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We propose a method for testing independence of functional variables by using an estimator of the Hilbert–Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We get asymptotic normality of this estimator both under independence hypothesis and under the alternative hypothesis. A simulation study that allows to compare the proposed test to an existing one is provided. [ABSTRACT FROM AUTHOR]

Abstract We establish the mean square convergence, with rate, for an introduced kernel estimator of the conditional density function when the response variable is twice censored. The common case of right censored data can be derived as a particular case. [ABSTRACT FROM AUTHOR]

Abstract We introduce modeling approaches for quantifying the spatiotemporal location and characteristics of clusters with application to the 1993 Jeffrey pine beetle (JPB) forest epidemic attack. [ABSTRACT FROM AUTHOR]

This contribution is part of the recent links between Functional Data and Big Data communities. A selected survey highlights how earlier ideas in high dimensional problems can be adapted in functional setting. [ABSTRACT FROM AUTHOR]

A literature review on spatial big data analysis is given. We show an application of Universal Kriging to a massive spatial dataset. We also present some perspectives of future work in this field. [ABSTRACT FROM AUTHOR]

We give a new large deviation inequality for sums of random variables of the form Z k = f ( X k , X t ) for k , t ∈ N , t fixed, where the underlying process X is β -mixing. The inequality can be used to derive concentration inequalities. We demonstrate its usefulness in the functional kernel regression model of Ferraty et al. (2007) where we study the consistency of dynamic forecasts. [ABSTRACT FROM AUTHOR]

In this note we provide a novel straightforward approach to calculating the significance for higher criticism statistics using a general result due to Steck (1971) coined Steck’s determinant. This result allows users to directly assess higher criticism significance without the need for simulation or asymptotic results. [ABSTRACT FROM AUTHOR]

We extend a current result in the literature by introducing a parametric family of matrix-valued cross-covariance functions, which would help describe multivariate space–time dependence structures for any number of variables. All the direct and cross-covariance functions belong to the Matérn class. The smoothness, space–time separability and scale parameters are allowed to be different for each variable. [ABSTRACT FROM AUTHOR]

In FPCA methods, it is common to assume that the eigenvalues are distinct in order to facilitate theoretical proofs. We relax this assumption, provide a stochastic expansion for the estimated functional principal component projections, and establish their asymptotic normality. [ABSTRACT FROM AUTHOR]

We look into minimax results for the anisotropic functional deconvolution model under the L p -risk, 1 ≤ p < ∞ . We construct lower bounds and show that the wavelet hard-thresholding estimator is asymptotically near-optimal in the L p -risk. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the nonparametric estimation of the functional expectile regression. We use the local linear approach to construct a new estimator of the studied model. The main result of this note is the establishment of the almost complete consistency of this estimator. Our results are obtained under standard assumptions using the Bahadur representation of the conditional expectile. Some simulation studies are carried out to show the finite sample performances of the proposed estimator. [ABSTRACT FROM AUTHOR]

The discrepancies have played an important role in quasi-Monte Carlo Methods. There are various discrepancies for measuring the uniformity of a set of points on unit hypercube and simplex. However, there is no discrepancy with explicit expressions on hyperspheres in the literature. In this paper, we propose a new measure of uniformity, called spherical discrepancy (SD), for designs on the unit hypersphere. Different with the pseudo F -discrepancy, the SD is directly defined on the unit hypersphere in terms of spherical coordinates. A computational formula of the new discrepancy is also given by the functional method. The properties of SD and some illustrative examples are also shown. [ABSTRACT FROM AUTHOR]

In this paper, based on techniques of Malliavin calculus, we obtain an explicit bound for tail probabilities of a general class of additive functionals. Applications to fractional Brownian motion and Cox–Ingersoll–Ross process are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for any k ≥ 1 . [ABSTRACT FROM AUTHOR]

In this paper, we investigate the presence of common intraday periodicity of assets using functional data analysis. We implement the information criterion to select the number of common intraday periodic factors, and model the volatility part using high-frequency data. [ABSTRACT FROM AUTHOR]

In this paper, we provide a strong formulation of the stochastic Gâteaux differentiability in order to study the sharpness of a new characterization, introduced in Mastrolia et al. (2014), of the Malliavin–Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion. [ABSTRACT FROM AUTHOR]

We explore the functional principal component method for estimating regression parameters in functional linear models. We demonstrate that the commonly made assumption concerning unique eigenvalues is unnecessary. Convergence rates are established allowing a variety of sample spaces and dependence structures. [ABSTRACT FROM AUTHOR]

