mathscr{H}, \mathscr{B})$. We consider the problem of testing the simple hypothesis $H: P = P_0$ against the simple alternative $K: P = P_1$ on the basis of $n$ independent random variables $X_1, X_2, \cdots, X_n$ with common distribution $P$. The method that is widely used in the literature for investigating large sample properties of optimal tests is the following: according to the Neyman-Pearson lemma an optimal test can be described by means of sums of independent random variables. Theorems from the theory of probabilities of large deviations or ergodic theorems then allow one to obtain results on the asymtotic behavior of the error probabilities of optimal tests. In this paper we use a representation of the power of an optimal test which has its origin in the duality theory of infinite linear programming, in order to derive upper and lower bounds for the power. The bounds holds for any sample size $n$. This is done in Section 1 for two different types of tests, namely for most powerful tests at leve $\alpha_n$ and for tests which minimize a weighted sum of the error probabilities. It turns out that those bounds allow one to derive the well-known asymptotic properties under slightly more general conditions, i.e., $\alpha_n$ is permitted to tend to zero faster than any negative power of $n$ (but not exponentially fast) and the weight $\lambda_n$ to tend exponentially fast to zero. This and another application are discussed in Section 2.

Power of the likelihood-ratio test of the general linear hypothesis in multivariate analysis

1-1. General background. In a basic paper on multivariate tests of linear hypotheses, Wilks (1932) applied the method of the likelihood ratio to the problem of testing the equality of mean vectors in k multivariate populations. The general approach of this early paper has been extended and expanded in the literature until, now, a procedure is available for testing multivariate linear hypotheses in a completely general form (see, for example, Anderson, 1958). For the problem of computing the power of these tests, however, no such general procedure exists. This is due to the fact that the noncentral distribution of the test criterion has not been expressed in a numerically feasible form. A first step towards the derivation of the non-central distribution, however, was taken when Anderson & Girshick (1944) attacked the problem of finding the distribution of the Wishart matrix in the non-central case. The result led Anderson (1946) to the derivation of the moments of the criterion for testing the hypothesis of the general multivariate regression problem (or rather the equivalent Wilks-Lawley hypothesis). Anderson's results were valid for a certain class of alternatives, which he called linear and planar. The moments for the linear alternative involve an infinite sum of expressions containing gamma functions and for the planar alternative, involve a triple infinite sum of the same type of expressions. This appears to be the extent of the progress on the problem of obtaining the power of the multivariate likelihood-ratio test of the general linear hypothesis.t