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1. Application of Change Point Analysis of Response Time Data to Detect Test Speededness

   https://doi.org/10.1177/00131644211046392  

   Ying Cheng; Can Shao (January 2022, Educational and psychological measurement)

   Computer-based and web-based testing have become increasingly popular in recent years. Their popularity has dramatically expanded the availability of response time data. Compared to the conventional item response data that are often dichotomous or polytomous, response time has the advantage of being continuous and can be collected in an unobstrusive manner. It therefore has great potential to improve many measurement activities. In this paper, we propose a change point analysis (CPA) procedure to detect test speededness using response time data. Specifically, two test statistics based on CPA, the likelihood ratio test and Wald test, are proposed to detect test speededness. A simulation study has been conducted to evaluate the performance of the proposed CPA procedure, as well as the use of asymptotic and empirical critical values. Results indicate that the proposed procedure leads to high power in detecting test speededness, while keeping the false positive rate under control, even when simplistic and liberal critical values are used. Accuracy of the estimation of the actual change point, however, is highly dependent on the true change point. A real data example is also provided to illustrate the utility of the proposed procedure and its contrast to the response-only procedure. Implications of the findings are discussed at the end. 

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2. Empirical likelihood test for a large-dimensional mean vector

   https://doi.org/10.1093/biomet/asaa005  

   Cui, Xia; Li, Runze; Yang, Guangren; Zhou, Wang (March 2020, Biometrika)

   null (Ed.)

   Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $$p$$ and the sample size $$n$$ satisfy $$p/n\rightarrow c\in [1,\infty)$$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $$n$$ observations in $$\mathbb{R}^p$$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data. 

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3. Empirical Likelihood-Based Inference for Functional Means with Application to Wearable Device Data

   https://doi.org/10.1111/rssb.12543  

   Chang, Hsin-wen; McKeague, Ian W. (November 2022, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract This paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study. 

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4. Nonparanormal graph quilting with applications to calcium imaging

   https://doi.org/10.1002/sta4.623  

   Chang, Andersen; Zheng, Lili; Dasarathy, Gautam; Allen, Genevera I. (September 2023, Stat)

   Abstract Probabilistic graphical models have become an important unsupervised learning tool for detecting network structures for a variety of problems, including the estimation of functional neuronal connectivity from two‐photon calcium imaging data. However, in the context of calcium imaging, technological limitations only allow for partially overlapping layers of neurons in a brain region of interest to be jointly recorded. In this case, graph estimation for the full data requires inference for edge selection when many pairs of neurons have no simultaneous observations. This leads to the graph quilting problem, which seeks to estimate a graph in the presence of block‐missingness in the empirical covariance matrix. Solutions for the graph quilting problem have previously been studied for Gaussian graphical models; however, neural activity data from calcium imaging are often non‐Gaussian, thereby requiring a more flexible modelling approach. Thus, in our work, we study two approaches for nonparanormal graph quilting based on the Gaussian copula graphical model, namely, a maximum likelihood procedure and a low rank‐based framework. We provide theoretical guarantees on edge recovery for the former approach under similar conditions to those previously developed for the Gaussian setting, and we investigate the empirical performance of both methods using simulations as well as real data calcium imaging data. Our approaches yield more scientifically meaningful functional connectivity estimates compared to existing Gaussian graph quilting methods for this calcium imaging data set. 

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5. Semi-parametric Learning of Structured Temporal Point Processes

   Xu, G.; Wang, M.; Bian, J.; Huang, H.; Burch, T.; Andrade, S.; Zhang, J.; Guan, Y. (January 2020, Journal of machine learning research)

   We propose a general framework of using a multi-level log-Gaussian Cox process to model repeatedly observed point processes with complex structures; such type of data have become increasingly available in various areas including medical research, social sciences, economics, and finance due to technological advances. A novel nonparametric approach is developed to efficiently and consistently estimate the covariance functions of the latent Gaussian processes at all levels. To predict the functional principal component scores, we propose a consistent estimation procedure by maximizing the conditional likelihood of super-positions of point processes. We further extend our procedure to the bivariate point process case in which potential correlations between the processes can be assessed. Asymptotic properties of the proposed estimators are investigated, and the effectiveness of our procedures is illustrated through a simulation study and an application to a stock trading dataset. 

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