We provide a proof for the functional Feynman–Kac theorem for jump diffusions with path-dependent coefficients and apply our results to the problem of Credit Value Adjustment (CVA) in a bilateral counterparty risk framework. We derive the corresponding functional CVA-PIDE and extend existing results on CVA to a setting which enables the pricing of path-dependent derivatives. [ABSTRACT FROM AUTHOR]

The paper establishes weak convergence in C [ 0 , 1 ] of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained. [ABSTRACT FROM AUTHOR]

Robust nonparametric equivariant M -estimators for the regression function have been extensively studied when the covariates are in R k . In this paper, we derive strong uniform convergence rates for kernel-based robust equivariant M -regression estimator when the covariates are functional. [ABSTRACT FROM AUTHOR]

Recently, Dombry and Éyi-Minko (2013) provided formulae for the distribution of a max-stable process conditional on its values at given sites and proposed a methodology for sampling from this distribution. We generalize their results by allowing for conditions stemming from max-linear functionals of the process. Furthermore, we show that the conditional distribution of the extremal functions, i.e. the spectral functions attaining the imposed conditions, is closely related to the normalized spectral representation. The results are illustrated in several examples. [ABSTRACT FROM AUTHOR]

We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X 0 with a certain probability. We show that if X 0 admits a density that is a Pólya frequency function with E [ X 0 ] = 0 , then k , a 1 , … , a k and π 1 , … , π k are identifiable for any k ≥ 1 . We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f 0 when the latter is symmetric. [ABSTRACT FROM AUTHOR]

In the study of complex organisms, clarifying the association between the evolution of coding genes and the measures of functional variables is of fundamental importance. However, traditional analysis of the evolutionary rate is either built on the assumption of independence between responses or fails to handle a mixture distribution problem. In this paper, we utilize the concept of generalized estimating equations to propose an estimating equation to accommodate continuous and binary probability distributions. The proposed estimate can be shown to have consistency and asymptotic normality. Simulations and data analysis are also presented to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the -estimator for slope function in functional linear regression models. We approximate the slope function by minimizing the loss function based explicitly on functional principal components analysis, and the loss function can be chosen according to what we are estimating. Under mild assumptions, the convergence rate of the estimator of infinite dimensional slope function is derived. A simulation study is conducted to illustrate the numerical performance of the proposed -estimator. [Copyright &y& Elsevier]

Abstract: The Laplace transform of partial sums of the square of a non-centered Gauss–Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced. [Copyright &y& Elsevier]

Abstract: We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation. [Copyright &y& Elsevier]

Abstract: In this paper, we derive the exact uniform convergence rate of the asymmetric normal distribution of the maximum and minimum to its extreme value limit. [Copyright &y& Elsevier]

Abstract: The -means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices. [Copyright &y& Elsevier]

A new nonparametric estimator of the conditional mode when the regressors are functionals is proposed. The main aim of this paper is to establish the almost complete convergence (with rate) of the constructed estimator is estimate under general assumptions in nonparametric functional statistics. A simulation study is carried out to examine, illustrate, the finite samples behavior of the constructed estimator. Finally, a discussion highlighting the impact of this new estimator in nonparametric functional data analysis is also given. [ABSTRACT FROM AUTHOR]

For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of functional CUSUM processes and standard binary segmentation. Our main results are established under conditions allowing for general serial dependence structures in the observations, and low moments. [ABSTRACT FROM AUTHOR]

The Itô formula was extended recently by Dupire (2009) to functionals of paths of continuous semimartingales, and by Cont and Fournié (2010a) to functionals of paths of RCLL semimartingales. In contrast to the traditional formula that applies to functions of the current value of a process, these extensions apply to functionals of the history of a process. By modifying Dupire’s setup we develop new proofs for both the continuous case and the more general RCLL case that are much simpler. We also examine an application to optimal control. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish moderate deviations of regression function estimator on functional data. The pointwise moderate deviation principles of Nadaraya–Watson type estimator is considered by exponential equivalence. Depending on the Vapnik–Chervonenkis size of the class, the uniform moderate deviations are also obtained. [Copyright &y& Elsevier]

Abstract: In this paper we define the class of conditional strong N-demimartingales given a -field . This class includes the partial sum of -negatively associated random variables as a special case. For functions of conditional strong N-demimartingales we compare the conditional expectation with the corresponding one of partial sums of conditionally independent random variables. [Copyright &y& Elsevier]

Abstract: In this work, we study the optimal reinsurance under the Haezendonck risk measure by minimizing the total risk of the insurer. Firstly, the optimal reinsurance model with the expectation premium principle is proposed. Then, on the basis of our model, the explicit solution is obtained, i.e. the stop-loss function. On the other hand, our result can be considered as a promotion of the optimal reinsurance under the CVaR risk measure since CVaR is only a specific case of the Haezendonck risk measure. [Copyright &y& Elsevier]

