Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.

A multi-scale assessment of physiological processes in arctic tundra plants under natural and simulated climate change scenarios

Climate warming is predicted to cause an increase in the growing season by as much as 30% for regions of the arctic tundra. This will have a significant effect on the physiological activity of the vascular plant species and the ecosystem as a whole. The need to understand the possible physiological change within this ecosystem is confounded by the fact that research in this extreme environment has been limited to periods when conditions are most favorable, mid June–mid August. This study attempted to develop the most comprehensive understanding to date of the physiological activity of seven tundra plant species in the Alaskan Arctic under natural and lengthened growing season conditions. Four interrelated lines of research, scaling from cellular signals to ecosystem processes, set the foundation for this study. ^ I established an experiment looking at the physiological response of arctic sedges to soil temperature stress with emphasis on the role of the hormone abscisic acid (ABA). A manipulation was also developed where the growing season was lengthened and soils were warmed in an attempt to determine the maximum physiological capacity of these seven vascular species. Additionally, the physiological capacities of four evergreens were tested in the subnivean environment along with the potential role anthocyanins play in their activity. The measurements were scaled up to determine the physiological role of these evergreens in maintaining ecosystem carbon fluxes. ^ These studies determined that soil temperature differentials significantly affect vascular plant physiology. ABA appears to be a physiological modifier that limits stomatal processes when root temperatures are low. Photosynthetic capacity was limited by internal plant physiological mechanisms in the face of a lengthened growing season. Therefore shifts in ecosystem carbon dynamics are driven by changes in species composition and biomass production on a per/unit area basis. These studies also found that changes in soil temperatures will have a greater effect of physiological processes than would the same magnitude of change in air temperature. The subnivean environment exhibits conditions that are favorable for photosynthetic activity in evergreen species. These measurements when scaled to the ecosystem have a significant role in limiting the system's carbon source capacity. ^

Across-scale patterning of plant-soil-water interactions surrounding tree islands in Southern Everglades landscapes

The freshwater Everglades is a complex system containing thousands of tree islands embedded within a marsh-grassland matrix. The tree island-marsh mosaic is shaped and maintained by hydrologic, edaphic and biological mechanisms that interact across multiple scales. Preserving tree islands requires a more integrated understanding of how scale-dependent phenomena interact in the larger freshwater system. The hierarchical patch dynamics paradigm provides a conceptual framework for exploring multi-scale interactions within complex systems. We used a three-tiered approach to examine the spatial variability and patterning of nutrients in relation to site parameters within and between two hydrologically defined Everglades landscapes: the freshwater Marl Prairie and the Ridge and Slough. Results were scale-dependent and complexly interrelated. Total carbon and nitrogen patterning were correlated with organic matter accumulation, driven by hydrologic conditions at the system scale. Total and bioavailable phosphorus were most strongly related to woody plant patterning within landscapes, and were found to be 3 to 11 times more concentrated in tree island soils compared to surrounding marshes. Below canopy resource islands in the slough were elongated in a downstream direction, indicating soil resource directional drift. Combined multi-scale results suggest that hydrology plays a significant role in landscape patterning and also the development and maintenance of tree islands. Once developed, tree islands appear to exert influence over the spatial distribution of nutrients, which can reciprocally affect other ecological processes.

An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.