Volcano distribution and tectonics: A planetoidic perspective

ABSTRACT Volcanic activity is ultimately controlled by processes that take place many kilometers beneath the surface of a planet. The deeper processes are unlikely to reach the surface without some degree of modification at shallower levels. Nevertheless, traces of those deeper processes may still be found when examining the final products at the surface. In this work, it is shown that it is possible to gain insights concerning the integrated contribution of deep structures through the study of the spatial distribution of volcanic vents at the surface. The method here described relies on the systematic use of increasing smoothing factors in Gaussian kernel estimations. The sequences of probability density functions thus generated are equivalent to images obtained with an increasing wavelength, which therefore have the power to penetrate deeper below the surface. Although the resolution of this method is much smaller than the resolution provided by seismic or other geophysical surveys, it has the advantages of ease of implementation, extremely low cost, and remote application. Thus, the reported method has great value as a first-order exploration tool to investigate the deep structure of a planet, and it can make important contributions to our understanding of the volcano-tectonic relationship, not only on Earth, but also across the various bodies of the solar system where volcanic activity has been documented.

A Comparison Between New Modification of ANWK and Classical ANWK Methods in Nonparametric Regression

Nonparametric kernel estimators are mostly used in a variety of statistical research fields. Nadaraya-Watson kernel estimator (NWK) is one of the most important nonparametric kernel estimator that is often used in regression models with a fixed bandwidth. In this article, we consider the four new Proposed Adaptive Nadaraya-Watson Kernel Regression Estimators (Interquartile Range, Standard Deviation, Mean Absolute Devotion, and Median Absolute Deviation) rather than (Fixed Bandwidth, Adaptive Geometric, Adaptive Mean, Adaptive Range, and Adaptive Median). The outcomes in both simulation and actual data in Leukemia Cancer show that the four new ANW Kernel Estimators (Interquartile Range, Standard Deviation, Mean Absolute devotion, and Median Absolute Deviation) is more effective than the kernel estimations with fixed bandwidth in previous studies using Mean Square Error (MSE) Criterion.

Adaptive Kernel Estimation of the Conditional Quantiles

In this paper, we define the adaptive kernel estimation of the conditional distribution function (cdf) for independent and identically distributed (iid) data using varying bandwidth. The bias, variance and the mean squared error of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated.<br /><br />The results of the simulation study show that the adaptive kernel estimation of the conditional quantiles with varying bandwidth have better performance than the kernel estimations with fixed bandwidth.

Interpolation of Missing Precipitation Data Using Kernel Estimations for Hydrologic Modeling

Precipitation is the main factor that drives hydrologic modeling; therefore, missing precipitation data can cause malfunctions in hydrologic modeling. Although interpolation of missing precipitation data is recognized as an important research topic, only a few methods follow a regression approach. In this study, daily precipitation data were interpolated using five different kernel functions, namely, Epanechnikov, Quartic, Triweight, Tricube, and Cosine, to estimate missing precipitation data. This study also presents an assessment that compares estimation of missing precipitation data throughKth nearest neighborhood (KNN) regression to the five different kernel estimations and their performance in simulating streamflow using the Soil Water Assessment Tool (SWAT) hydrologic model. The results show that the kernel approaches provide higher quality interpolation of precipitation data compared with theKNN regression approach, in terms of both statistical data assessment and hydrologic modeling performance.

A Criterion for the Fuzzy Set Estimation of the Regression Function

We propose a criterion to estimate the regression function by means of a nonparametric and fuzzy set estimator of the Nadaraya-Watson type, for independent pairs of data, obtaining a reduction of the integrated mean square error of the fuzzy set estimator regarding the integrated mean square error of the classic kernel estimators. This reduction shows that the fuzzy set estimator has better performance than the kernel estimations. Also, the convergence rate of the optimal scaling factor is computed, which coincides with the convergence rate in classic kernel estimation. Finally, these theoretical findings are illustrated using a numerical example.