Nonparametric Kernel Estimation Research Articles

Spatiotemporal evolution of dengue outbreaks in Brazil.

Dengue is a mosquito-borne febrile disease infecting millions of people worldwide. Identification of high-risk areas will allow public health services to concentrate their efforts in areas where outbreaks are most likely to occur. The present study focuses on describing the spatiotemporal evolution of dengue outbreaks in Brazil from 2000 to 2018. To assess the pattern behaviour and spatiotemporal trend of dengue outbreaks, the non-parametric kernel estimator method and the Mann-Kendall test, respectively, were used. Bivariate global Moran's I statistic was used to test the spatial correlation between dengue outbreaks, temperature, precipitation and population data. Our results revealed that the transmission cycles of dengue outbreaks vary in different spatiotemporal scenarios, with intermittent periods of outbreaks. In the period of study, outbreak clusters were primarily concentrated in the Northeast region and the transmission of dengue extended throughout Brazil until 2018. The probability of occurrence of dengue outbreaks was higher in high temperatures. Further, these space-time fluctuations in the number of outbreaks in the different regions were probably related to the high mobility between the populations of these regions, circulating serotypes and susceptible populations. The distribution of dengue outbreaks is not random; it can be modified by socioeconomic and climatic moving boundaries.

TTT-SiZer: A graphic tool for aging trends recognition

A new graphic tool is presented to test aging trends based on lifetime data. The graphical test is developed by means of scale and space inference about the Total-Time-on-Test transform and its first and second derivatives. The graphic tool TTT-SiZer is defined considering nonparametric local polynomial kernel estimators and constructing the corresponding (simultaneous as well as punctual) confidence intervals around three different curves. The finite sample properties of the method are evaluated by a simulation study and the comparison with other non-graphical tests shows that the graphical test helps localize discrepancies of empirical data concerning a given hypothesized aging property, thus allowing to solve the problem locally.

Estimation of a nonparametric model for bond prices from cross-section and time series information

We develop a novel estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time series context. The resulting estimator is used for predicting individual bond prices given the full schedule of their future payments. In addition, it is able to capture the yield curve shapes and dynamics commonly observed in the fixed income markets. We establish the consistency, the rate of convergence, and the asymptotic normality of the proposed estimator. A Monte Carlo exercise illustrates the good performance of the method under different scenarios. We apply our methodology to the daily CRSP bond market dataset, and compare ours with the popular Diebold and Li (2006) method.

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

Measuring Granger Causality in Quantiles

ABSTRACT We consider measures of Granger causality in quantiles, which detect and quantify both linear and nonlinear causal effects between random variables. The measures are based on nonparametric quantile regressions and defined as logarithmic functions of restricted and unrestricted expectations of quantile check loss functions. They can consistently be estimated by replacing the unknown expectations of check loss functions by their nonparametric kernel estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measures. We establish the asymptotic distribution of this estimator, which can be used to build tests for the statistical significance of the measures. Thereafter, we show the validity of a smoothed local bootstrap that can be used in finite-sample settings to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite-sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, we provide an empirical application to illustrate the usefulness of measuring Granger causality in quantiles. We quantify the degree of predictability of the quantiles of equity risk premium using the variance risk premium, unemployment rate, inflation, and the effective federal funds rate. The empirical results show that the variance risk premium and effective federal funds rate have a strong predictive power for predicting the risk premium when compared to that of the predictive power of the other two macro variables. In particular, the variance risk premium is able to predict the center, lower, and upper quantiles of the distribution of the risk premium; however, the effective federal funds rate predicts only the lower and upper quantiles. Nevertheless, unemployment and inflation rates have no effect on the risk premium.

A perturbation analysis of Markov chains models with time-varying parameters

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process developed in the literature and that can be used for studying a wide class of Markov processes. To this end, for some families of $V$-geometrically ergodic Markov kernels indexed by a real parameter $u$, we give conditions under which the invariant probability distribution is differentiable with respect to $u$, in the sense of signed measures. Our results also complete the existing literature for the perturbation analysis of Markov chains, in particular when exponential moments are not finite. Our conditions are checked on several original examples of locally stationary processes such as integer-valued autoregressive processes, categorical time series or threshold autoregressive processes.

A robust hierarchical clustering for georeferenced data

The detection of spatially contiguous clusters is a relevant task in geostatistics since near located observations might have similar features than distant ones. Spatially compact groups can also improve clustering results interpretation according to the different detected subregions. In this paper, we propose a robust metric approach to neutralize the effect of possible outliers, i.e. an exponential transformation of a dissimilarity measure between each pair of locations based on non-parametric kernel estimator of the direct and cross variograms (Fouedjio, 2016) and on a different bandwidth identification, suitable for agglomerative hierarchical clustering techniques applied to data indexed by geographical coordinates. Simulation results are very promising showing very good performances of our proposed metric with respect to the baseline ones. Finally, the new clustering approach is applied to two real-word data sets, both giving locations and top soil heavy metal concentrations.