Abstract: Wavelets have been successfully used for nonparametric function estimation, but for density and hazard functions, estimators must be nonnegative. In this paper, we develop a quasi-continuous nonnegative “wavelet” basis from Daubechies wavelets with good approximation properties. Using this basis, we develop a Bayesian nonparametric estimator of the hazard function for randomly right-censored data. [Copyright &y& Elsevier]

Abstract: We prove a functional central limit theorem for the Hausdorff measure of level sets generated by a smooth Gaussian random field. [Copyright &y& Elsevier]

Abstract: We study subsampling estimators for the limit variance of partial sums of a stationary stochastic process . We establish -consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals of strongly mixing processes. Motivated by recent applications to rank tests, we also study estimators for the series , where is the distribution function of . Simulations illustrate the usefulness of the proposed estimators and of a mean squared error optimal rule for the choice of the block length. [Copyright &y& Elsevier]

Abstract: We consider the estimation of a semiparametric additive isotonic regression model with error-prone covariates. We show the limiting distributions of the proposed estimators of the parametric component as well as the functional component. A simulation study is carried out to investigate the performance of the proposed estimators. [Copyright &y& Elsevier]

Abstract: We treat the topic of the distribution of functionals of discrete ordinal variables. We focus on the probability mass functions of several summary measures and of two important -estimators that can be profitably used in data analysis. What is proposed is illustrated by means of a practical application in customer satisfaction. [Copyright &y& Elsevier]

Abstract: Let be a -valued measurable strictly stationary spatial process, where is a semi-metric space. We study a kernel estimator of the conditional mode of the univariate response variable given the functional variable . The main aim of this paper is to prove the almost complete convergence (with rate) of this estimate [Copyright &y& Elsevier]

Abstract: This paper considers a Sparre Andersen model in which the inter-claim times have a phase-type distribution and the premium rate is a step function depending on the current surplus level. We derive the system of piecewise integro-differential equations for the Gerber–Shiu discounted penalty functions and obtain the closed form expressions of the Gerber–Shiu functions if the claim amount distribution belongs to the rational family. We provide a recursive approach to calculate Gerber–Shiu functions and present an example. [Copyright &y& Elsevier]

Abstract: We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold. [Copyright &y& Elsevier]

Abstract: We prove the existence of the local time of the Ornstein–Uhlenbeck type process driven by a general Lévy process. The conditions of the continuity in time variable and the regularity property of the local time are given, under mild regularity conditions on the driving Lévy process. These results give information about the local properties of sample functions of the process. [Copyright &y& Elsevier]

Abstract: Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see ). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to , the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions. [Copyright &y& Elsevier]

Abstract: This note deals with the study of a functional linear model for time series prediction which combines a functional endogenous predictor and real and functional exogenous variables. A penalized -spline type estimator for the real and functional coefficients is presented and some weak consistency results are derived under suitable conditions. [Copyright &y& Elsevier]

Abstract: In this paper we give an approximation theorem for Rosenblatt processes with , using martingale differences. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a semi-functional linear model in which a scalar response variable is explained by a linear operator of a random function and a nonparametric function of a real-valued random variable. We study the spline estimators of the functional coefficient and nonparametric function and obtain the rates of convergence of the spline estimators. Finally, we present some simulation results that illustrate the performance of our estimation method. [Copyright &y& Elsevier]

Abstract: Let be a family of i.i.d. random vectors in , and be the distributions in of the empirical means . Without imposing any conditions, a new and elementary approach is presented in this note for showing the lower bound of the large deviation principle for , for some rate function which is defined in this note. [Copyright &y& Elsevier]

Abstract: In this paper, some limit processes of occupation time fluctuations of the branching particle systems with varied branching laws from site to site are obtained. The results show that the varied branching laws can not affect the limit processes and the scaling parameters in the case of large dimensions, but in the case of critical dimensions, under suitable assumptions, it changes the limit processes with simple and isotropic spatial structures to those with complicated and anisotropic spatial structures and gives corrections in the scaling parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the conditional least squares estimator (CLSE) of the offspring mean of a branching process with non-stationary immigration based on the observation of population sizes. In the supercritical case, assuming that the immigration variables follow known distributions, conditions guaranteeing the strong consistency of the proposed estimator will be derived. The asymptotic normality of the estimator will also be proved. The proofs are based on direct probabilistic arguments, unlike the previous papers, where functional limit theorems for the process were used. [Copyright &y& Elsevier]