Kendall Transformation: A Robust Representation of Continuous Data for Information Theory

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when discretisation becomes problematic.In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach.The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data.

Estimation of value at risk for stock prices in mobile phone industry

Risk management and market losses prediction played a vital role in the financial sector. Value-at-Risk (VaR) is one of the effective measures for financial risk management. This research studies three mobile phone companies which are Apple Inc, Google Inc and Microsoft Corporation. The stocks of these companies are listed under the National Association of Securities Dealers Automated Quotations stock exchange (NASDAQ). The Value-at-Risk is evaluated by using two non-parametric methods and four parametric methods. Two non-parametric methods used are the basic historical method and age-weighted historical method, while the four parametric methods are normal distribution, student’s t-distribution, generalized extreme value distribution, and variance gamma distribution. Shapiro-Wilk normality test indicates that the return series of the selected companies are not normally distributed. This study found that, at 95% confidence level, the risks of the selected stocks are different for each method, and the stock of Microsoft Corporation is the least risky stock as it gives the lowest VaR. Through the conditional coverage test, this study founds that the age-weighted historical method overestimated the VaR. In addition, this study also concludes that the basic historical method, generalized extreme value distribution and variance gamma distribution are superior to other methods in the backtesting procedure.

Possibilities of predicting lesions of the hepatobiliary system in children with community-acquired pneumonia

Annotation. The prognostic criteria of complications of community-acquired pneumonia and the possibility of developing disorders of the hepatobiliary system (HBS) depending on the concentration in the serum of the secretory leukocyte protease inhibitor (SLPI) were studied. The data of clinical and laboratory examination of 338 children with community-acquired pneumonia aged from one to three years were analyzed. Statistical processing of the results was performed using the system “IBM SPSS Statistica” 12 using parametric and non-parametric methods. It was found that in young children with pneumonia in the serum increases the concentration of SLPI, the level of which depends on the course and severity of pneumonia. It has been shown that the development of lobar pneumonia is significantly higher in patients from the SLPI cohort IV quartile (OR – 1.986, 95% CI – 1.864-2.356), compared with children from the cohort SLPI II and III quartile (OR – 0.476, 95% CI – 0.405- 0.559, OR – 0.494, 95% CI – 10.423-0.576, respectively). At the same time, at the values of SLPI at the level of III-IV quartile (OR – 1.923, 95% CI – 1.457-1.866) there is the development of community-acquired pneumonia. It was found that the development of pathological processes in the organs of HBS is associated with increased levels of SLPI. Thus, patients with polysegmental pneumonia and SLPI III/IV quartile (OR – 2.190, 95% CI – 1.810-2,754) are twice as likely to develop pathology of the hepatobiliary system than children with SLPI I/II quartile (OR – 1.153, 95% CI – 1.071-1.527). The established fact indicates the involvement of SLPI in the pathogenesis not only of pneumonia, but also in disorders of HBS.

Revisiting the cosmic distance duality relation with machine learning reconstruction methods: the combination of HII galaxies and ultra-compact radio quasars

In this paper, we carry out an assessment of cosmic distance duality relation (CDDR) based on the latest observations of HII galaxies acting as standard candles and ultra-compact structure in radio quasars acting as standard rulers. Particularly, two machine learning reconstruction methods [Gaussian Process (GP) and Artificial Neural Network (ANN)] are applied to reconstruct the Hubble diagrams from observational data. We show that both approaches are capable of reconstructing the current constraints on possible deviations from the CDDR in the redshift range $$z\sim 2.3$$ z ∼ 2.3 . Considering four different parametric methods of CDDR, which quantify deviations from the CDDR and the standard cosmological model, we compare the results of the two different machine learning approaches. It is observed that the validity of CDDR is in well agreement with the current observational data within $$1\sigma $$ 1 σ based on the reconstructed distances through GP in the overlapping redshift domain. Moreover, we find that ultra-compact radio quasars could provide $$10^{-3}$$ 10 - 3 -level constraints on the violation parameter at high redshifts, when combined with the observations of HII galaxies. In the framework of ANN, one could derive robust constraints on the violation parameter at a precision of $$10^{-2}$$ 10 - 2 , with the validity of such distance duality relation within $$2\sigma $$ 2 σ confidence level.

Spatio-Temporal Mixed Pixel Analysis of Savanna Ecosystems: A Review

Reliable estimates of savanna vegetation constituents (i.e., woody and herbaceous vegetation) are essential as they are both responders and drivers of global change. The savanna is a highly heterogenous biome with high variability in land cover types while also being very dynamic at both temporal and spatial scales. To understand the spatial-temporal dynamics of savannas, using Earth Observation (EO) data for mixed-pixel analysis is crucial. Mixed pixel analysis provides detailed land cover data at a sub-pixel level which are essential for conservation purposes, understanding food supply for herbivores, quantifying environmental change, such as bush encroachment, and fuel availability essential for understanding fire dynamics, and for accurate estimation of savanna biomass. This review paper consulted 197 studies employing mixed-pixel analysis in savanna ecosystems. The review indicates that studies have so far attempted to resolve the savanna mixed-pixel issues by using mainly coarse resolution data, such as Terra-Aqua MODIS and AVHRR and medium resolution Landsat, to provide fractional cover data. Hence, there is a lack of spatio-temporal mixed-pixel analysis for savannas at high spatial resolutions. Methods used for mixed-pixel analysis include parametric and non-parametric methods which range from pixel-unmixing models, such as linear spectral mixture analysis (SMA), time series decomposition, empirical methods to link the green vegetation parameters with Vegetation Indices (VIs), and machine learning methods, such as regression trees (RT) and random forests (RF). Most studies were undertaken at local and regional scale, highlighting a research gap for savanna mixed pixel studies at national, continental, and global level. Parametric methods for modeling spatio-temporal mixed pixel analysis were preferred for coarse to medium resolution remote sensing data, while non-parametric methods were preferred for very high to high spatial resolution data. The review indicates a gap for long time series spatio-temporal mixed-pixel analysis of savannas using high resolution data at various scales. There is potential to harmonize the available low resolution EO data with new high-resolution sensors to provide long time series of the savanna mixed pixel, which, according to this review, is missing.

Airborne SAR Autofocus Based on Blurry Imagery Classification

Existing airborne SAR autofocus methods can be classified as parametric and non-parametric. Generally, non-parametric methods, such as the widely used phase gradient autofocus (PGA) algorithm, are only suitable for scenes with many dominant point targets, while the parametric ones are suitable for all types of scenes, in theory, but their efficiency is generally low. In practice, whether many dominant point targets are present in the scene is usually unknown, so determining what kind of algorithm should be selected is not straightforward. To solve this issue, this article proposes an airborne SAR autofocus approach combined with blurry imagery classification to improve the autofocus efficiency for ensuring autofocus precision. In this approach, we embed the blurry imagery classification based on a typical VGGNet in a deep learning community into the traditional autofocus framework as a preprocessing step before autofocus processing to analyze whether dominant point targets are present in the scene. If many dominant point targets are present in the scene, the non-parametric method is used for autofocus processing. Otherwise, the parametric one is adopted. Therefore, the advantage of the proposed approach is the automatic batch processing of all kinds of airborne measured data.