The germination percentage (GP) is commonly employed to estimate the viability of a seed population. Statistical methods such as analysis of variance (ANOVA) and logistic regression are frequently used to analyse GP data. While ANOVA has a long history of usage, logistic regression is considered more suitable for GP data due to its binomial nature. However, both methods have inherent issues that require attention. In this study, we address previously unexplored challenges associated with these methods and propose the utilization of a likelihood ratio test as a solution. We demonstrate the advantages of employing the likelihood ratio test for GP data analysis through simulations and real data analysis.

Crop scientists occasionally compute sample correlations between traits based on observed data from designed experiments, and this is often accompanied by significance tests of the null hypothesis that traits are uncorrelated. This simple approach does not account for effects due to the randomization layout and treatment structure of the experiments and hence statistical inference based on standard procedures is not appropriate. The present paper describes how valid inferences accounting for all relevant effects can be obtained using bivariate mixed linear model procedures. A salient feature of the approach is that the bivariate model is commensurate with the model used for univariate analysis of individual traits and allows bivariate correlations to be computed at the level of effects. Heterogeneity of correlations between effects can be assessed by likelihood ratio tests or by graphical inspection of bivariate scatter plots of effect estimates. if heterogeneity is found to be substantial, it is crucial to focus on the correlation of effects, and usually, the main interest will be in the treatment effects. If heterogeneity is judged to be negligible, the marginal correlation can be estimated from the bivariate model for an overall assessment of association. The proposed methods are illustrated using four examples. Hints are given to alternative routes of analysis accounting for all treatment and design effects such as regression with groups and analysis of covariance.

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is a k parameter. k is a nonspatial aggregation parameter related to the variance at a given mean value. The k parameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of the k parameter across field sites was assessed using the likelihood ratio test There was no stable or common k value across field sites and years for all weed species populations. The lack of stability in k across field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Because k is not stable across field sites, k must be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

A few studies have examined the association between vitamin D and telomere length, and fewer still have examined the relationship in black or male populations. We investigated the cross-sectional association between the vitamin D metabolite 25-hydroxyvitamin D (25(OH)D) concentration in plasma and relative leucocyte telomere length (LTL) in 1154 US radiologic technologists who were 48–93 years old (373 white females, 278 white males, 338 black females, 165 black males). Plasma 25(OH)D concentration was measured by the chemiluminescence immunoassay, and relative LTL was measured by quantitative PCR. Logistic regression was used to obtain OR and 95 % CI for long v. short (based on median) LTL in relation to continuous 25(OH)D, quartiles of 25(OH)D and 25(OH)D deficiency. We found no significant association between continuous 25(OH)D and long LTL in all participants (Ptrend=0·440), nor in white females (Ptrend=0·845), white males (Ptrend=0·636), black females (Ptrend=0·967) or black males (Ptrend=0·484). Vitamin D deficiency (defined as 25(OH)D<30 nmol/l), however, was significantly associated with short LTL in whites (P=0·024), but not in other groups. In this population, we found little evidence to support associations between 25(OH)D and long LTL over the entire range of 25(OH)D in the overall study population or by sex and race.

The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent regime switches). In this framework, we give sufficient conditions to keep the LRTS tight and compute its the asymptotic distribution. Second, we consider the extension of the ideas in Gassiat [Ann. Inst. Henri Poincaré 38 (2002) 897–906] to autoregressive models with regimes switches according to a Markov chain. In this case, it is shown that the marginal likelihood is no longer a contrast function and cannot be used to select the number of regimes. Some numerical examples illustrate the results and their convergence properties.

This paper deals with the likelihood ratio test (LRT) for testing hypotheseson the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRTstatisticsunder some conditions that are proved to be almost necessary.A detailed solution is given for two testing problems: thetest of a single distribution against any mixture, with application to Gaussian, Poisson andbinomial distributions; the test of the number of populations in afinite mixture with or without structural parameter.

We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime.We prove that the LRT statistic converges to infinity in probability as the number of observations tends to infinity. This is a consequence of a convergence result of the LRT statistic for a subproblem where the parameters are restricted to a subset of the whole parameter set.

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection.

Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator and of the likelihood ratio statistic λn are examined when the model chosen for their construction is incorrect—that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if and λn are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λn is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on λn when the statistic is constructed from an incorrect model.

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.