Likelihood Ratio Test For Hypothesis Research Articles

System Identification of Feedback and "Causality" Structure Using Canonical Variate Analysis

This paper addresses the problem of identification of components of a system that may involve unknown feedback around such a component as well as the presence of unmeasured disturbances. Further, the problem of comparing various hypotheses concerning the feedback structure among various components of an unknown system is discussed. The basic tool developed is an expression for the joint likelihood function of a process in terms of individual components of a system where measurements of the inputs and outputs of each component are available. It is show that maximum likelihood estimation of the whole structure decomposes into the separate maximum likelihood estimation of each component. This provides the basis for likelihood ratio tests of hypotheses for different feedback structures of the system. Canonical variate analysis provides a computationally stable procedure for the identification of state space models of the various component systems. These can then be combined to find the best system structure describing feedback and Granger causality.

Likelihood Ratio-Based Confidence Intervals in Survival Analysis

Abstract Confidence intervals for the survival function and the cumulative hazard function are considered. These confidence intervals are based on an inversion of the likelihood ratio statistic. To do this, two extensions of the likelihood, each of which yields meaningful likelihood ratio hypothesis tests and subsequent confidence intervals, are considered. The choice of the best extension is difficult. In the failure time setting, the binomial extension is best in constructing confidence intervals concerning the survival function and the Poisson extension is best in constructing confidence intervals concerning the cumulative hazard. Simulations indicate that these two methods perform as well as or better than competitors based on the asymptotic normality of the estimator.

Efficiency of observation schemes for proportional hazard regression models with censoring

Proportional hazard regression models are considered. The scheme of observation in which observed and censored survival times are available for analysis is compared with the simpler binary scheme in which it is only known whether or not individuals survived the censoring times. A bound on the expected information matrix for the second scheme is given in terms of the information matrix for the first scheme. When the censoring variables are of degenerate type giving fixed censoring times, it is shown that the loss of efficiency from using the binary scheme of observation will be unimportant provided that there is at least a moderate degree of censoring. Power comparisons for likelihood ratio tests of hypotheses for the regression coefficients in an exponential regression model with a logarithmic link for the failure rate function are made for the two schemes of observation.

Nonrandom sampling in genetic epidemiology: an implementation of the Hanis-Chakraborty method for multifactorial analysis.

The method of Hanis and Chakraborty: [Statistics in Medicine 6:629-646, 1987] is known to yield unbiased estimates of familial correlations from family data ascertained according to just about any method of nonrandom sampling. For multifactorial analysis of such family data, the method is implemented here so as to provide a unique solution, handle variable sibship sizes, and provide likelihood ratio tests of hypotheses. Simulation results are presented to illustrate the utility of the proposed implementation.

Evaluation of path analysis through computer simulation: effect of incorrectly assuming independent distribution of familial correlations.

Path analysis of family data has been widely applied to resolve genetic and environmental patterns of familial resemblance. A prevalent statistical approach in path analysis has been, first, to estimate the familial correlations and, second, by assuming these estimates to be independently distributed, define a likelihood function from which maximum likelihood estimates of model parameters can be obtained and likelihood ratio tests of hypotheses performed. Although it is generally known that the independence assumption does not hold when multiple familial correlations are estimated from the same family data, this statistical method has still been used in these situations owing, in part, to the lack of any viable alternatives and, in part, to the lack of any knowledge about the specific quantitative effects of not meeting the assumption of independence. Here, using computer-simulation methods, we evaluate the robustness of this statistical method to deviations from the assumption of independence. In general, we found that the failure to meet the assumption of independence leads to a conservative test of the goodness-of-fit of the path model, although likelihood ratio tests of specific null hypotheses were at times liberal, at times conservative, and at times nearly exact. Although the test statistics were found to be distorted, the parameter estimates using this method were nearly unbiased.

Resolution of linkage for irregular phenotype systems.

A method is given to resolve pleiotropy from linkage; to detect and estimate recombination free of incomplete penetrance, etiological heterogeneity, and other phenomena; and to estimate gametic frequencies for the main and test loci jointly. Large pedigrees, a liability indicator specifying risk groups (based on age, sex, or other factors), gametic disequilibrium, different recombination values in the two sexes, multiple alleles at the test locus, and a mixture of linked and unlinked marker loci are provided for. Parametrization of the marker locus is the same as for segregation analysis with pointers. The output includes standard errors, likelihood ratio tests of hypotheses, and a standard lod table for each sex separately. A model of closely linked complementing factors which can simulate recombination is also considered.

