Second-order asymptotic loss of the MLE of a truncation parameter for a truncated exponential family of distributions

For a truncated exponential family of distributions with a truncation parameter γ and a natural parameter θ as a nuisance parameter, the stochastic expansions of bias-adjusted maximum likelihood estimators and of γ when θ is known and when θ is unknown, respectively, are derived. The second-order asymptotic loss of relative to is also obtained through their asymptotic variances. Further, some examples are given

AN INFORMATION INEQUALITY FOR THE BAYES RISK IN A FAMILY OF UNIFORM DISTRIBUTION

For a family of uniform distribution on the interval [8 - (1/2), e - (1/2)]\u27 the informationinequality for the bayes risk of any estimator of e is given under the quadratic Joss and the uniform priordistribution on an interval [-c,c]. The lower bound for the Bayes risk is shown to be sharp. And also thelower bound for the limit inferior of Bayes risk as c -jo 00 is seen to be attained by the mid-range estimator

The Asymptotic Bound by the Kiefer-Type Information Inequality and Its Attainment

In non-regular cases when the regularity conditions does not hold, the Chapman–Robbins (1951) inequality for the variance of unbiased estimators is well known, but the lower bound by the inequality is not attainable. In this article, we extend the Kiefer-type information inequality applicable to the non-regular case to the asymptotic situation, and we apply it to the case of a family of truncated distributions, in which the lower bound by the Kiefer-type inequality derived from an appropriate prior distribution is attained by the asymptotically unbiased estimator. It also follows from the completeness of the sufficient statistic that the lower bound is asymptotically best. Some examples are also given

A Higher Order Approximation to a Percentage Point of the Distribution of a Noncentral t-Statistic Without the Normality Assumption

Noncentral distributions appear in two sample problems and are often used in several fields, for example, in biostatistics. A higher order approximation for a percentage point of the noncentral t-distribution under normality is given by Akahira (1995) and is also shown to be numerically better than others. In this article, without the normality assumption, we obtain a higher order approximation to a percentage point of the distribution of a noncentral t-statistic, in a similar way to Akahira (1995) where the statistic based on a linear combination of a normal random variable and a chi-statistic takes an important role. Its application to the confidence limit and the confidence interval for a noncentrality parameter are also given. Further, a numerical comparison of the higher order approximation with the limiting normal distribution is done and the former one is shown to be more accurate. As a result of the numerical calculation, the higher order approximation seems to be useful in practical situations, when the size of sample is not so small.Journal online　著者版(author)　Table 1　⇒　Table 4.1　Table 2　⇒　Table 4.2　Table 3　⇒　Table 4.3　Table 4　⇒　Table 4.4　Table 5　⇒　Table 4.5　Table 6　⇒　Table 4.6　Table 7　⇒　Table 4.7　Table 8　⇒　Table 4.8　Table 9　⇒　Table 5.1　Table 10　⇒　Table 5.2　Table 11　⇒　Table 5.

Assessment of the toll-like receptor 4 Asp299Gly, Thr399Ile and interleukin-8 -251 polymorphisms in the risk for the development of distal gastric cancer

<p>Abstract</p> <p>Background</p> <p>The intensity of the inflammation induced by <it>Helicobacter pylori </it>colonization is associated with the development of distal gastric cancer (GC). The host response to <it>H</it>. <it>pylori </it>has been related to genetic polymorphisms that influence both innate and adaptive immune responses.</p> <p>Our aim was to investigate whether the presence of the <it>TLR4 Asp299Gly</it>, <it>TLR4 Thr399Ile </it>and <it>IL-8-251 </it>A/T polymorphisms had any influence in the development of distal GC in a Mexican population.</p> <p>Methods</p> <p>We studied 337 patients that were divided in two groups: 78 patients with histologically confirmed distal GC and 259 non-cancer controls. The presence of <it>H. pylori </it>in the control population was defined by positive results of at least two of four diagnostic tests: serology, histology, rapid urease test and culture. Human DNA was purified and genotyped for <it>TLR4 Asp299Gly </it>polymorphism by pyrosequencing, for <it>TLR4 Thr399Ile </it>by PCR-RFLP and for <it>IL8-251 </it>by the amplification refractory mutation system (ARMS)-PCR.</p> <p>Results</p> <p>The non-cancer control group was found to be in Hardy-Weinberg equilibrium at the polymorphic loci studied (chi-square _H-W= 0.58 for <it>IL8-251</it>, 0.42 for <it>TLR4 Asp299Gly </it>and 0.17 for <it>TLR4 Thr399Ile</it>). The frequencies of mutated alleles (homozygous plus heterozygous) were compared between cases and controls. We found no significant difference for <it>TLR4- Asp299Gly </it>[the 7.7% of distal GC patients and 7.7 % non-cancer controls (p = 0.82)] and for <it>TLR4 Thr399Ile </it>[the 1.3% of GC patients and the 5% of the control population (p = 0.2)]. In contrast, for <it>IL-8-251 </it>A/T, 80.77% of the GC patients and 66.4% in the control group age and gender matched had at least one copy of mutated allele (OR = 2.12, 95% CI = 1.1–4.2) (p = 0.023).</p> <p>Conclusion</p> <p>This study showed that the <it>IL8-251*A </it>allele could be related to the development of distal gastric cancer in this Mexican population.</p

A Meta-Analysis of Interleukin-8 -251 Promoter Polymorphism Associated with Gastric Cancer Risk

Background: Potential functional allele A/T single nucleotide polymorphism (SNP) of Interleukin 8 (IL-8) promoter-251has been implicated in gastric cancer risk. Methods: We aimed to explore the role of A/T SNP of IL-8-251 in the susceptibility to gastric cancer through a systematic review and meta-analysis. Each initially included article was scored for quality appraisal. Desirable data were extracted and registered into databases. Eighteen studies were ultimately eligible for the meta-analysis of IL-8- 251 A/T SNP. We adopted the most probably appropriate genetic model (codominant model). Potential sources of heterogeneity were sought out via stratification and sensitivity analyses, and publication biases were estimated. Results: Between IL-8-251 AA genotype with gastric cancer risk, statistically significant association could be noted with overall gastric cancer, evidently noted in Asians, witnessed in high quality subgroup, and apparently noted in intestinal-type gastric cancer. Conclusions: Our meta-analysis indicates that IL-8-251 AA genotype is associated with the overall risk of developing gastric cancer and may seem to be more susceptible to overall gastric cancer in Asian populations. IL-8-251 AA genotype is more associated with the intestinal-type gastric cancer. IL-8-251 AA genotype is not associated with Helicobacter Pylori infection status in our meta-analysis