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1. Estimation of the covariance structure of heavy-tailed distributions

   Minsker, Stanislav ; Wei, Xiaohan ( December 2017 , NIPS)

   We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance matrices corresponding to sub-Gaussian distributions is well-understood, much less in known in the case of heavy-tailed data. As K. Balasubramanian and M. Yuan write, "data from real-world experiments oftentimes tend to be corrupted with outliers and/or exhibit heavy tails. In such cases, it is not clear that those covariance matrix estimators .. remain optimal" and "what are the other possible strategies to deal with heavy tailed distributions warrant further studies." We make a step towards answering this question and prove tight deviation inequalities for the proposed estimator that depend only on the parameters controlling the intrinsic dimension'' associated to the covariance matrix (as opposed to the dimension of the ambient space); in particular, our results are applicable in the case of high-dimensional observations. 

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2. Model-Based Trust Assessment for Internet of Things Networks

   Adams, Stephen ; Beling, Peter A ; Greenspan, Steven ; Velez-Rojas, Maria ; Mankovski, Serge ( January 2018 , 2018 17th IEEE International Conference On Trust, Security And Privacy In Computing And Communications/12th IEEE International Conference On Big Data Science And Engineering (TrustCom/BigDataSE))

   Trust in data collected by and passing through Internt of Things (IoT) networks is paramount. The quality of decisions made based on this collected data is highly dependent upon the accuracy of the data. Currently, most trust assessment methodologies assume that collected data follows a stationary Gaussian distribution. Often, a trust score is estimated based upon the deviation from this distribution. However, the underlying state of a system monitored by an IoT network can change over time, and the data collected from the network may not consistently follow a Gaussian distribution. Further, faults that occur within the estimated Gaussian distribution may go undetected. In this study, we present a model-based trust estimation system that allows for concept drift or distributions that can change over time. The presented methodology uses data-driven models to estimate the value of the data produced by a sensor using the data produced by the other sensors in the network. We assume that an untrustworthy piece of data falls in the tails of the residual distribution, and we use this concept to assign a trust score. The method is evaluated on a smart home data set consisting of temperature, humidity, and energy sensors. 

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3. Modified Arcsine Law for One-Bit Sampled Stationary Signals with Time-Varying Thresholds

   Eamaz, A ; Yeganegi, F. ; Soltanalian, M. ( January 2021 , Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing)

   null (Ed.)

   One-bit quantization has attracted considerable attention in signal processing for communications and sensing. The arcsine law is a useful relation often used to estimate the normalized covariance matrix of zero-mean stationary input signals when they are sampled by one-bit analog-to-digital converters (ADCs)---practically comparing the signals with a given threshold level. This relation, however, only considers a zero threshold which can cause a remarkable information loss. For the first time in the literature, this paper introduces an approach to extending the arcsine law to the case where one-bit ADCs apply time-varying thresholds. In particular, the proposed method is shown to accurately recover the variance and autocorrelation of the stationary signals of interest. 

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4. Study on U.S. Parents' Divisions of Labor During COVID-19, Waves 1-2

   https://doi.org/10.3886/E183142V2  

   Carlson, Daniel L. ; Petts, Richard J. ( January 2022 , ICPSR - Interuniversity Consortium for Political and Social Research)

   The COVID-19 pandemic has dramatically altered family life in the United States. Over the long duration of the pandemic, parents had to adapt to shifting work conditions, virtual schooling, the closure of daycare facilities, and the stress of not only managing households without domestic and care supports but also worrying that family members may contract the novel coronavirus. Reports early in the pandemic suggest that these burdens have fallen disproportionately on mothers, creating concerns about the long-term implications of the pandemic for gender inequality and mothers’ well-being. Nevertheless, less is known about how parents’ engagement in domestic labor and paid work has changed throughout the pandemic, what factors may be driving these changes, and what the long-term consequences of the pandemic may be for the gendered division of labor and gender inequality more generally.
   
   The Study on U.S. Parents’ Divisions of Labor During COVID-19 (SPDLC) collects longitudinal survey data from partnered U.S. parents that can be used to assess changes in parents’ divisions of domestic labor, divisions of paid labor, and well-being throughout and after the COVID-19 pandemic. The goal of SPDLC is to understand both the short- and long-term impacts of the pandemic for the gendered division of labor, work-family issues, and broader patterns of gender inequality.
   
   Survey data for this study is collected using Prolifc (www.prolific.co), an opt-in online platform designed to facilitate scientific research. The sample is comprised U.S. adults who were residing with a romantic partner and at least one biological child (at the time of entry into the study). In each survey, parents answer questions about both themselves and their partners. Wave 1 of SPDLC was conducted in April 2020, and parents who participated in Wave 1 were asked about their division of labor both prior to (i.e., early March 2020) and one month after the pandemic began. Wave 2 of SPDLC was collected in November 2020. Parents who participated in Wave 1 were invited to participate again in Wave 2, and a new cohort of parents was also recruited to participate in the Wave 2 survey. Wave 3 of SPDLC was collected in October 2021. Parents who participated in either of the first two waves were invited to participate again in Wave 3, and another new cohort of parents was also recruited to participate in the Wave 3 survey. This research design (follow-up survey of panelists and new cross-section of parents at each wave) will continue through 2024, culminating in six waves of data spanning the period from March 2020 through October 2024. An estimated total of approximately 6,500 parents will be surveyed at least once throughout the duration of the study.
   
