Equivariance and generalized inference in location-scale family

In this thesis, we revisit some statistical problems, where classical inference can not provide small-sample optimal solution. These problems motivated Tsui and Weerahandi (1989), and Weerahandi (1993) to introduce the concepts of generalized inference which consist in constructing generalized test variable (GTV) and generalized pivotal quantity (GPQ). However, in general location-scale family, the existing literatures do not provide any systematic method for deriving these quantities. To overcome this problem, the equivariance principle is applied to construct GTV and GPQ in location-scale family. Namely, we construct the GPQ and GTV for the parameters of interest in one-sample and two-sample families cases. Particularly, we study inference problem concerning the difference between two location parameters. The simulation studies show that the suggested methods preserve the nominal level, and provides satisfactory power in small and moderate sample sizes. Finally, some real data sets are analyzed in order to illustrate the application of the suggested procedures

Optimal Inference Methods in Linear Models with Change-points

In this dissertation, we consider an estimation problem of the regression coefficients in both multiple regression model and multivariate multiple regression model with several unknown change-points. More precisely, we consider the cases where the target parameters (vectors or matrices) are suspected to satisfy some restrictions. In particular, we generalize in four ways, some recent statistical methods in the literatures. First, we relax some assumptions about the dependance structure of the noise and the regressors given in recent literature. Namely, in this dissertation, the dependance structure is as weak as that of an L 2 -mixingale arrays of size -1/2. Second, under such weak assumptions, we derive the joint asymptotic normality between the RE and UE. Third, in the context of change-points models, the estimation problem of a vector of the regression coefficients is extended to that of a matrix of the regression coefficients. Fourth, we propose a class of estimators which includes as a special cases shrinkage estimators (SEs) as well as the unrestricted estimator (UE) and the restricted estimator (RE). We also derive a more general condition for the SEs to dominate the UE in mean square error. To this end, we generalize some identities for the evaluation of the bias and risk functions of shrinkage-type estimators (vectors or matrices). As illustrative example, our method is applied to the gross domestic product\u27\u27 data set of 10 countries including USA, Canada, UK, France and Germany. The simulation results corroborate our theoretical findings

Equivariance and Generalized Inference in Two-Sample Location-Scale Families

We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity (GPQ) and generalized P value (GPV) for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators (MREs), and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets

Study of an Arctic blowing snow-induced bromine explosion event in Ny-Ålesund, Svalbard

Bromine explosion events (BEEs) are important processes that influence the atmospheric oxidation capacity, especially in the polar troposphere during spring. Although sea ice surface is thought to be a significant bromine source, bromine release mechanisms remain unclear. High-resolution ground-based observations of reactive bromine, such as BrO, are important for assessing the potential impacts on tropospheric ozone and evaluating chemical models. However, previous model studies paid little attention to Svalbard, which is surrounded by both open ocean and sea ice. In this paper, we present continuous BrO slant column densities and vertical column densities derived by Multi-Axis Differential Optical Absorption Spectroscopy deployed at Ny-Ålesund (78.92°N, 11.93°E) in March 2017. We focused on one BEE in mid-March, during which the vertical column densities of BrO surged from 4.26 × 1013 molecular cm−2 to the peak at 1.23 × 1014 molecular cm−2 on March 17, surface ozone depleted from a background level of 46.25 parts per billion by volume (ppbv) to 13.9 ppbv. This case study indicates that the BEE was strongly associated with blowing snow induced by the cyclone systems that approached Svalbard from March 14 to 18. By considering meteorological conditions, sea ice coverage, and airmass trajectory history, we demonstrate that sea salt aerosols (SSAs) from blowing snow on sea ice, rather than from open ocean, are attributed to the occurrence of this BEE. Model results from a parallelized-tropospheric offline model of chemistry and transport (p-TOMCAT) indicate that this BEE was mainly triggered by a blowing snow event associated with a low-pressure cyclone system. The concentration of blowing-snow-sourced SSAs surged to peak when the airmass pass across the sea-ice-covered area under high wind speed, which is a critical factor in the process of bromine explosion observed in Ny-Ålesund. Due to the coarse resolution, the possible delayed timing of bromine release from SSA and the model-data discrepancies still exist

LeafletAnalyzer, an Automated Software for Quantifying, Comparing and Classifying Blade and Serration Features of Compound Leaves during Development, and among Induced Mutants and Natural Variants in the Legume Medicago truncatula

Diverse leaf forms ranging from simple to compound leaves are found in plants. It is known that the final leaf size and shape vary greatly in response to developmental and environmental changes. However, changes in leaf size and shape have been quantitatively characterized only in a limited number of species. Here, we report development of LeafletAnalyzer, an automated image analysis and classification software to analyze and classify blade and serration characteristics of trifoliate leaves in Medicago truncatula. The software processes high quality leaf images in an automated or manual fashion to generate size and shape parameters for both blades and serrations. In addition, it generates spectral components for each leaflets using elliptic Fourier transformation. Reconstruction studies show that the spectral components can be reliably used to rebuild the original leaflet images, with low, and middle and high frequency spectral components corresponding to the outline and serration of leaflets, respectively. The software uses artificial neutral network or k-means classification method to classify leaflet groups that are developed either on successive nodes of stems within a genotype or among genotypes such as natural variants and developmental mutants. The automated feature of the software allows analysis of thousands of leaf samples within a short period of time, thus facilitating identification, comparison and classification of leaf groups based on leaflet size, shape and tooth features during leaf development, and among induced mutants and natural variants