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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.

The aim of this study was to provide an updated meta-analysis assessing the therapeutic equivalence between follitropin alfa biosimilars and the reference medication in women undergoing assisted reproductive technologies (ART).The studies included in the analysis were pooled together in order to estimate the log odds ratio (OR) for binary outcomes and the mean difference (MD) for continuous outcomes along with the corresponding 95% confidence intervals (CI) by using a random effects model. The heterogeneity between the studies was evaluated with the Higgins and χNo differences were found concerning the number of oocytes retrieved at ovum pick-up, the primary endpoint recommended by the European Medicines Agency (EMA) (MD -0.04 CI [-0.78, 0.71], P=0.92). A significantly higher clinical pregnancy rate (OR 0.70 CI [0.53, 0.93], P=0.01) was observed in the reference product group in comparison to the biosimilar follitropin alfa, whereas no statistically significant differences were found for biochemical pregnancy rate, take home baby rate, total follitropin alfa dose, duration of stimulation, and ovarian hyperstimulation syndrome risk.The non-inferiority of biosimilar formulations in comparison to the reference product, with respect to number of oocytes retrieved at ovum pick-up, was shown.

The package implements nonparametric (smooth) regression for spherical data in , and is freely available from the Comprehensive Archive Network (CRAN), licensed under the MIT License. It can be use...

Until now the problem of estimating circular densities when data are observed with errors has been mainly treated by Fourier series methods. We propose kernel-based estimators exhibiting simple construction and easy implementation. Specifically, we consider three different approaches: the first one is based on the equivalence between kernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored, despite its potential for application also in the Euclidean setting. The second approach relies on estimators whose weight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires ad hoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimators which use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all the proposed estimators, we derive asymptotic properties, provide some simulation results, and also discuss some possible generalizations and extensions. Real data case studies are also included.

Fluconazole is a bis-triazole agent used in the treatment of superficial and systemic fungal infections, with vaginal candidiasis being one of the commonest indications to fluconazole treatment. There is increasing concern regarding the teratogenic potential of fluconazole. The aim of this meta-analysis is to pool the literature data in order to evaluate the possible association between fluconazole exposure during pregnancy and birth defects. A total of nine studies were included in the meta-analysis. Results were expressed as odds ratios (OR) with 95 % confidence intervals (CI) and statistical heterogeneity between the studies was evaluated with Higgins index (I2) and Q-test (Q). A p-value

Recently published multicentre, randomized phase III studies suggested the therapeutic equivalence of biosimilar follitropin alpha medicaments compared to the reference product. The aim of this meta-analysis is to pool the results of the three phase III trials in order to provide an overall analysis about the clinical bioequivalence between biosimilars and the originator.The studies included in the analysis were pooled together in order to estimate the log odds ratio (OR) for binary outcomes and the weighted mean difference (WMD) for continuous outcomes along with the corresponding 95% confidence intervals (CI) by using a random effects model. The heterogeneity between the studies was evaluated with the Higgins and Chi-square tests.No differences were found in term of number of oocytes retrieved at ovum pick-up, the primary endpoint recommended by the European Medicines Agency. No statistical differences were also found for biochemical pregnancy rate, take home baby rate, total follitropin alpha dose, duration of stimulation, and OHSS risk. A significantly higher clinical pregnancy rate (Biosimilar follitropin alpha medicaments resulted comparable in comparison to the reference product with respect to the number of oocytes retrieved, that is the primary endpoint recommended by the European Medicines Agency .Further study is needed to evaluate the therapeutic bioequivalence between follitropin alpha biosimilar and the reference medication with respect to secondary endpoints.

We consider the problem of nonparametrically estimating a circular density from data contaminated by angular measurement errors. Specifically, we obtain a kernel-type estimator with weight functions that are reminiscent of deconvolution kernels. Here, differently from the Euclidean setting, discrete Fourier coefficients are involved rather than characteristic functions. We provide some simulation results along with a real data application.

There is convincing evidence that cigarette smoking can impair female reproductive potential. This meta-analysis updates the knowledge regarding the effects of cigarette smoking on clinical outcomes of assisted reproductive technologies (ART). Twenty-six studies were included in this meta-analysis. Results were expressed as odds ratios (OR) with 95% confidence intervals (CI) and statistical heterogeneity between the studies was evaluated with Higgins (I2), Breslow (τ2), Birge’s ratio (H2) indices and Chi-square test (χ2). A P-value

Classifying observations coming from two different spherical populations by using a nonparametric method appears to be an unexplored field, although clearly worth to pursue. We propose some decision rules based on spherical kernel density estimation and we provide asymptotic L 2 properties. A real-data application using global climate data is finally discussed.

We discuss local regression estimators when the predictor lies on the d -dimensional sphere and the response is binary. Despite Di Marzio et al. (2018b), who introduce spherical kernel density classification, we build on the theory of local polynomial regression and local likelihood. Simulations and a real-data application illustrate the effectiveness of the proposals.

