Statistical inference for spherical functional autoregressions

The main purpose of this thesis is to address some foundational questions regarding time-dependent spherical random fields and, then, to investigate some new estimation procedures for the class of spherical functional autoregressions

Parametric estimation for functional autoregressive processes on the sphere

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as weak consistency and asymptotic normalit

Context factors and student achievement in the IEA studies: evidence from TIMSS

Abstract Background The present study investigates what factors related to the school context influence student achievement on TIMSS mathematics tests across countries. A systematic review of the literature on PIRLS, TIMSS, and ICCS was conducted upstream to identify those school, teacher, and classroom factors shown to be useful predictors of student performance in previous IEA studies. Data of student samples representative of grade 8 students from 28 countries who participated in TIMSS 2011 were analysed. The main aim of the present study is to verify what school and teacher characteristics are positively associated with students' mathematics achievement, mainly focusing on disadvantaged schools. Furthermore, it aims at identifying how school context variables contribute to explaining the performance of students in disadvantaged schools in comparison with more advantaged schools. Methods A separate analysis was carried out for each considered country, and the same multilevel regression model was used on the sampled schools as a whole and treating schools with high (highest tertile) and low (lowest tertile) socio-economic backgrounds as distinct groups. Results The results confirmed that a high socio-economic status has a significant and positive effect on student achievement: compared with students from socio-economic disadvantaged schools, students from advantaged schools performed better in mathematics achievement. This difference is more evident in countries where the gap between rich and poor people as measured by the Gini coefficient, which measures how much an economy deviates from perfect equality, is wider. However, this difference is restricted in countries with a smaller gap between rich and poor people. Conclusions According to the literature in the field, the results show significant differences across countries in relation to the school and teacher characteristics that have an impact on mathematics achievement of students from low and high SES schools. Different patterns were also found within countries for low and high SES schools

MultiScale CUSUM Tests for Time-Dependent Spherical Random Fields

This paper investigates the asymptotic behavior of structural break tests in the harmonic domain for time-dependent spherical random fields. In particular, we prove a Functional Central Limit Theorem result for the fluctuations over time of the sample spherical harmonic coefficients, under the null of isotropy and stationarity; furthermore, we prove consistency of the corresponding CUSUM test, under a broad range of alternatives. Our results are then applied to NCEP data on global temperature: our estimates suggest that Climate Change does not simply affect global average temperatures, but also the nature of spatial fluctuations at different scales

LASSO estimation for spherical autoregressive processes

The purpose of the present paper is to investigate a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular, consistency and oracle inequalities