Nonparametric Time-Varying Panel Data Models with Heterogeneity

Panel data subject to heterogeneity in both cross-sectional and time-serial directions are commonly encountered across social and scientific fields. To address this problem, we propose a class of time-varying panel data models with individual-specific regression coefficients and interactive common factors. This results in a model capable of describing heterogeneous panel data in terms of time-varyingness in the time-serial direction and individual-specific coefficients among cross-sections. Another striking generality of this proposed model relies on its compatibility with endogeneity in the sense of interactive common factors. Model estimation is achieved through a novel duple least--square (DLS) iteration algorithm, which implements two least--square estimation methods recursively and incorporates nonparametric kernel estimation for time-varying coefficients simultaneously. Its unified ability in estimation is nicely illustrated according to flexible applications on various cases with exogenous or endogenous common factors. Established asymptotic theory for the proposed DLS estimators benefits practitioners by demonstrating the effectiveness of iteration in eliminating estimation biases gradually along with iterative steps. We further show that our model and estimation method perform well on simulated data in various scenarios as well as an OECD healthcare expenditure dataset. The time--variation and heterogeneity among cross-sections are confirmed by our empirical analysis.

Forecasting With Dynamic Panel Data Models

This paper considers the problem of forecasting a collection of short time series using cross‐sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross‐sectional information to transform the unit‐specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a nonparametric kernel estimate of the Tweedie correction is asymptotically equivalent to the risk of a predictor that treats the correlated random effects distribution as known (ratio optimality). Our empirical Bayes predictor performs well compared to various competitors in a Monte Carlo study. In an empirical application, we use the predictor to forecast revenues for a large panel of bank holding companies and compare forecasts that condition on actual and severely adverse macroeconomic conditions.

Kernel-based Volatility Generalised Least Squares

The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T-consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.

On Hybridizations of Fourth Order Kernel of the Beta Polynomial Family.

The usual second order nonparametric kernel estimators are of wide uses in data analysis and visualization but constrained with slow convergence rate. Higher order kernels provide a faster convergence rates and are known to be bias reducing kernels. In this paper, we propose a hybrid of the fourth order kernel which is a merger of two successive fourth order kernels and the statistical properties of these hybrid kernels were study. The results of our simulation reveals that the proposed higher order hybrid kernels outperformed their corresponding parent’s kernel functions using the asymptotic mean integrated squared error.

Analysis of interval-grouped data in weed science: The binnednp Rcpp package.

Weed scientists are usually interested in the study of the distribution and density functions of the random variable that relates weed emergence with environmental indices like the hydrothermal time (HTT). However, in many situations, experimental data are presented in a grouped way and, therefore, the standard nonparametric kernel estimators cannot be computed.Kernel estimators for the density and distribution functions for interval‐grouped data, as well as bootstrap confidence bands for these functions, have been proposed and implemented in the binnednp package. Analysis with different treatments can also be performed using a bootstrap approach and a Cramér‐von Mises type distance. Several bandwidth selection procedures were also implemented. This package also allows to estimate different emergence indices that measure the shape of the data distribution. The values of these indices are useful for the selection of the soil depth at which HTT should be measured which, in turn, would maximize the predictive power of the proposed methods.This paper presents the functions of the package and provides an example using an emergence data set of Avena sterilis (wild oat).The binnednp package provides investigators with a unique set of tools allowing the weed science research community to analyze interval‐grouped data.

Discrete multivariate associated kernel estimators using two multiplicative bias correction methods

Two multiplicative bias correction (MBC) approaches for nonparametric multivariate associated kernel estimators for joint probability mass functions in the context of discrete supported data are proposed. Both techniques reach an optimal rate of convergence of the mean integrated squared error. We show some properties of the MBC multivariate associated kernel estimators like bias, variance and mean integrated square error. A simulation study and an application on a real count data set illustrate the performance of the MBC estimators based on the Dirac Discrete Uniform associated kernel in terms of the integrated squared error and integrated squared bias.

A semiparametric approach for modelling multivariate nonlinear time series

AbstractIn this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada

Nonparametric Kernel Method to Hedge Downside Risk

AbstractWe propose a nonparametric kernel estimation method (KEM) that determines the optimal hedge ratio by minimizing the downside risk of a hedged portfolio, measured by conditional value‐at‐risk (CVaR). We also demonstrate that the KEM minimum‐CVaR hedge model is a convex optimization. The simulation results show that our KEM provides more accurate estimations and the empirical results suggest that, compared to other conventional methods, our KEM yields higher effectiveness in hedging the downside risk in the weather‐sensitive markets.

