Criterion For Testing Hypotheses Research Articles

Species Paraphyly and Social Parasitism: Phylogenomics, Morphology, and Geography Clarify the Evolution of thePseudomyrmex elongatulusGroup (Hymenoptera: Formicidae), a Mesoamerican Ant Clade

AbstractUsing genetic, morphological, and geographical evidence, we investigate the species-level taxonomy and evolutionary history of the Pseudomyrmex elongatulus group, a clade of ants distributed from southwestern United States to Costa Rica. Through targeted enrichment of 2,524 UCE (ultraconserved element) loci we generate a phylogenomic data set and clarify the phylogenetic relationships and biogeographic history of these ants. The crown group is estimated to have originated ~8 Ma, in Mexico and/or northern Central America, and subsequently expanded into southern Central America and the southwestern Nearctic. The P. elongatulus group contains a mix of low- and high-elevation species, and there were apparently multiple transitions between these habitat types. We uncover three examples of one species—of restricted or marginal geographical distribution—being embedded phylogenetically in another species, rendering the latter paraphyletic. One of these cases involves an apparent workerless social parasite that occurs sympatrically with its parent species, with the latter serving as host. This suggests a sympatric origin of the parasite species within the distribution range of its host. Species boundaries are tested using three molecular delimitation approaches (SODA, bPTP, BPP) but these methods generate inflated species estimates (26–46 species), evidently because of a failure to distinguish population structure from species differences. In a formal taxonomic revision of the P. elongatulus group, based on almost 3,000 specimens from ~625 localities, we allow for geographic variation within species and we employ distinctness-in-sympatry criteria for testing hypotheses about species limits. Under these guidelines we recognize 13 species, of which nine are new: P. arcanus, sp. nov. (western Mexico); P. capillatus, sp. nov. (western Mexico); P. cognatus, sp. nov. (Chiapas, Mexico to Nicaragua); P. comitator, sp. nov. (Chiapas, Mexico); P. ereptor, sp. nov. (Veracruz, Mexico); P. exoratus, sp. nov. (southeastern Mexico, Honduras); P. fasciatus, sp. nov. (Chiapas, Mexico to Costa Rica); P. nimbus, sp. nov. (Costa Rica); and P. veracruzensis, sp. nov. (Veracruz, Mexico). Our study highlights the value of combining phylogenomic, phenotypic, and geographical data to resolve taxonomic and evolutionary questions.

A new criterion for testing hypothesis about the covariance function of the homogeneous and isotropic random field

In this paper, we consider a continuous in mean square homogeneous and isotropic Gaussian random field. A criterion for testing hypotheses about the covariance function of such field using estimates for its norm in the space $L_p(\mathbb{T}), p\geq 1$ is constructed.

A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.

A criterion for testing hypotheses about the covariance function of a Gaussian stationary process

A criterion for testing hypotheses about the covariance function of a Gaussian stationary process

Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches.

Preface 1. Approaches to testing the hypothesis of adequate specification 2. Inequalities between criteria for testing hypotheses in linear regression models 3. The Lagrange multiplier test and testing for misspecification: an extended analysis 4. Tests for misspecification of regression equations 5. Tests for misspecification of simultaneous equation models 6. Tests for qualitative and limited dependent variable models Bibliography Index.

Some properties of beta functions and the distribution for the product of independent beta random variables

Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this article we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration, the exact null density of Wilks’A for testing linear hypothesis in the real Gaussian case is derived. Furthermore, it will be shown that this method is applicable also to problems of a more general nature.

Statistical inference for Markov processes when the model is incorrect

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.

Statistical inference for Markov processes when the model is incorrect

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 λ n 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 λ n are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λ n 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 λ n when the statistic is constructed from an incorrect model.

Conflict Among Criteria for Testing Hypotheses: Extensions and Comments

Conflict Among Criteria for Testing Hypotheses: Extensions and Comments

Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model

This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.

Statistically correct determination of long-period trends in geophysical data series

Linear trend analysis of geophysical time series is considered in connection with the problem of determining long-period variations (possibly of man-made origin) in the presence of short period noise of larger amplitude. Criteria for testing hypotheses about linear trends are presented for the cases of independent observations and of the observations whose correlation function is known. The possibility of increasing the precision of the results using area-averaged values is investigated. Examples are given of the long time series analysis of air temperature, carbon dioxide and water vapor content. Time series of total atmospheric ozone content at some stations are also considered, and conditions for correct statistical analysis of such data are given.

Analysis of Dispersion with Incomplete Observations on One of the Characters

Summary In analysis of dispersion (multivariate generalization of the analysis of variance) Wilks' A criterion for testing hypotheses on all the multiple characters simultaneously cannot be applied if some observations on one or more of the characters are missing. In this article is provided a suitable criterion when data become incomplete due to missing observations in one of the characters only. This is the likelihood ratio criterion with a slight modification. The exact moments of this criterion have been found and the distribution has been exhibited in an asymptotic series with the first few terms providing a powerful approximation. Using only the first term one Chi-square and two variance ratio approximations have been suggested, and the Chi-square approximation is recommended for use as the other approximations by themselves without correction terms seem to distort the probabilities.