We discuss nonparametric estimation of conditional quantiles of a circular distribution when the conditioning variable is either linear or circular. Two different approaches are pursued: inversion of a conditional distribution function estimator, and minimization of a smoothed check function. Local constant and local linear versions of both estimators are discussed. Simulation experiments and a real data case study are used to illustrate the usefulness of the methods.

Circular data occur when the sample space is the unit circle. The peculiarity of a circular measurement scale is that its beginning and its end coincide. After both an origin and an orientation have been chosen, a circular observation can be measured, in radians, by an angle θ ∈ [−pi, pi). Circular data often arise in biology (migration paths, flight directions of animals), meteorology (wind and marine current directions), and geology (orientations of joints and faults, landforms, oriented stones). For comprehensive accounts see, for example, [9] and [1].

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.

Regression of data represented as points on a hypersphere has traditionally been treated using parametric families of transformations that include the simple rigid rotation as an important, special case. On the other hand, nonparametric methods have generally focused on modeling a scalar response through a spherical predictor by representing the regression function as a polynomial, leading to component-wise estimation of a spherical response. We propose a very flexible, simple regression model where for each location of the manifold a specific rotation matrix is to be estimated. To make this approach tractable, we assume continuity of the regression function that, in turn, allows for approximations of rotation matrices based on a series expansion. It is seen that the nonrigidity of our technique motivates an iterative estimation within a Newton–Raphson learning scheme, which exhibits bias reduction properties. Extensions to general shape matching are also outlined. Both simulations and real data are used to illustrate the results. Supplementary materials for this article are available online.

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.

Regression for compositional data has been considered only from a parametric point of view. We introduce local constant and local linear smoothing for this problem, and treat the cases when the response, the predictor or both of them are compositions. To this end, we introduce suitable series expansions of the regression function at a point, along with a class of simplicial kernels. Our methods are formulated according to the Aitchison geometry of the simplex and then, using some relevant properties of the isometric log-ratio transformation, are developed following the principle of ‘working on coordinates’. Asymptotic properties and real-data case studies show the effectiveness of the methods.

Smooth nonparametric estimators based on a kernel method are proposed for cumulative distribution functions (CDFs) and quantiles of circular data. A sound motivation for this is that although for euclidean data similar estimators have been widely studied, for circular data nothing similar seems to exist; albeit, remarkably, in the circular-setting local methods are implemented more easily because of the absence of boundaries on the circle. The only alternative to our method seems to be the empirical CDF, that does not take into account circularity of data when the estimate is near the cut-point, as our local method naturally does. The definition of circular CDF is different from its euclidean counterpart in many respects, and this will give rise to estimators exhibiting some ‘unusual’ features such as, for example, global efficiency measures containing a location parameter and a covariance term. Simulations along with real data case studies illustrate the findings.

Measuring the quality of determined protein structures is a very important problem in bioinformatics. Kernel density estimation is a well-known nonparametric method which is often used for exploratory data analysis. Recent advances, which have extended previous linear methods to multi-dimensional circular data, give a sound basis for the analysis of conformational angles of protein backbones, which lie on the torus. By using an energy test, which is based on interpoint distances, we initially investigate the dependence of the angles on the amino acid type. Then, by computing tail probabilities which are based on amino-acid conditional density estimates, a method is proposed which permits inference on a test set of data. This can be used, for example, to validate protein structures, choose between possible protein predictions and highlight unusual residue angles.

Kernel density estimation for multivariate, circular data has been formulated only when the sample space is the sphere, but theory for the torus would also be useful. For data lying on a d-dimensional torus (d >= 1), we discuss kernel estimation of a density, its mixed partial derivatives, and their squared functionals. We introduce a specific class of product kernels whose order is suitably defined in such a way to obtain L-2-risk formulas whose structure can be compared to their Euclidean counterparts. Our kernels are based on circular densities; however, we also discuss smaller bias estimation involving negative kernels which are functions of circular densities. Practical rules for selecting the smoothing degree, based on cross-validation, bootstrap and plug-in ideas are derived. Moreover, we provide specific results on the use of kernels based on the von Mises density. Finally, real-data examples and simulation studies illustrate the findings.

We consider local smoothing of datasets where the design space is the d-dimensional (d≥ 1) torus and the response variable is real-valued. Our purpose is to extend least squa res local polynomial fitting to this situation. We give both theoretical and empirical results.

Confidence intervals for densities built on the basis of standard nonparametric theory are doomed to have poor coverage rates due to bias. Studies on coverage improvement exist, but reasonably behaved interval estimators are needed. We explore the use of small bias kernel-based methods to construct confidence intervals, in particular using a geometric density estimator that seems better suited for this purpose.

We introduce a class of excited random walks defined on trees. The transience on the supercritical Galton–Watson tree for some processes in this class is proved as well as a conjecture of [Volkov, S., 2003. Excited random walk on trees. Electronic Journal of Probability 8, 1–15] which is closely related.

In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with L2boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast, and the variance diverges exponentially slow. The firs t boosting step is analyzed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data.

