A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

Developmental Genetic Analysis of Brown Rice Weight Under Different Environmental Conditions in indica Rice

Analysis of genetic main effects and genotype x environment (GE) interaction effects for brown rice weight (BRW) at four different filling stages in indica lice (Oryza sativa L.) was conducted for two-year experimental data by using developmental genetic models and corresponding statistical approaches for quantitative traits of seeds in cereal crops. It was indicated that the genetic main effects and their GE interaction effects of triploid endosperm, cytoplasmic and diploid maternal plant genes were important for BRW at different filling stages of rice, especially for endosperm or maternal additive main effects and their additive interaction effects. Because of the higher additive effects and additive interaction effects for BRW at different filling stages, the better improving effects for this trait could be expected by selection in rice breeding. The results of conditional genetic variance components showed that the new expression of quantitative genes in endosperm and maternal plant for BRW was mostly found at all different filling stages of rice. The gene expression, however, was most active at the early filling stages especially for the first (1-7 d) and the second filling stages (8-14 d after flowering). The phenomena that some genes were spasmodically expressible among filling stages of rice were detected for some genetic effects especially for net cytoplasmic main effects or its interaction effects and net dominance main effects. Predicted genetic effects at different filling stages of rice showed that some parents such as V20 and Zuo 5 were better than others for improving the BRW.

Longitudinal genetic analysis of growth-related traits in red swamp crayfish Procambarus clarkii (Girard)

The red swamp crayfish,Procambarus clarkii,is an economically important species especially in China.Their exoskeleton places serious constraints on growth and culture management.Their growth is achieved through intermittent molting/ecdysis.The longitudinal genetic dynamics for growth-related traits at different ecdysial points in P.clarkii has been unclear to date.In this study,conditional genetic analysis was carried out for growth-related traits(body weight,body length,chela length,and cephalothorax length)based upon a mixed genetic model with conditional additive,dominance,and genotype by environment effects in P.clarkii.A complete diallel cross was made among three geographic populations of P.clarkii for the genetic mating design.Results of the conditional genetic analysis showed that from 4 th molt to 9 th molt the conditional additive variations were increased significantly whereas the conditional non-additive genetic variations(dominance and genotype by environment interaction)were decreased significantly for these growth-related traits.This indicated that lots of new expression of additive effect genes for body weight,body length,chela length,and cephalothorax length occurred during ontogeny,and environment played a signifi cant role in the expression of genes affecting these growth-related traits.Growth of the four traits was mainly affected by non-additive genetic effects in early developmental stage(prior to 4 th molt).The cumulative conditional additive variation for the growth-related traits from 4 th molt to 9 th molt accounted for a large majority of the total conditional additive variations from 2 nd molt to 9 th molt,indicating that this period was very important for the growth of this species.Using the conditional analysis method,dynamics of growth-related traits during an important ontogenetic phase of red swamp crayfish was uncovered.Our results provide valuable insights into refining production of this species.

Developmental Analysis of Genetic Behavior of Brown Rice Width in indica-japonica Hybrids

The developmental genetic behaviors of brown rice width （BRW） have been studied in indica-japonica hybrid rice （Oryza sativa L.）, in which seven indica male sterile lines and five japonica restorer lines were applied, by using the developmental genetic models and corresponding statistical approaches for quantitative traits of triploid in cereal crops. The BRW of indica-japonica hybrid rice was co-determined by gene expression of tdploid endosperm, cytoplasm, diploid maternal plant and their genotype × environmental interaction effects. Unconditional analysis showed that the endosperm additive and matemal additive effects were predominant for the development of BRW from early- to late-stage of the grain development, but the endosperm dominant effect together with matemal effect and cytoplasmic effect became the major factor determing the BRW at the ripening stage. Moreover, conditional analysis found that there were new onset and offset of gene expression at different developmental stages of BRW in indica-japonica hybrid rice. Maternal and cytoplasm general heritabilities and their interaction heritabilities were more important compared to other components of heritability for BRW at all the five developmental stages.

Confidence Intervals of Variance Functions in Generalized Linear Model

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.