Nonparametric kernel estimation of expected shortfall under negatively associated sequences

In this article, Bahadur type expansions of a nonparametric kernel estimator for ES under NA sequences are given. The strong consistency and the uniformly asymptotic normality of the estimator are yielded from the Bahadur type expansions, while the convergence rates of the above asymptotic properties are also obtained. Moreover, the expectation, the variance and the mean squared error (MSE) of the estimator are given. Besides, the optimal bandwidth selection of this estimator is discussed. We point out that all above results are based on the NA sequences. Finally, we conduct numerical simulations and compare performances of some ES estimators.

Human\u2013vegetation interactions during the Holocene in North America

Between the initial colonization of North America and the European settlement period, Indigenous American land use practices shaped North American landscapes and ecosystems, but a critical question is the extent of these impacts on the land, and how these influenced the distributions of the flora and fauna. The present study addresses this question by estimating the spatial correlation between continental-scale records of fossil pollen and archaeological radiocarbon data, and provides a detailed analysis of the spatiotemporal relationship between palaeo-populations and ten important North American pollen taxa. Maps of Indigenous American population density, based on the Canadian Archaeological Radiocarbon Database, are compared to maps of plant abundance as estimated by pollen records from the Neotoma Paleoecology Database, using nonparametric kernel estimators and cross-correlation techniques. Periods of high spatial cross-correlation (either positive or negative) between population density and plant abundance were identified, but these associations were intermittent and did not increase towards the present. In many cases, high values of population density corresponded with high values of a particular taxon in one region, but simultaneously corresponded with low values in other regions, lessening the overall correlation between the two fields. This analysis suggests that human impacts were not significant enough to be identified at a continental scale, either due to low population numbers or land use, implying significant impacts of ancient human activities on the vegetation were regional rather than continental.

Nonparametric Blind Super-Resolution Using Adaptive Heavy-Tailed Priors

Single-image nonparametric blind super-resolution is a fundamental image restoration problem yet largely ignored in the past decades among the computational photography and computer vision communities. An interesting phenomenon is observed that learning-based single-image super-resolution (SR) has been experiencing a rapid development since the boom of the sparse representation in 2005s and especially the representation learning in 2010s, wherein the high-res image is generally blurred by a supposed bicubic or Gaussian blur kernel. However, the parametric assumption on the form of blur kernels does not hold in most practical applications because in real low-res imaging a high-res image can undergo complex blur processes, e.g., Gaussian-shaped kernels of varying sizes, ellipse-shaped kernels of varying orientations, curvilinear kernels of varying trajectories. The paper is mainly motivated by one of our previous works: Shao and Elad (in: Zhang (ed) ICIG 2015, Part III, Lecture notes in computer science, Springer, Cham, 2015). Specifically, we take one step further in this paper and present a type of adaptive heavy-tailed image priors, which result in a new regularized formulation for nonparametric blind super-resolution. The new image priors can be expressed and understood as a generalized integration of the normalized sparsity measure and relative total variation. Although it seems that the proposed priors are simple, the core merit of the priors is their practical capability for the challenging task of nonparametric blur kernel estimation for both super-resolution and deblurring. Harnessing the priors, a higher-quality intermediate high-res image becomes possible and therefore more accurate blur kernel estimation can be accomplished. A great many experiments are performed on both synthetic and real-world blurred low-res images, demonstrating the comparative or even superior performance of the proposed algorithm convincingly. Meanwhile, the proposed priors are demonstrated quite applicable to blind image deblurring which is a degenerated problem of nonparametric blind SR.

Image offset density distribution model and recognition of hand knuckle

The accurate description of hand posture plays an important role in the man-machine interaction involved in coordinated assembly. Knuckle image extraction and recognition are of great significance to refine and enrich hand-pose information. These are based on nonparametric density kernel estimation observation sets corresponding to unilateral and bilateral excursion of the hand knuckle gray image. In this paper, sets of pixel positions belonging to the upper- and middle-density intervals are used as two types of image targets. Random clustering and random field multi-classification target modeling are used to learn and estimate the two target distributions of the image. The discriminant field classification learning method is used to fuse the two kinds of target models. A comprehensive representation of the image offset features is obtained. Finally, the knuckle image sample set is used to train the model, and the adaptive threshold is used to identify the hand knuckle image. The results show that the proposed method is feasible.

Estimation of a Nonparametric model for Bond Prices from Cross-section and Time series Information

We develop estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time series context. The resulting estimator is used for predicting individual bond prices given the full schedule of their future payments. In addition, it is able to capture the yield curve shapes and dynamics commonly observed in the fixed income markets. We establish the consistency, the rate of convergence, and the asymptotic normality of the proposed estimator. A Monte Carlo exercise illustrates the good performance of the method under different scenarios. We apply our methodology to the daily CRSP bond market dataset, and compare ours with the popular Diebold and Li (2006) method.