Residual Renyi entropy of k-record values

ABSTRACT

In this article, the residual Renyi entropy (RRE) of k-record values arising from an absolutely continuous distribution is considered. A representation of RRE of k-records arising from an arbitrary distribution in terms of RRE of k-record values arising from uniform distribution is given. Some properties for RRE of k-records are also discussed.     

Semiparametric median residual life model and inference

For randomly censored data, the authors propose a general class of semiparametric median residual life models. They incorporate covariates in a generalized linear form while leaving the baseline median residual life function completely unspecified. Despite the non‐identifiability of the survival function for a given median residual life function, a simple and natural procedure is proposed to estimate the regression parameters and the baseline median residual life function. The authors derive the asymptotic properties for the estimators, and demonstrate the numerical performance of the proposed method through simulation studies. The median residual life model can be easily generalized to model other quantiles, and the estimation method can also be applied to the mean residual life model. The Canadian Journal of Statistics 38: 665–679; 2010 © 2010 Statistical Society of Canada     

Exact moments of the symmetric cubic assignment statistic

Hubert (1987Assignment Methods in Combinatorial Data Analysis) presented a class of permutation, or random assignment, techniques for assessing correspondence between general k-dimensional proximity measures on a set of “objects.” A major problem in higher-order assignment models is the prohibitive level of computation that is required. We present the first three exact moments of a test statistic for the symmetric cubic assignment model. Efficient computational formulas for the first three moments have been derived, thereby permitting approximation of the permutation distribution using well-known methods.     

Some aspects of probability forecasting

The problems of assessing, comparing and combining probability forecasts for a binary events sequence are considered. A Gaussian threshold model (analytically of closed form) is introduced which allows generation of different probability forecast sequences valid for the same events. Chi - squared type test statistics, and also a marginal-conditional method are proposed for the assessment problem, and an asymptotic normality result is given. A graphical method is developed for the comparison problem, based upon decomposing arbitrary proper scoring rules into certain elementary scoring functions. The special role of the logarithmic scoring rule is examined in the context of Neyman - Pearson theory.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Bayesian goodness-of-fit test for censored data

We propose a Bayesian computation and inference method for the Pearson-type chi-squared goodness-of-fit test with right-censored survival data. Our test statistic is derived from the classical Pearson chi-squared test using the differences between the observed and expected counts in the partitioned bins. In the Bayesian paradigm, we generate posterior samples of the model parameter using the Markov chain Monte Carlo procedure. By replacing the maximum likelihood estimator in the quadratic form with a random observation from the posterior distribution of the model parameter, we can easily construct a chi-squared test statistic. The degrees of freedom of the test equal the number of bins and thus is independent of the dimensionality of the underlying parameter vector. The test statistic recovers the conventional Pearson-type chi-squared structure. Moreover, the proposed algorithm circumvents the burden of evaluating the Fisher information matrix, its inverse and the rank of the variance–covariance matrix. We examine the proposed model diagnostic method using simulation studies and illustrate it with a real data set from a prostate cancer study.     

SOME REMARKS ON THE MEAN, MEDIAN, MODE AND SKEWNESS

Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. The paper presents a theorem that unifies already known results, gives some counter-examples, and considers the cases of Pearson distributions.     

Likelihood Ratio Tests for Fixed Model Terms using Residual Maximum Likelihood

Likelihood ratio tests for fixed model terms are proposed for the analysis of linear mixed models when using residual maximum likelihood estimation. Bartlett-type adjustments, using an approximate decomposition of the data, are developed for the test statistics. A simulation study is used to compare properties of the test statistics proposed, with or without adjustment, with a Wald test. A proposed test statistic constructed by dropping fixed terms from the full fixed model is shown to give a better approximation to the asymptotic χ²-distribution than the Wald test for small data sets. Bartlett adjustment is shown to improve the χ²-approximation for the proposed tests substantially.     

盐酸阿莫地喹溶剂残留顶空气相色谱法测定的方法学研究

建立顶空气相色谱法分析盐酸阿莫地喹中溶剂残留。采用顶空气相色谱法,用DB-FFAP大口径毛细管柱,以正丙醇为内标进行定量。甲醛,乙醇,甲苯的线性范围分别为2.7￣32.7μg·mL-1(r=0.9992),4.4￣52.8μg·mL-1(r=0.9996),2.1￣25.2μg·mL-1(r=0.9987),回收率分别为92.3%,109.1%,114.4%。本方法简单,准确,灵敏度高,重现性好。