   SPDLC data will be released to the public two years after data is collected; Waves 1 and 2 are currently publicly available. Wave 3 will be publicly available in October 2023, with subsequent waves becoming available yearly. Data will be available to download in both SPSS (.sav) and Stata (.dta) formats, and the following data files will be available: (1) a data file for each individual wave, which contains responses from all participants in that wave of data collection, (2) a longitudinal panel data file, which contains longitudinal follow-up data from all available waves, and (3) a repeated cross-section data file, which contains the repeated cross-section data (from new respondents at each wave) from all available waves. Codebooks for each survey wave and a detailed user guide describing the data are also available. Response Rates: Of the 1,157 parents who participated in Wave 1, 828 (72%) also participated in the Wave 2 study. Presence of Common Scales: The following established scales are included in the survey:
   

   • Self-Efficacy, adapted from Pearlin's mastery scale (Pearlin et al., 1981) and the Rosenberg self-esteem scale (Rosenberg, 2015) and taken from the American Changing Lives Survey
   • Communication with Partner, taken from the Marriage and Relationship Survey (Lichter & Carmalt, 2009)
     
   • Gender Attitudes, taken from the National Survey of Families and Households (Sweet & Bumpass, 1996)
     
   • Depressive Symptoms (CES-D-10)
   • Stress, measured using Cohen's Perceived Stress Scale (Cohen, Kamarck, & Mermelstein, 1983)
     

   Full details about these scales and all other items included in the survey can be found in the user guide and codebook
   The second wave of the SPDLC was fielded in November 2020 in two stages. In the first stage, all parents who participated in W1 of the SPDLC and who continued to reside in the United States were re-contacted and asked to participate in a follow-up survey. The W2 survey was posted on Prolific, and messages were sent via Prolific’s messaging system to all previous participants. Multiple follow-up messages were sent in an attempt to increase response rates to the follow-up survey. Of the 1,157 respondents who completed the W1 survey, 873 at least started the W2 survey. Data quality checks were employed in line with best practices for online surveys (e.g., removing respondents who did not complete most of the survey or who did not pass the attention filters). After data quality checks, 5.2% of respondents were removed from the sample, resulting in a final sample size of 828 parents (a response rate of 72%).
   
   In the second stage, a new sample of parents was recruited. New parents had to meet the same sampling criteria as in W1 (be at least 18 years old, reside in the United States, reside with a romantic partner, and be a parent living with at least one biological child). Also similar to the W1 procedures, we oversampled men, Black individuals, individuals who did not complete college, and individuals who identified as politically conservative to increase sample diversity. A total of 1,207 parents participated in the W2 survey. Data quality checks led to the removal of 5.7% of the respondents, resulting in a final sample size of new respondents at Wave 2 of 1,138 parents.
   
   In both stages, participants were informed that the survey would take approximately 20 minutes to complete. All panelists were provided monetary compensation in line with Prolific’s compensation guidelines, which require that all participants earn above minimum wage for their time participating in studies.
   To be included in SPDLC, respondents had to meet the following sampling criteria at the time they enter the study: (a) be at least 18 years old, (b) reside in the United States, (c) reside with a romantic partner (i.e., be married or cohabiting), and (d) be a parent living with at least one biological child. Follow-up respondents must be at least 18 years old and reside in the United States, but may experience changes in relationship and resident parent statuses. Smallest Geographic Unit: U.S. State

   This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. In accordance with this license, all users of these data must give appropriate credit to the authors in any papers, presentations, books, or other works that use the data. A suggested citation to provide attribution for these data is included below:            
   
   Carlson, Daniel L. and Richard J. Petts. 2022. Study on U.S. Parents’ Divisions of Labor During COVID-19 User Guide: Waves 1-2.  

   To help provide estimates that are more representative of U.S. partnered parents, the SPDLC includes sampling weights. Weights can be included in statistical analyses to make estimates from the SPDLC sample representative of U.S. parents who reside with a romantic partner (married or cohabiting) and a child aged 18 or younger based on age, race/ethnicity, and gender. National estimates for the age, racial/ethnic, and gender profile of U.S. partnered parents were obtained using data from the 2020 Current Population Survey (CPS). Weights were calculated using an iterative raking method, such that the full sample in each data file matches the nationally representative CPS data in regard to the gender, age, and racial/ethnic distributions within the data. This variable is labeled CPSweightW2 in the Wave 2 dataset, and CPSweightLW2 in the longitudinal dataset (which includes Waves 1 and 2). There is not a weight variable included in the W1-W2 repeated cross-section data file.
    

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5. Robust Functional Principal Component Analysis via a Functional Pairwise Spatial Sign Operator

   https://doi.org/10.1111/biom.13695  

   Wang, Guangxing ; Liu, Sisheng ; Han, Fang ; Di, Chong-Zhi ( May 2022 , Biometrics)

   Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women.

    

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