Identification of local clusters for count data: a model-based Moran's I test

We set out I_DR as a loglinear-model-based Moran's I test for Poisson count data that resembles the Moran's I residual test for Gaussian data. We evaluate its type I and type II error probabilities via simulations, and demonstrate its utility via a case study. When population sizes are heterogeneous, I_DR is effective in detecting local clusters by local association terms with an acceptable type I error probability. When used in conjunction with local spatial association terms in loglinear models, I_DR can also indicate the existence of first-order global cluster that can hardly be removed by local spatial association terms. In this situation, I_DR should not be directly applied for local cluster detection. In the case study of St. Louis homicides, we bridge loglinear model methods for parameter estimation to exploratory data analysis, so that a uniform association term can be defined with spatially varied contributions among spatial neighbors. The method makes use of exploratory tools such as Moran's I scatter plots and residual plots to evaluate the magnitude of deviance residuals, and it is effective to model the shape, the elevation and the magnitude of a local cluster in the model-based test.     

Testing for lack of dependence in the functional linear model

The authors consider the linear model Y_n = ψX_n + ?_n relating a functional response with explanatory variables. They propose a simple test of the nullity of ψ based on the principal component decomposition. The limiting distribution of their test statistic is chi‐squared, but this distribution is also an excellent approximation in finite samples. The authors illustrate their method using data from terrestrial magnetic observatories.     

Inference for the common mean of several Birnbaum–Saunders populations

The Birnbaum–Saunders distribution is a widely used distribution in reliability applications to model failure times. For several samples from possible different Birnbaum–Saunders distributions, if their means can be considered as the same, it is of importance to make inference for the common mean. This paper presents procedures for interval estimation and hypothesis testing for the common mean of several Birnbaum–Saunders populations. The proposed approaches are hybrids between the generalized inference method and the large sample theory. Some simulation results are conducted to present the performance of the proposed approaches. The simulation results indicate that our proposed approaches perform well. Finally, the proposed approaches are applied to analyze a real example on the fatigue life of 6061-T6 aluminum coupons for illustration.     

A signed rank test for censored paired lifetimes

A locally most powerful signed rank test is proposed for the comparison of two independent lifetimes under the accelerated failure time model.

The test is based on N independent pairs(X_i, Y_i), i = 1, …, N: it is supposed that the shortest lifetime in each pair is observed and the experiment is stopped after r(r≤N and fixed) such lifetimes are available (type II censoring).

Actual scores of the test statistic are computed for some specific source distributions of the observations. The asymptotic distribution of the test statistic, as well as the asymptotic power and efficiency are given. The values of these efficiencies are computed for the case where the X_i follow and exponential, Weibull Gamma or Rayleigh distribution.     

Inference based on conditional speclfication

The first bibliography in the area of inference based on conditional specification was published in 1977, A second bibliography is compiled, and a combined subject index is given.     

Testing equality of conditionally jfclhwdqw exponential distributions

For the models given V = v (a common random stress), X and Y are independently exponentially distributed with failure rates λ₁and λ₂v, testing H₀λ₁λ₂using a random ‘paired’ sample is considered. It is shown that a uniformly most powerful invariant test does not exist even for one sided alternatives; locally most powerful invariant tests are derived and compared with existing procedures. The method is illustrated with reliability data. Finally, the robustness of the tests when the relationships of the failure rates to V is more complex are established.     

Sequential analysis applied to testing the scale parameter in the problem of the nile

The parameter O in the problem of the Nile is tested using the Sequential Probability Ratio Test (SPRT). It is observed that the test can be used to discriminate between two one–sided hypotheses.     

A General formula for the upper tail significance levels of empirical distribution function test statistics

In this paper ve obtain an asymptotic expression for the upper tail area of the distribution of an infinite weighted sum of chi-square random variables and show how this can be applied to distributions of various goodness of fit test statistics. Results obtained by this general approach are comparable with those reported previously in the literature. In the case of the Cramer-von Mises statistic an empirical adjustment is given vhich significantly improves on previous approximations. For the Kuiper statistic the corresponding empirical adjustment leads to an existing highly accurate approximation.     

Testing for a separation between two normal distributions

Three tests are proposed for testing for a specified degree of overlap between two normal distributions, The hypotheses considered are an extension of the Behrens-Fisher problem, A simulation study of the performance of the tests is presented.