FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode

In this paper we present a new estimator of the conditional density and mode when the co-variables are of functional kind. This estimator is a combination of both, the k-Nearest Neighbours procedure and the functional local linear estimation. Then, for each statistical parameter (conditional density or mode), results concerning the strong consistency and rate of convergence of the estimators are presented. Finally, their performances, for finite sample sizes, are illustrated by using simulated data.     

Assessing the Performance of a Classification‐Based Vulnerability Analysis Model

In this article, a classification model based on the majority rule sorting (MR‐Sort) method is employed to evaluate the vulnerability of safety‐critical systems with respect to malevolent intentional acts. The model is built on the basis of a (limited‐size) set of data representing (a priori known) vulnerability classification examples. The empirical construction of the classification model introduces a source of uncertainty into the vulnerability analysis process: a quantitative assessment of the performance of the classification model (in terms of accuracy and confidence in the assignments) is thus in order. Three different app oaches are here considered to this aim: (i) a model–retrieval‐based approach, (ii) the bootstrap method, and (iii) the leave‐one‐out cross‐validation technique. The analyses are presented with reference to an exemplificative case study involving the vulnerability assessment of nuclear power plants.     

On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method

We investigate the asymptotic behaviour of the recursive Nadaraya–Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya–Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya–Watson estimate. We also illustrate our semiparametric estimation procedure on simulated data.     

How does cultural capital affect educational performance: Signals or skills?

In this paper, we test two mechanisms through which cultural capital might affect educational performance: (a) teachers misinterpreting cultural capital as signals of academic brilliance and (b) cultural capital fostering skills in children that enhance educational performance. We analyse data from the ECLS-K and ECLS-K:2011 from the United States and focus on three aspects of children’s cultural capital: participation in performing arts, reading interest and participation in athletics and clubs. We find that (1) none of the three aspects of cultural capital that we consider affects teachers’ evaluations of children’s academic skills; (2) reading interest has a direct positive effect on educational performance; and (3) the direct effect of reading interest on educational performance does not depend on schooling context. Our results provide little support for the hypothesis that cultural capital operates via signals about academic brilliance. Instead, they suggest that cultural capital fosters skills in children that enhance educational performance. We discuss the theoretical implications of our findings.     

A seasonal mixed-POT model to estimate high flood quantiles from different event types and seasons

Flood events can be caused by several different meteorological circumstances. For example, heavy rain events often lead to short flood events with high peaks, whereas snowmelt normally results in events of very long duration with a high volume. Both event types have to be considered in the design of flood protection systems. Unfortunately, all these different event types are often included in annual maximum series (AMS) leading to inhomogeneous samples. Moreover, certain event types are underrepresented in the AMS. This is especially unsatisfactory if the most extreme events result from such an event type. Therefore, monthly maximum data are used to enlarge the information spectrum on the different event types. Of course, not all events can be included in the flood statistics because not every monthly maximum can be declared as a flood. To take this into account, a mixture Peak-over-threshold model is applied, with thresholds specifying flood events of several types that occur in a season of the year. This model is then extended to cover the seasonal type of the data. The applicability is shown in a German case study, where the impact of the single event types in different parts of a year is evaluated.     

Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression

In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of Lévy processes involved in econometric time series models. To obtain an asymptotic distribution for the proposed estimators, we establish a general asymptotic theory for partial sums of bivariate functionals of time and nonstationary variables. These results show that the proposed estimators in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Finite sample simulations are provided to evaluate the finite sample performance of the proposed model and estimation method.     

A new extension of the FGM copula for negative association

In this paper we introduced a single parameter, absolutely continuous and radially symmetric bivariate extension of the Farlie-Gumbel-Morgenstern (FGM) family of copulas. Specifically, this extension measures the higher negative dependencies than most FGM extensions available in literature. Closed-form formulas for distribution, quantile, density, conditional distribution, regression, Spearman's rho, Kendall's tau, and Gini's gamma are obtained. In addition, a formula for random variate generations is presented in closed-form to facilitate simulation studies. We conduct both paired and multiple comparisons with Frank, Gaussian, and Plackett copulas to investigate the performance based on Vuong's test. Furthermore, the new copula is compared with Frank, Gaussian, and Plackett copulas using both Kolmogorov-Smirnov and Cramér-von Mises type test statistics. Finally, a bivariate dataset is analyzed to compare and illustrate the flexibility of the new copula for negative dependence.     

Simultaneous estimation and inference for multiple response variables

Multivariate data arise frequently in biomedical and health studies where multiple response variables are collected across subjects. Unlike a univariate procedure fitting each response separately, a multivariate regression model provides a unique opportunity in studying the joint evolution of various response variables. In this paper, we propose two estimation procedures that improve estimation efficiency for the regression parameter by accommodating correlations among the response variables. The proposed procedures do not require knowledge of the true correlation structure nor does it estimate the parameters associated with the correlation. Theoretical and simulation results confirm that the proposed estimators are more efficient than the one obtained from the univariate approach. We further propose simple and powerful inference procedures for a goodness-of-fit test that possess the chi-squared asymptotic properties. Extensive simulation studies suggest that the proposed tests are more powerful than the Wald test based on the univariate procedure. The proposed methods are also illustrated through the mother’s stress and children’s morbidity study.     

Nonparametric beta kernel estimator for long and short memory time series

In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long- and the short-range dependency of the process. A cross-validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada     

Inference of the derivative of nonparametric curve based on confidence distribution

Abstract

This paper focuses on inference based on the confidence distributions of the nonparametric regression function and its derivatives, in which dependent inferences are combined by obtaining information about their dependency structure. We first give a motivating example in production operation system to illustrate the necessity of the problems studied in this paper in practical applications. A goodness-of-fit test for polynomial regression model is proposed on the basis of the idea of combined confidence distribution inference, which is the Fisher’s combination statistic in some cases. On the basis of this testing results, a combined estimator for the p-order derivative of nonparametric regression function is provided as well as its large sample size properties. Consequently, the performances of the proposed test and estimation method are illustrated by three specific examples. Finally, the motivating example is analyzed in detail. The simulated and real data examples illustrate the good performance and practicability of the proposed methods based on confidence distribution.