Likelihood ratio tests of hypotheses: Comments on Pitz's article and some alternative procedures.

Likelihood ratio tests of hypotheses: Comments on Pitz's article and some alternative procedures.

Likelihood ratio tests of hypotheses: Comments on Pitz's article and some alternative procedures.

Likelihood ratio tests of hypotheses: Comments on Pitz's article and some alternative procedures.

Maximum likelihood estimation in multidimensional scaling

A variety of distributional assumptions for dissimilarity judgments are considered, with the lognormal distribution being favored for most situations. An implicit equation is discussed for the maximum likelihood estimation of the configuration with or without individual weighting of dimensions. A technique for solving this equation is described and a number of examples offered to indicate its performance in practice. The estimation of a power transformation of dissimilarity is also considered. A number of likelihood ratio hypothesis tests are discussed and a small Monte Carlo experiment described to illustrate the behavior of the test of dimensionality in small samples.

Improved likelihood ratio tests for complete contingency tables

SUMMARY Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the -2 log A test statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic x2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators. An asymptotic likelihood ratio test of a composite null hypothesis against a composite alternative can in general be obtained by comparing -2 log A with a x2 distribution, where A is the ratio of maximized likelihoods under the two hypotheses. Lawley (1956) showed that such tests can be improved by multiplying -2 log A by a scale factor chosen so that the null distribution of the resulting statistic has the same moments as X2 ignoring quantities of order n-2, where n is the size of the sample. When the statistic - 2 log A can be expressed as an explicit function of the observations the multiplier is most easily found by calculating directly its expectation as far as terms of order n-1. These improved likelihood ratio tests have been most used in the area of multivariate analysis. In recent years considerable progress has been made in developing methods for analyzing multidimensional contingency tables using log linear models. A comprehensive review is given by Plackett (1 974). In these models the cell frequencies may be regarded as independent Poisson variables whose log expectations are linear in a hierarchical set of main effect and interaction parameters. The -2 log A statistic for testing the goodness of fit of a given model takes the form S = 2EX log (X/u), where the X are the cell frequencies and the ,u are the maximum likelihood estimators of their expectations. In practice X log (X/,u) can be replaced by zero when X = 0. Following Nelder & Wedderburn (1972), S will be termed the deviance of the model. To test a given model with deviance S1 against an alternative with additional estimated parameters and deviance S2, the likelihood ratio test statistic iS S1-S2

Corrections to Likelihood Ratio Tests of Hypotheses Concerning the Parameters of Markov Chains

Corrections to Likelihood Ratio Tests of Hypotheses Concerning the Parameters of Markov Chains

Corrections to likelihood ratio tests of hypotheses concerning the parameters of Markov chains

Multiplying factors are presented which substantially increase the rate at which the likelihood ratio test statistic converges to its limiting chi-squared distribution as the number of observations increases. The corrections apply to the following hypotheses about Markov chain sequences: that the transition probabilities are stationary over time; that the chain is of a given order; and that several samples come from the same chain. Some technical features of the corrections are discussed and their applicability via computer programs is mentioned.

Asymtotic confidence regions and likelihood ratio tests of hypothesis for location and scale parameters based on type II censored samples

Asymtotically smallest confidence regions and asymptotically consistent likelihood ratio tests for(1) the location or scale parameter when the other is known, and(ii) both location and scale parameters, of a population based on Type II censored samples are considered.

Applications of space-time decision and estimation theory to antenna processing system design

A mathematical solution to the problem of optimum radar target detection and parameter estimation in receiver noise and heavy clutter has been achieved by means of space-time decision theory. The theory leads to a conceptual design for an antenna processing system that is optimum in the sense that it makes least risk parameter estimates and least probability of error decisions. The system can be instrumented by separately demodulating the individual radiator outputs and feeding them simultaneously and in parallel to a digital computer, Hypothesis testing problems such as target detection are formulated by means of a generalized likelihood ratio test. Optimum mean-square estimation is carried out by instrumenting the mean of the parameter in question conditioned on the observed signal. With the aid of a priori statistics available or assumed, the a posteriori likelihood function is derived. From this function, the required generalized likelihood ratio hypothesis tests and parameter estimators are synthesized. Specific illustrations include systems for detection and angular location estimation for one or two targets in a clutter environment. Optimum tests as well as optimum and suboptimum estimators are realized as flow diagrams for computation by the special-purpose digital processor.