We consider the mean response estimation and inference in semi-supervised settings in the first two chapters. Such settings consist of a relatively small labeled dataset and an extensive unlabeled dataset. Chapter 1 considers the classical semi-supervised setup that the outcome is missing completely at random (MCAR). Our goal is to improve the efficiency of the supervised sample mean estimator using the additional unlabeled data. We proposed a semi-supervised mean estimator based on flexible working models, including high-dimensional and non-parametric models. In Chapter 2, we further consider the situation that a selection bias may appear. Our goal is to remove the bias originating from the dependence between the missing and outcome. We propose a semi-supervised doubly robust mean estimator with valid inference results when some product rate condition holds. Our work fills in the gap between the semi-supervised literature and the missing data literature. We allow selection bias -- this extends the semi-supervised literature. We also allow extremely unbalanced labeled/unlabeled groups and violate the usual positivity condition, which is always assumed throughout the missing data literature.

The last two chapters consider the estimation and inference of the dynamic treatment effect (DTE) when the treatment variable is longitudinal and the covariates are possibly high dimensional. Chapter 3 proposes a doubly robust DTE estimator based on (imputed) Lasso-type nuisance estimators. We established root-n inference when all the nuisance models are correctly specified and some sparsity conditions hold. Chapter 4 further provides root-n inference for the DTE even when model misspecification occurs. This is achieved based on special ``moment targeting'' nuisance estimators. We provide valid inference as long as one of the nuisance models is correctly specified at each time spot -- such a result is better than all the existing literature, even containing the low-dimensional works.

Nitrate uptake characteristics and ammonium effects were compared between upland rice (Brazilian upland rice) and paddy rice (Wuyujing 3 and Yangdao 6) through the glass microelectrode technique and the concentration gradient method of uptake kinetics. Results indicated that nitrate uptake by rice seedlings and ammonium effects were related to transmembrane potential difference, and upland rice and paddy rice presented obviously different responses. Nitrate induced a rapid depolarization and then a slow repolarization of transmembrane potential in root epidermal cells, and even hyperpolarization was observed when nitrate concentration was low. Resting transmembrane potential of epidermal cells in Brazilian upland rice roots was lower and its response to NO3- was bigger than that of two paddy rice species. Depolarization of membrane potential was amplified when ammonium was simultaneously added with nitrate into the measure medium, but repolarization was reduced, even disappeared. Brazilian upland rice seedlings had high Vmax of nitrate uptake and low Km, furthermore, Vmax and Km were little affected by ammonium, but Vmax of Wuyujing 3 was reduced significantly. Therefore, inhibition of ammonium to nitrate uptake possibly due to decrease of membrane potential and influence of nitrate transporters. Moreover, inhibition of NH4+ differed obviously between upland rice and paddy rice.

Most of plants uptook NO3--N faster at the low pH 4.0 than at pH 6.0 and uptook NH4+-N slower, but few experimental plants showed different tendency. The exceptions probably due to excessive nitrate outflux of some maize and wheat varieties (Suyu 19. Zhendan958 and Yangmai12) at low pH. Some other experimental plants (Huaidao 8. Nongda108 and Yangmai12) even show no obvious NH4+ toxic symptoms at pH 4.0. The effect of low pH on uptake rate of NH4+-N and NO3--N varied with plant species, varieties, and the difference increased with the growth age of seedlings.

Unlabelled

Implications