The present study offers a meta-analysis of published randomized controlled trials (RCTs) evaluating the outcomes of in vitro fertilization (IVF) cycles using corifollitropin alfa for controlled ovarian stimulation (COS) in comparison with daily recombinant FSH (rFSH). The study examined seven RCTs including 2138 patients receiving corifollitropin alfa and 1788 women receiving daily rFSH for COS. As a novel aspect, this meta-analysis included two specific subpopulations of IVF patients, i.e. egg donors and poor responders. There were no significant differences between corifollitropin alfa and rFSH with respect to the majority of the clinical parameters considered, and comparable were the outcomes in terms of live birth rate, ongoing pregnancy rate, and clinical pregnancy rate. Women receiving corifollitropin alfa had a significantly higher number of metaphase II oocytes at ovum pick-up, and number of formed embryos, in comparison to rFSH. The risk of cycle cancellation due to overstimulation was significantly higher in the corifollitropin alfa group. Ovarian hyperstimulation syndrome (OHSS) incidence was statistically comparable between patients receiving long lasting or daily rFSH. Nevertheless, in view of the fact that corifollitropin alfa resulted in a higher number of metaphase II oocytes collected and a higher number of cycles cancelled due to overstimulation, corifollitropin alfa should be cautiously considered in women with the potential of being hyper responders.

Statistical learning is emerging as a promising field where a number of algorithms from machine learning are interpreted as statistical methods and vice-versa. Due to good practical performance, boosting is one of the most studied machine learning techniques.

In this study simple nonparametric techniques have been adopted to estimate the trend surface of the Swiss rainfall data. In particular we employed the Nadaraya-Watson smoother and in addition, an adapted-by boosting-version of it. Additionally, we have explored the use of the Nadaraya-Watson estimator for the construction of pointwise confidence intervals. Overall, boosting does seem to improve the estimate as much as previous examples and the results indicate that cross-validation can be successfully used for parameter selection on real datasets. In addition, our estimators compare favorably with most of the techniques previously used on this dataset.

Typically, parametric approaches to spatial problems require restrictive assumptions. On the other hand, in a wide variety of practical situations nonparametric bivariate smoothing techniques has been shown to be successfully employable for estimating small or large scale regularity factors, or even the signal content of spatial data taken as a whole.

SUMMARY This paper proposes an algorithm for boosting kernel density estimates. We show that boosting is closely linked to a previously proposed method of bias reduction and indicate how it should enjoy similar properties. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

In present days it is commonly recognized that firm production datasets are affected by some level of random perturbation, and that consequently production frontiers have a stochastic nature. Mathematical programming methods, traditionally employed for frontier evaluation, are then reputed capable of mistaking errors for technical (in)efficiency. Therefore, recent literature is oriented towards a statistical view: frontiers are designed by enveloping data that have been preliminarly filtered from noise. In this paper a nonparametric smoother for filtering panel production data is presented. We pursue a recent approach of Kneip and Simar (1996), and frame it into a more general formulation whose a setting constitutes our specific proposal. The major feature of the method is that noise reduction and outlier detection are faced separately: i) a high order local polynomial fit is used as smoother; and ii) data are weighted by robustness scores. An extensive numerical study on some common production models yields encouraging results from a competition with Kneip and Simar’s filter.

We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability, and ease of implementation widely observed in the standard setting. Our estimates have a multi-output nature, meaning that each coordinate is separately estimated, within a scheme of a regression with a linear response. The main properties include linearity and rotational equivariance. This research has been motivated by the fact that very few models describe this kind of regression. Such current methods are surely not widely employable since they have a parametric nature, and also require the same dimensionality for prediction and response spaces, along with nonrandom design. Our approach does not suffer these limitations. Real-data case studies and simulation experiments are used to illustrate the effectiveness of the method.

A boosting algorithm [1, 2] could be seen as a way to improve the fit of statistical models. Typically, M predictions are operated by applying a base procedure—called a weak learner—to M reweighted samples. Specifically, in each reweighted sample an individual weight is assigned to each observation. Finally, the output is obtained by aggregating through majority voting. Boosting is a sequential ensemble scheme, in the sense the weight of an observation at step m depends (only) on the step m − 1. It appears clear that we obtain a specific boosting scheme when we choose a loss function, which orientates the data re-weighting mechanism, and a weak learner.

We discuss kernel density estimation for data lying on the d-dimensional torus (d ≥ 1). We consider a specific class of product kernels, and formulate exact and asymptotic L 2 properties for the estimators equipped with these kernels. We also obtain the optimal smoothing for the case when the kernel is defined by the product of von Mises densities. A brief simulation study illustrates the main findings.

It is well known that the kernel estimation of multidimensional densities is a difficult task due to the so-called “curse of dimensionality”. The greater the data dimension, the greater is the sample size required to obtain efficient estimates. To reduce such dimensionality effects, we introduce further smoothing sources in addition to the usual bandwidth parametrization. In particular, preliminary kernel estimates are interpreted as smoothed samples and form the basis for successive density estimates, whose average (weights are given by empirical likelihoods of the observed sample) define the proposed sequential density estimator.