A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models

Constructing confidence intervals for the coefficients of high-dimensional sparse linear models remains a challenge, mainly because of the complicated limiting distributions of the widely used estimators, such as the lasso. Several methods have been developed for constructing such intervals. Bootstrap lasso+ols is notable for its technical simplicity, good interpretability, and performance that is comparable with that of other more complicated methods. However, bootstrap lasso+ols depends on the beta-min assumption, a theoretic criterion that is often violated in practice. Thus, we introduce a new method, called bootstrap lasso+partial ridge, to relax this assumption. Lasso+partial ridge is a two-stage estimator. First, the lasso is used to select features. Then, the partial ridge is used to refit the coefficients. Simulation results show that bootstrap lasso+partial ridge outperforms bootstrap lasso+ols when there exist small, but nonzero coefficients, a common situation that violates the beta-min assumption. For such coefficients, the confidence intervals constructed using bootstrap lasso+partial ridge have, on average, $50\%$ larger coverage probabilities than those of bootstrap lasso+ols. Bootstrap lasso+partial ridge also has, on average, $35\%$ shorter confidence interval lengths than those of the de-sparsified lasso methods, regardless of whether the linear models are misspecified. Additionally, we provide theoretical guarantees for bootstrap lasso+partial ridge under appropriate conditions, and implement it in the R package "HDCI.

What Does It Meme? A Qualitative Analysis Of Adolescents’ Perceptions Of Tobacco And Marijuana Messaging

With increasing popularity of e-cigarettes and legalization of marijuana, messaging from online sites and platforms are shaping product perceptions and use. Quantitative studies have examined social media statistics of posts; however, there is a lack of research explaining the aesthetic appeal of these advertisements from the adolescents and young adults (AYA) perspective. Twenty-four participants were recruited from a larger study of adolescents\u27 perceptions and tobacco use (N=772 high school students). Participants were grouped by whether or not they had used tobacco or marijuana products before, with N=8 non-users and N=16 users. Data were collected through individual semi-structured interviews, where participants were asked about their experiences with tobacco and marijuana advertisements online. Interview protocols were developed to understand appeal of advertisements and to learn about the nuances of social media. Interviews were recorded and transcribed. Key themes emerged from the interviews: (1) Interactions with Online Platforms and Social Media, (2) Direct Appeal of Advertisements to AYA, (3) Trusting Source of Messaging, and (4) Attitudes and Agency. These findings suggest the need to continue to incorporate personal empowerment and understanding AYA’s role of spreading information through social media in prevention curricula, as well as increased regulation around social media messaging around tobacco and marijuana. Although this study aimed to understand online influences, the influences of personal agency and peers were still major factors in tobacco and marijuana decision-making

Pillars Of Prosperity: Leveraging Regional Assets To Grow Minnesota's Economy

Minnesota has always been rich with assets -- a skilled labor force, good jobs in diverse industries, globally competitive companies, and abundant lakes and parks that provide a high quality of life for the people who call it home.However, to maintain its strong economy and quality of life, Minnesota must adapt to fast-changing trends in the global economy, trends that affect each of the state's regions and communities differently.This report explores how the state of Minnesota -- the governor's administration together with the Minnesota Legislature -- can partner with regional networks to foster economic growth and extend prosperity to greater numbers of Minnesotans

Graph Replacement Systems for Julia Sets of Quadratic Polynomials

Belk and Forrest construct a specific class of graph replacement systems that give sequences of graphs that converge to fractals. Given a polynomial, we have an algorithm that gives a replacement system that leads to a graph sequence which we conjecture converges to the Julia set. We prove the conjecture for the quadratic polynomial $z^2+c$ where $c$ is a real number and the critical point is in a three cycle. We present some additional results and observations on replacement systems obtained from certain polynomials

Maternal bargaining power, parental compensation and non-cognitive skills in rural China

The importance of non-cognitive skills in determining long-term human capital and labor market outcomes is widely acknowledged, but relatively little is known about how non-cognitive skills may shape educational investments by parents early in life. This paper evaluates the parental response to variation in non-cognitive skills among their children in rural Gansu province, China, employing a household fixed effects specification. The results suggest that on average, parents invest no more in terms of educational expenditure in children who have better non-cognitive skills relative to their siblings. However, there is significant heterogeneity with respect to maternal education; less educated mothers appear to reinforce differences in non-cognitive skills between their children, while more educated mothers compensate for these differences. The evidence is consistent with this pattern corresponding to greater bargaining power for more educated mothers and different preferences for compensation among more educated women. In addition, there is evidence that these compensatory investments lead to catch-up in non-cognitive skills over time for children of more educated mothers

