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As such skin care house philippines buy benzac on line amex, none is immediately applicable to highdimensional regression analysis acne redness purchase benzac 20gr with visa, where the number of predictors p far exceeds the sample size n. On the other hand, nowadays prevailing in both science and business are data with unprecedented size and dimensionality, calling for the development of high-dimensional influence diagnosis. Detection of influential observations in high-dimensional data analysis, in our opinion, is equally, or to some extent, even more important than in a classical setup. This is partly because the increased dimensionality and complexity of the data may amplify both the chance of an observation being influential as well as its potential impact on the analysis. Moreover, the peculiar data observations themselves may be of practical importance in addition to data modeling. The diagnosis task, nevertheless, is more challenging in high-dimensional data analysis, and is far from a direct extension of existing diagnosis approaches. To the best of our knowledge, influence diagnosis in a high-dimensional setting has received little attention despite its evident importance. In other words, which feature of the analysis should one choose such that its substantial alternation defines an influential observation? In the classical setup, an observation is deemed influential if it incurs serious change in regression coefficient estimate. In high-dimensional regression where p > n, the ordinary least squares estimator is highly unstable as the gram matrix is not invertible. Underlying all those selection methods, one statistic plays a critical role and, that is, the marginal covariance, or equivalently, marginal correlation between the response and the individual covariates. Motivated by this vital observation, we choose the marginal correlation as the feature that defines influential observation. The new measure is applicable to high-dimensional setting where p > n, and is very fast and easy to compute. The choice of the marginal correlation as the defining feature of our influence diagnosis does not imply that the marginal correlation is our ultimate goal of interest. Instead, it reflects influence on important analysis features including parameter estimation, variable selection and screening. This definition of influential observation in a high-dimensional setting can be viewed as our first contribution. Our second contribution is that the explicit asymptotic distribution for the proposed influence measure is derived. Availability of this asymptotic theory offers a principled guidance to determine the critical value for the influence measure. Subsequently, we propose a false discovery rate based procedure for that purpose [5, 6]. However, such a bootstrap procedure requires a parametric model assumption and can be computationally expensive especially for high-dimensional data. By contrast, the asymptotic distribution of the proposed influence measure is attainable in our setup, since the predictor dimension goes to infinity along with the sample size, and the threshold is easy to obtain. First, this solution interweaves influence diagnosis with variable selection, which can be flawed if the influence is reflected on variable selection itself. Moreover, while there exist many competing variable selection methods, it is unclear which selection method is the best choice in the context of influence diagnosis. By contrast, our influence measure is not constrained by any particular variable selection method, and this flexibility could benefit downstream analysis. Before we proceed, we quickly show a simulated example to illustrate two points: first, how various aspects of a high-dimensional regression analysis, including regression coefficient estimation, variable selection and variable screening, can be seriously affected by influential observations, and second, how our proposed measure can help limit such influence. The data was generated from a linear model with p = 1000 predictors, n = 100 observations, among which 10 observations were influential. The magnitude of the influence was dictated by a scalar with a larger value indicating a larger influence. The results are averaged over 200 simulation replicates, and are reported in Figure 1. It is clearly seen from the plot that, influential observations could have drastic effects on various features for highdimensional data analysis.

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Many wells were both shallow and water-intensive skin care 15 days before marriage safe benzac 20 gr, with significant variation in water use from state to state skin care 777 buy benzac 20 gr without prescription. First, wastewater from California fracking operations is sometimes used for crop irrigation, in which case contaminants may seep from the surface of agricultural areas into groundwater. Second, nearly 60 percent of fracking wastewater in California is disposed of in unlined, open-air pits, a practice that is banned in almost all other states. There are 900 such waste disposal pits in the state, most of which are located in Kern County. Third, for many years, fracking wastewater in California has been mistakenly sent, via injection wells, directly into protected aquifers containing clean freshwater. Stream vulnerability to widespread and emergent stressors: a focus on unconventional oil and gas. The depths of hydraulic fracturing and accompanying water use across the United States. Conceding this mistake, the agency has shut down 23 injection wells for fracking waste disposal and established a two-year timetable for phasing out other wells injecting waste into aquifers that should have been protected. While this volume of water represents a small percentage of overall annual water consumption in California, fracking-related water use is, the study noted, disproportionately concentrated in areas of the state already suffering from water shortages. Further drawdowns of these aquifers may interfere with agricultural and municipal water needs. The absence of evidence for direct contamination of groundwater by fracking, the study concluded, reflects absence of investigation rather than evidence of safety. It shows wide geographic and temporal variation in the amount of water used to frack a single well. Median annual water volumes needed to frack a single horizontal oil or gas well increased dramatically-by a factor of 25 or more-between 2000 and 2014. A typical gas or oil well that is horizontally fracked now requires between six and eight Olympic-sized swimming pools of water. In 2014, the majority (58 percent) of new hydraulically fracked oil and gas wells were horizontally drilled. The watersheds where the most water was consumed for hydraulic fracturing are mostly located in southern or southwestern states and correspond to the following shale formations: the Eagle Ford and Barnett Shales in Texas; the HaynesvilleBossier Shale in Texas and Louisiana; the Fayetteville Shale in Arkansas; the Tuscaloosa Shale in Louisiana and Mississippi; and the Woodford Shale in Oklahoma. The Marcellus and Utica Shales-which underlie watersheds in parts of Ohio, Pennsylvania, West Virginia, and New York-were also in the top seven water-consuming shale plays in the United States. Hydraulic fracturing water use variability in the United States and potential environmental implications. The study, which analyzed 550 water samples from public and private water wells, found elevated levels of 19 different hydrocarbon compounds associated with fracking (including the carcinogen benzene and the reproductive toxicant, toluene), detections of methanol and ethanol, and strikingly high levels of 10 different metals. The report also identified potential mechanisms, both above and below ground, by which drinking water resources can be contaminated by fracking. In some cases, drinking water was contaminated by spills of fracking fluid and wastewater. Of the total known spills, 300 reached an environmental receptor such as surface water or groundwater. To the contrary, this report confirmed that drilling and fracking activities have contaminated drinking water in some cases and acknowledged that it cannot ascertain 354 Belitz, K. The message of this report is that we have identified vulnerabilities in the water system that are really important to know about and address to keep risks as low as possible. This finding represents the first fully documented case of a commonly used fracking chemical entering a drinking water source. They can extend deep underground, and can act like superhighways for escaped gas and liquids from drill wells to travel along, for distances greater than a mile away. Of 996 fracking fluid compounds known to be in use, researchers screened 659 of them for their ability to persist, migrate, and reach groundwater aquifers over a short time scale. Of the fifteen compounds so identified, two were commonly used in fracking operations: naphthalene and 2-butoxyethanol. The authors noted that 2-butoxyethanol has been detected in drinking water in a heavily fracked area of Pennsylvania. Naphthalene is a possible human carcinogen that is toxic to red blood cells and contributes to kidney and liver damage. Researchers did not consider the impact of mixtures, interactions between contaminants, or chemical transformations during the fracking or flowback process and noted, "the need for data on the degradation of many 358 U. Assessment of the potential impacts of hydraulic fracturing for oil and gas on drinking water resources (External review draft).

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