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For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.

Knowledge of the dependence structure between financial assets is crucial to improve the performance in financial risk management. It is known that the copula completely summarizes the dependence structure among multiple variables. We propose a multivariate exponential series estimator (ESE) to estimate copula densities nonparametrically. The ESE has an appealing information-theoretic interpretation and attains the optimal rate of convergence for nonparametric density estimations in Stone (1982). More importantly, it overcomes the boundary bias of conventional nonparametric copula estimators. Our extensive Monte Carlo studies show the proposed estimator outperforms the kernel and the log-spline estimators in copula estimation. It also demonstrates that two-step density estimation through an ESE copula often outperforms direct estimation of joint densities. Finally, the ESE copula provides superior estimates of tail dependence compared to the empirical tail index coefficient. An empirical examination of the Asian financial markets using the proposed method is provided.

This strategy significantly reduces the computational overhead and storage overhead required when using the kernel density estimation method to calculate the abnormal evaluation value of the test sample.

To effectively deal with the security threats of botnets to the home and personal Internet of Things (IoT), especially for the objective problem of insufficient resources for anomaly detection in the home environment, a novel kernel density estimation-based federated learning-based lightweight Internet of Things anomaly traffic detection based on nuclear density estimation (KDE-LIATD) method. First, the KDE-LIATD method uses Gaussian kernel density estimation method to estimate every normal sample in the training set. The eigenvalue probability density function of the dimensional feature and the corresponding probability density; then, a feature selection algorithm based on kernel density estimation, obtained features that make outstanding contributions to anomaly detection, thereby reducing the feature dimension while improving the accuracy of anomaly detection; finally, the anomaly evaluation value of the test sample is calculated by the cubic spine interpolation method and anomaly detection is performed.

The simulation experiment results show that the proposed KDE-LIATD method is relatively strong in the detection of abnormal traffic for heterogeneous IoT devices.

With its robustness and compatibility, it can effectively detect abnormal traffic of household and personal IoT botnets.

Scientific collaboration is becoming a common pattern in the social organization of knowledge production. The paper tries to figure out the relationship between scientific collaboration team size and scientific output.

Based on ESI database from year 2009–2019, the paper describes changes of collaboration team size from one author to more than 10 authors in 22 disciplines. Kernel density estimation and multidimensional kernel density estimation method are used to calculate optimal collaboration team size and appropriate collaboration team size in 22 disciplines. As bandwidth is one of the major issues in construction of kernel density estimation, the paper uses five different algorithms to calculate bandwidth. The method with the lowest mean absolute percentage error is chosen. Robustness test is conducted based on different sets of data.

The results show that scientific collaboration becomes more widely and deeply. As time goes by, collaboration team size is becoming larger and larger. Natural science disciplines have larger collaboration team size and faster growth rate than social science disciplines. Considering both qualitative and quantitative measures, the paper proves the universality of optimal and appropriate scientific collaboration team size among 22 disciplines and calculates the specific number.

The paper tries to investigate the law of scientific collaboration team size variation and provide a full picture of evolution of collaboration team size among 22 disciplines in 10 years. The paper first applies distribution method to figure out the relationship between scientific collaboration team size and scientific output and provides optimal collaboration team size and appropriate collaboration team size.

The study aims to reinvestigate the regional urbanization gap in China and some projects are to be presented for reducing the gap.

An innovative weighted kernel density approach is applied for identifying the regional urbanization development with population migration and investment and evaluating the projects.

The regional urbanization gap is 7 and 9 percent with the unconditional estimation, 13 (23) percent and 13 (23) percent with population (investment) weighted estimation between eastern and middle region, eastern and western region, respectively. The project on the interior migration of population by 30 percent and the project on the selective investment enhancement by 30 percent both reduce the regional urbanization gap by about 4 percent between middle and eastern region.

Focus is only on the investigation of urbanization development level with single population migration or investment enhancement; the identifications and projects with joint impact of population and investment are not considered.

The study not only measures the urbanization development with the nonparametric approach but also designs some practicable projects for reducing the regional urbanization gap, which is helpful for the Chinese Government in the policymaking process.

A new, direct method is developed for reducing, to an arbitrary order, the boundary bias of kernel density and density derivative estimators. The basic asymptotic properties of the estimators are derived. Simple examples are provided. A number of simulations are reported, which demonstrate the viability and efficacy of the approach compared to several popular alternatives.

The R environment for statistical computing and graphics (R Development Core Team, 2008) offers practitioners a rich set of statistical methods ranging from random number generation and optimization methods through regression, panel data, and time series methods, by way of illustration. The standard R distribution (base R) comes preloaded with a rich variety of functionality useful for applied econometricians. This functionality is enhanced by user-supplied packages made available via R servers that are mirrored around the world. Of interest in this chapter are methods for estimating nonparametric and semiparametric models. We summarize many of the facilities in R and consider some tools that might be of interest to those wishing to work with nonparametric methods who want to avoid resorting to programming in C or Fortran but need the speed of compiled code as opposed to interpreted code such as Gauss or Matlab by way of example. We encourage those working in the field to strongly consider implementing their methods in the R environment thereby making their work accessible to the widest possible audience via an open collaborative forum.

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

This chapter reviews recent developments in the density discontinuity approach. It is well known that agents having perfect control of the forcing variable will invalidate the popular regression discontinuity designs (RDDs). To detect the manipulation of the forcing variable, McCrary (2008) developed a test based on the discontinuity in the density around the threshold. Recent papers have noted that the sorting patterns around the threshold are often either the researcher’s object of interest or may relate to structural parameters such as tax elasticities through known functions. This, in turn, implies that the behavior of the distribution around the threshold is not only informative of the validity of a standard RDD; it can also be used to recover policy-relevant parameters and perform counterfactual exercises.

The purpose of this paper is to study the dynamics of the distribution of per capita income of Indian states in the post‐reform period, in order to identify trends towards convergence‐club formation, polarization or stratification during this period.

The authors adopt the “distribution dynamics” framework that involves estimating kernel density functions, stochastic kernels and ergodic distributions in order to identify these trends.

The results show that there is polarization in India in the post‐reform period and this is due to the contrary growth dynamics of the middle‐income states resulting in the “vanishing middle” of the distribution.

This is the first study that highlights the contrary growth dynamics among the middle‐income states as the driving force behind the polarization of Indian states in the post‐reform period.