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Register a new userSemiparametric curve alignment and shift density estimation for biological data
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Added by
Tom Trigano
Publication date
2010
fields
Mathematical Statistics
and research's language is
English
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Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective appears in several biological applications like neuroscience or ECG signal processing, in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal-noise ratio, and without a knowledge of the pulse shape is of interest. We suggest an M-estimator leading to a three-stage algorithm: we split our data set in blocks, on which the estimation of the shifts is done by minimizing a cost criterion based on a functional of the periodogram; the estimated shifts are then plugged into a standard density estimator. We show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution. The theory is applied both to simulations and to alignment of real ECG signals. The estimator of the shift distribution performs well, even in the case of low signal-to-noise ratio, and is shown to outperform the standard methods for curve alignment.
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Air pollution constitutes the highest environmental risk factor in relation to heath. In order to provide the evidence required for health impact analyses, to inform policy and to develop potential mitigation strategies comprehensive information is required on the state of air pollution. Information on air pollution traditionally comes from ground monitoring (GM) networks but these may not be able to provide sufficient coverage and may need to be supplemented with information from other sources (e.g. chemical transport models; CTMs). However, these may only be available on grids and may not capture micro-scale features that may be important in assessing air quality in areas of high population. We develop a model that allows calibration between multiple data sources available at different levels of support by allowing the coefficients of calibration equations to vary over space and time, enabling downscaling where the data is sufficient to support it. The model is used to produce high-resolution (1km $times$ 1km) estimates of NO$_2$ and PM$_{2.5}$ across Western Europe for 2010-2016. Concentrations of both pollutants are decreasing during this period, however there remain large populations exposed to levels exceeding the WHO Air Quality Guidelines and thus air pollution remains a serious threat to health.
Currently, novel coronavirus disease 2019 (COVID-19) is a big threat to global health. The rapid spread of the virus has created pandemic, and countries all over the world are struggling with a surge in COVID-19 infected cases. There are no drugs or other therapeutics approved by the US Food and Drug Administration to prevent or treat COVID-19: information on the disease is very limited and scattered even if it exists. This motivates the use of data integration, combining data from diverse sources and eliciting useful information with a unified view of them. In this paper, we propose a Bayesian hierarchical model that integrates global data for real-time prediction of infection trajectory for multiple countries. Because the proposed model takes advantage of borrowing information across multiple countries, it outperforms an existing individual country-based model. As fully Bayesian way has been adopted, the model provides a powerful predictive tool endowed with uncertainty quantification. Additionally, a joint variable selection technique has been integrated into the proposed modeling scheme, which aimed to identify possible country-level risk factors for severe disease due to COVID-19.
Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not efficiently handle functional data and runs into a curse-of dimensionality when presented with high-resolution curves and surfaces. Furthermore, in settings with heteroskedasticity or multimodality, a regression point estimate with standard errors do not fully capture the uncertainty in our predictions. A more informative quantity is the conditional density p(y | x) which describes the full extent of the uncertainty in the response y given covariates x. In this paper we show how random forests can be efficiently leveraged for conditional density estimation, functional covariates, and multiple responses without increasing computational complexity. We provide open-source software for all procedures with R and Pyth
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from multivariatedata analysis: the data depth plot (DD-plot). This DD-plot is a generalization of theunivariate Q-Q plot (quantile-quantile plot). We propose some statistics based onthese DD-plots, and we use bootstrapping techniques to estimate their distributions.We estimate the finite-sample size and power of our test via simulation, obtainingbetter results than other homogeneity test proposed in the literature. Finally, weillustrate the procedure in samples of real heterogeneous data and get consistent results.
Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of $N$ assets from $T$ periods of historical data. Problematically, $N$ is typically of the same order as $T$, which makes the sample covariance matrix estimator perform poorly, both empirically and theoretically. While various other general purpose covariance matrix estimators have been introduced in the financial economics and statistics literature for dealing with the high dimensionality of this problem, we here propose an estimator that exploits the fact that assets are typically positively dependent. This is achieved by imposing that the joint distribution of returns be multivariate totally positive of order 2 ($text{MTP}_2$). This constraint on the covariance matrix not only enforces positive dependence among the assets, but also regularizes the covariance matrix, leading to desirable statistical properties such as sparsity. Based on stock-market data spanning over thirty years, we show that estimating the covariance matrix under $text{MTP}_2$ outperforms previous state-of-the-art methods including shrinkage estimators and factor models.
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