Pointwise Ergodic Theorems for Uniformly Behaved in N{\mathbb N} Sequences

We define a uniformly behaved in ${\mathbb N}$ arithmetic sequence ${\bf a}$ and an ${\bf a}$-mean Lyapunov stable dynamical system $f$. We consider the mean partial sum of a continuous function $\phi$ over the ${\bf a}$-orbit of $f$ up to $N$. The main result we prove in the paper is that the mean partial sum converges pointwise if ${\bf a}$ is uniformly behaved in ${\mathbb N}$ and $f$ is minimal and uniquely ergodic and ${\bf a}$-mean Lyapunov stable. In addition, if ${\bf a}$ is also completely additive, we then prove that the mean partial sum of a continuous function $\phi$ over the square-free ${\bf a}$-orbit of $f$ up to $N$ converges pointwise as well. All equicontinuous dynamical systems are ${\bf a}$-mean Lyapunov stable for any sequence ${\bf a}$. When ${\bf a}$ is uniformly distributed in ${\mathbb Z}$, we give two non-trivial examples of ${\bf a}$-mean Lyapunov stable dynamical systems. We give several examples of uniformly behaved in ${\mathbb N}$ sequences, including the counting function of the prime factors in natural numbers, the subsequence of natural numbers indexed by the Thue-Morse (or Rudin-Shapiro) sequence, and the sequence of even (or odd) prime factor natural numbers. We also show that the sequence of square-free natural numbers (or even (or odd) prime factor square-free natural numbers) is rotationally distributed in ${\mathbb N}$ but not uniformly distributed in ${\mathbb Z}$, thus not uniformly behaved in ${\mathbb N}$. We derive other consequences from the main result relevant to number theory and ergodic theory/dynamical systems.Comment: 2

Accounting narratives and impression management on social media

In this paper, we examine the defensive and assertive impression management strategies and the impact of firm performance on accounting narratives by investigating the earnings disclosures of FTSE 100 companies on Twitter. Social media has become the prevailing venue for organisational self-presentation because it provides firms with more control over the image they intend to establish and maintain through the communication and content they deliver online. Our findings show that firms minimise the disclosures of negative information but employ various patterns and dissemination techniques to emphasise positive information. Specifically, improving performers are more willing to post and disseminate earnings-related tweets to achieve a higher degree of stakeholder engagement than declining performers. Based on these findings, we conclude that firms present themselves on social media opportunistically to construct a positive public image

A longitudinal analysis of corporate greenhouse gas disclosure strategy

Purpose This paper aims to investigate the extent to which greenhouse gas (GHG) -sensitive companies in the FTSE 100 disclose carbon emission information in their annual reports and standalone reports during the period of 2004–2012, and how they respond to the launch of legally binding GHG reduction schemes – the EU Emission Trading Scheme (EU ETS) and the Climate Change Act (CCA). Design/methodology/approach A 42-item disclosure index is constructed to analyse the quality of corporate GHG disclosures. We initially chart the development of corporate GHG disclosure from 2004 to 2012, analyse the trend of disclosure development and compare variances for the convergence of disclosures. Subsequently we carry out a t-test to assess the significance of post-EU ETS and -CCA changes and the difference between GHG trading account holders and non-account holders. Findings The results show that GHG disclosures have been increasing over time, both in number of firms making disclosures and in the amount of information being reported, which indicates the movement towards normativity. We also find that the disclosures reach the peak after the enactment of EU ETS and CCA, and firms with carbon trading accounts are more responsive to these schemes than those without accounts. Nevertheless, the quality of the disclosure remains low, which may justify the further government intervention of mandating carbon reporting. Originality/value This is the first paper that has examined the regulatory effects on GHG disclosures in an environment where GHG emission triggers direct cost for companies

A new approach to the chronology of caves 268/272/275 in the Dunhuang Mogao Grottoes: combining radiocarbon dates and archaeological information within a Bayesian statistical framework

The construction chronology of three of the earliest Dunhuang Mogao Grottoes (Caves 268, 272, and 275) has been the subject of ongoing debate for over half a century. This chronology is a crucial topic in terms of further understanding of the establishment of the Dunhuang Mogao Grottoes, early Buddhism in the Gansu corridor, and its relationship with Buddhism developed in the Central Plains. Building upon archaeological, art historical and radiocarbon (14C) dating studies, we integrate new 14C data with these previously published findings utilizing Bayesian statistical modeling to improve the chronological resolution of this issue. Thus, we determine that all three of these caves were constructed around AD 410–440, suggesting coeval rather than sequential construction

Dimensional Changes of Upper Airway after Rapid Maxillary Expansion: A Prospective Cone-beam Computed Tomography Study

Introduction: The aim of this prospective study was to use cone-beam computed tomography to assess the dimensional changes of the upper airway in orthodontic patients with maxillary constriction treated by rapid maxillary expansion. Methods: Fourteen orthodontic patients (mean age, 12.9 years; range, 9.7-16 years) were recruited. The patients with posterior crossbite and constricted maxilla were treated with rapid maxillary expansion as the initial part of their comprehensive orthodontic treatments. Before and after rapid maxillary expansion conebeam computed tomography scans were taken to measure the retropalatal and retroglossal airway changes in terms of volume, and sagittal and cross-sectional areas. The transverse expansions by rapid maxillary expansion were assessed between the midlingual alveolar bone plates at the maxillary first molar and first premolar levels. The measurements of the before and after rapid maxillary expansion scans were compared by using paired t tests with the Bonferroni adjustment for multiple comparisons. Results: After rapid maxillary expansion, significant and equal amounts of 4.8 mm of expansion were observed at the first molar (P 5 0.0000) and the first premolar (P 5 0.0000) levels. The width increase at the first premolar level (20.0%) was significantly greater than that at the first molar level (15.0%) (P 5 0.035). As the primary outcome variable, the cross-sectional airway measured from the posterior nasal spine to basion level was the only parameter showing a significant increase of 99.4 mm2 (59.6%) after rapid maxillary expansion (P 5 0.0004). Conclusions: These results confirm the findings of previous studies of the effect of rapid maxillary expansion on the maxilla. Additionally, we found that only the cross-sectional area of the upper airway at the posterior nasal spine to basion level significantly gains a moderate increase after rapid maxillary expansion