Circular local likelihood

We introduce a class of local likelihood circular density estimators, which includes the kernel density estimator as a special case. The idea lies in optimizing a spatially weighted version of the log-likelihood function, where the logarithm of the density is locally approximated by a periodic polynomial. The use of von Mises density functions as weights reduces the computational burden. Also, we propose closed-form estimators which could form the basis of counterparts in the multidimensional Euclidean setting. Simulation results and a real data case study are used to evaluate the performance and illustrate the results

A note on nonparametric estimation of circular conditional densities

The conditional density offers the most informative summary of the relationship between explanatory and response variables. We need to estimate it in place of the simple conditional mean when its shape is not well-behaved. A motivation for estimating conditional densities, specific to the circular setting, lies in the fact that a natural alternative of it, like quantile regression, could be considered problematic because circular quantiles are not rotationally equivariant. We treat conditional density estimation as a local polynomial fitting problem as proposed by \cite{Fan et al.:1996} in the euclidean setting, and discuss a class of estimators in the cases when the conditioning variable is either circular or linear. Asymptotic properties for some members of the proposed class are derived. The effectiveness of the methods for finite sample sizes is illustrated by simulation experiments and an example using real data

Nonparametric estimating equations for circular probability density functions and their derivatives

We propose estimating equations whose unknown parameters are the values taken by a circular density and its derivatives at a point. Specifically, we solve equations which relate local versions of population trigonometric moments with their sample counterparts. Major advantages of our approach are: higher order bias without asymptotic variance inflation, closed form for the estimators, and absence of numerical tasks. We also investigate situations where the observed data are dependent. Theoretical results along with simulation experiments are provided

Temperature effect on the sensitivity of the copepod Eucyclops serrulatus (Crustacea, Copepoda, Cyclopoida) to agricultural pollutants in the hyporheic zone

Abstract The sensitivity of freshwater invertebrates to agricultural pollutants is supposed to increase with rising temperature due to global warming. The aim of this study was to measure the effect of temperature on the lethal toxicity of ammonia-N, the herbicide Imazamox and the mixture of the two chemicals, in the adults and the juveniles of a population of the copepod Eucyclops serrulatus. This is a widely distributed species found in surface waters, in transitional habitats between surface water and groundwater, and in genuine groundwater environments. We tested the sensitivity by short-term bioassays (96 h) at 15°C and 18°C, respectively. Our results highlighted the following: (1) increasing temperature affected the sensitivity of the adults to ammonia-N and of the juveniles to the mixture, all of which were more sensitive to its detrimental effects at 18°C; (2) the juvenile stages were more sensitive than the adults to all toxicants, and (3) for all combinations of chemicals and temperatures, the effects were synergistic and approximately one order of magnitude greater than those expected according to a concentration addition model when comparing the LC50 for each chemical in the mixture with the LC50s of chemicals individually assayed. Overall, in a context of global change, ammonia-N and mixtures of agricultural pollutants may affect the survival rate of species that spend a part or the whole life-cycle in the hyporheic habitat, with detrimental effects to biodiversity and ecosystem services provided by the hyporheic biota

Kernel regression for errors-in-variables problems in the circular domain

We study the problem of estimating a regression function when the predictor and/or the response are circular random variables in the presence of measurement errors. We propose estimators whose weight functions are deconvolution kernels defined according to the nature of the involved variables. We derive the asymptotic properties of the proposed estimators and consider possible generalizations and extensions. We provide some simulation results and a real data case study to illustrate and compare the proposed methods

Sarcopenia and vitamin d deficiency in patients with crohn’s disease: Pathological conditions that should be linked together

Sarcopenia is a prevalent condition in patients with Crohn’s disease (CD), representing an independent predictor factor for the development of major postoperative complications. Thus, a proper assessment of the muscle strength, by using different validated tools, should be deemed an important step of the clinical management of these patients. Patients with CD are frequently malnourished, presenting a high prevalence of different macro-and micro-nutrient deficiencies, including that of vitamin D. The available published studies indicate that vitamin D is involved in the regulation of proliferation, differentiation, and regeneration of muscle cells. The relationship between vitamin D deficiency and sarcopenia has been extensively studied in other populations, with interesting evidence in regards to a potential role of vitamin D supplementation as a means to prevent and treat sarcopenia. The aim of this review was to find studies that linked together these pathological conditions

Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research