The Pitman Inequality For Exchangeable Random Vectors

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X1,X2,…,Xn) without the assumption of continuity and symmetry for each component Xi: P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 , where all αi≥0 are special weights with ∑i=1nαi=1

Sequential boundaries approach in clinical trials with unequal allocation ratios

BACKGROUND: In clinical trials, both unequal randomization design and sequential analyses have ethical and economic advantages. In the single-stage-design (SSD), however, if the sample size is not adjusted based on unequal randomization, the power of the trial will decrease, whereas with sequential analysis the power will always remain constant. Our aim was to compare sequential boundaries approach with the SSD when the allocation ratio (R) was not equal. METHODS: We evaluated the influence of R, the ratio of the patients in experimental group to the standard group, on the statistical properties of two-sided tests, including the two-sided single triangular test (TT), double triangular test (DTT) and SSD by multiple simulations. The average sample size numbers (ASNs) and power (1-β) were evaluated for all tests. RESULTS: Our simulation study showed that choosing R = 2 instead of R = 1 increases the sample size of SSD by 12% and the ASN of the TT and DTT by the same proportion. Moreover, when R = 2, compared to the adjusted SSD, using the TT or DTT allows to retrieve the well known reductions of ASN observed when R = 1, compared to SSD. In addition, when R = 2, compared to SSD, using the TT and DTT allows to obtain smaller reductions of ASN than when R = 1, but maintains the power of the test to its planned value. CONCLUSION: This study indicates that when the allocation ratio is not equal among the treatment groups, sequential analysis could indeed serve as a compromise between ethicists, economists and statisticians

On the asymmetry of biological frequency distributions

The long-standing problem of determining whether the skewness in a sample frequency distribution is the manifestation of the intermixing of disparate groups characterizable by a normal mixture distribution or the manifestation of non-mixture, skew-producing determinants is discussed. Biometrical tools for modeling and quantifying the significance of the skewness in a trait of interest that invite interpretations other than those formed in mixtures or “subgroups” are elaborated. Statistical methods for testing whether a normal mixture distribution better characterizes a set of data than the proposed (or any other) skewed, single-population-oriented models are offered. The power of these tests is examined through Monte Carlo experimentation. A brief application in hypertension research demonstrates some of the problems and methods discussed in the paper.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38499/1/1370070605_ftp.pd

A comparison of the molecular mechanisms underpinning high-intensity, pulsed polychromatic light and low-intensity UV-C hormesis in tomato fruit

Postharvest treatment of tomato fruit with high-intensity, pulsed polychromatic light (HIPPL) has previously been shown to induce delayed ripening and disease resistance comparable to that of low-intensity UV-C (LIUV). Little, however, is known of the mechanisms underpinning postharvest HIPPL hormesis in tomato fruit. Expression of genes involved in plant hormone biosynthesis, defence, secondary metabolism and ripening were monitored 24 h post treatment (24 HPT), 10 d post treatment (10 DPT) and 12 h post inoculation with Botrytis cinerea (12 HPI). All genes monitored were constitutively expressed and changes in expression profiles following treatment were highly similar for both HIPPL and LIUV treatments. Expression of pathogenesis-related proteins P4, β-1,3,-Glucanase and Chitinase 9 and a jasmonate biosynthesis enzyme (OPR3), were significantly upregulated at 10 DPT and 12 HPI. Both treatments significantly downregulated the expression of polygalacturonase and flavonol synthase at 10 DPT and 12 HPI. Ethylene biosynthesis enzyme ACO1 and β-carotene hydroxylase were significantly upregulated at 24 HPT, and phenylalanine ammonia-lyase (PAL) was significantly upregulated at 12 HPI. Both HIPPL and LIUV treatments stimulate defence responses that are mediated by salicylic acid, jasmonic acid and ethylene. This may lead to broad range resistance against both necrotrophic and biotrophic pathogens as well as abiotic stresses and herbivorous pests. Following inoculation with B. cinerea only PAL showed indication of a gene priming response for HIPPL- and LIUV-treated fruit

Information For Estimating The Parameters In Mixtures Of Exponential And Normal Distributions.

PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/183905/2/6505876.pd