Perturbation selection and influence measures in local influence analysis

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a differential--geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model. Moreover, we will introduce new influence measures that are applicable to objective functions at any point. Examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations.Comment: Published in at http://dx.doi.org/10.1214/009053607000000343 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Advances in the Genetic Engineering of Insect-Resistant Soybeans

This paper reviewed the recent advances in research on, and the modification of the resistance genes, in the construction of vectors, methods of genetic transformation, and the resistance in transgenic plants.Originating text in Chinese.Citation: Zhu, Chengsong, Gu, Heping, Chen, Xin. (1999). Advances in the Genetic Engineering of Insect-Resistant Soybeans. Soybean Science, 18(3), 260-264

Research on the Impact of Vocational Education on Total Factor Productivity and Mediating Effects

As an important type of education for cultivating high-quality technical and skilled talents, vocational education provides significant human capital support for the high-quality development of the economy. Based on panel data from 30 provinces (autonomous regions, municipalities) in China from 2005 to 2020, this study employs the Malmquist productivity index to measure Total Factor Productivity (TFP). Using a two-way fixed effects and mediation effects model, the study empirically analyzes the impact and mechanisms of vocational education on TFP. The results show that the expansion of higher vocational education has a more significant effect on TFP growth compared to secondary vocational education, with a particularly pronounced influence in the eastern and western regions. The analysis of the mediating mechanisms reveals that human capital and technological innovation are important pathways through which vocational education promotes TFP growth. Therefore, to achieve high-quality development of vocational education and enhance TFP growth, it is recommended to moderately expand the scale, improve the vocational education training system, increase support for vocational education to narrow regional disparities, promote the integration of vocational education with industry to enhance the conversion rate of technological innovation, shift the focus from scale expansion to internal improvement, and promote regional coordinated development

Nonparametric statistical inference via metric distribution function in metric spaces

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric only. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces, laying the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop a homogeneity test and a mutual independence test for non-Euclidean random objects and present comprehensive empirical evidence to support the performance of our proposed methods. Supplementary materials for this article are available online

A SIMPLE Approach to Provably Reconstruct Ising Model with Global Optimality

Reconstruction of interaction network between random events is a critical problem arising from statistical physics and politics to sociology, biology, and psychology, and beyond. The Ising model lays the foundation for this reconstruction process, but finding the underlying Ising model from the least amount of observed samples in a computationally efficient manner has been historically challenging for half a century. By using the idea of sparsity learning, we present a approach named SIMPLE that has a dominant sample complexity from theoretical limit. Furthermore, a tuning-free algorithm is developed to give a statistically consistent solution of SIMPLE in polynomial time with high probability. On extensive benchmarked cases, the SIMPLE approach provably reconstructs underlying Ising models with global optimality. The application on the U.S. senators voting in the last six congresses reveals that both the Republicans and Democrats noticeably assemble in each congresses; interestingly, the assembling of Democrats is particularly pronounced in the latest congress

Assessment of spray distribution with water-sensitive paper

The purpose of this article is to highlight the limitations of water-sensitive paper in characterizing spray droplet distribution and deposition in field application.  Spatial distributions of spray droplets discharged from an airblast sprayer were sampled on pairs of absorbent paper (AP) and water-sensitive paper (WSP) targets at several distances from the sprayer.  Spray solutions, containing a fluorescent tracer, were discharged from two nozzle sizes to achieve low and high volume rates commonly used in citrus applications.  Spray deposits on AP targets were measured by fluorometry and spray coverage areas on WSP cards were assessed by three independent image analysis systems.  Generally, there were good correlations (R2 = 0.9085 to 0.9748) among the three imaging systems in measuring WSP percent area coverage.  Lower volume rate (smaller droplets) provided more useful WSP targets than higher volume rate (larger droplets).  Overall, there were somewhat weak correlations between WSP area coverage and AP spray deposition measurements.  Volume median diameter and number of droplet stains on WSP cards, obtained by only two imaging systems, showed noticeable differences between the measurements of the two systems.    Keywords: WSP, image analysis, spray volume rate, spray coverage, spray droplet siz

Unmanned aerial vehicle based tree canopy characteristics measurement for precision spray applications

The critical components for applying the correct amount of agrochemicals are fruit tree characteristics such as canopy height, canopy volume, and canopy coverage. An unmanned aerial vehicle (UAV)-based tree canopy characteristics measurement system was developed using image processing approaches. The UAV captured images using a high-resolution red-green-blue (RGB) camera. A digital surface model (DSM) and a digital terrain model (DTM) were generated from the captured images. A tree canopy height map was generated from the subtraction of DSM and DTM. A total of 24 apple trees were randomly targeted to measure the canopy characteristics. Region of interest (ROI) was generated across the boundary of each targeted tree. The height of all pixels within each ROI was computed separately. The pixel with maximum height was considered as the height of the respective tree. For computing canopy volume, the sum of all pixel heights from individual ROI was multiplied by the square of ground sample distance (GSD) of 5.69 mm·pixel−1. A segmentation method was employed to calculate the canopy coverage of the individual trees. The segmented canopy pixel area was divided by the total pixel area within the ROI. The results showed an average relative error of 0.2 m(6.64%) while comparing automatically measured tree height with ground measurements. For tree canopy volume, a mean absolute error of 0.25 m3 and a root mean square error of 0.33 m3 were achieved. The study estimated the possible agrochemical requirement for spraying the fruit trees, ranging from 0.1 to 0.32 l based on tree canopy volumes. The overall investigations suggest that the UAV-based tree canopy characteristics measurements could be a potential tool to calculate the pesticide requirement for precision spraying applications in tree fruit orchards

A genome-wide association analysis of Framingham Heart Study longitudinal data using multivariate adaptive splines

The Framingham Heart Study is a well known longitudinal cohort study. In recent years, the community-based Framingham Heart Study has embarked on genome-wide association studies. In this paper, we present a Framingham Heart Study genome-wide analysis for fasting triglycerides trait in the Genetic Analysis Workshop16 Problem 2 using multivariate adaptive splines for the analysis of longitudinal data (MASAL). With MASAL, we are able to perform analysis of genome-wide data with longitudinal phenotypes and covariates, making it possible to identify genes, gene-gene, and gene-environment (including time) interactions associated with the trait of interest. We conducted a permutation test to assess the associations between MASAL selected markers and triglycerides trait and report significant gene-gene and gene-environment interaction effects on the trait of interest