Kernel Smoothing Research Articles

Evmix: An R package for Extreme Value Mixture Modeling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

evmix is an R package (R Core Team 2017) with two interlinked toolsets: i) for extreme value modeling and ii) kernel density estimation. A key issue in univariate extreme value modeling is the choice of threshold beyond which the asymptotically motivated extreme value models provide a suitable tail approximation. The package implements almost all existing extreme value mixture models, which permit objective threshold estimation and uncertainty quantification. Some traditional diagnostic plots for threshold choice are provided. Kernel density estimation with a range of kernels is provided, including cross-validation maximum likelihood inference for the bandwidth. A key contribution over existing kernel smoothing packages in R is that a wide range of boundary corrected kernel density estimators are implemented, which are designed for populations with bounded support. These non-parametric density estimators are also incorporated into the extreme value mixture model framework to describe the density below the threshold. The quartet of density, distribution, quantile and random number generation functions is provided along with parameter estimation by likelihood inference and standard model fit diagnostics, for both the mixture models and kernel density estimators. The key features of the mixture models and (boundary corrected) kernel density estimators are described and their implementation using the package demonstrated.

Smoothed Conditional Scale Function Estimation in AR(1)-ARCH(1) Processes

The estimation of the Smoothed Conditional Scale Function for time series was taken out under the conditional heteroscedastic innovations by imitating the kernel smoothing in nonparametric QAR-QARCH scheme. The estimation was taken out based on the quantile regression methodology proposed by Koenker and Bassett. And the proof of the asymptotic properties of the Conditional Scale Function estimator for this type of process was given and its consistency was shown.

Inference of high-dimensional linear models with time-varying coefficients

We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge regression estimator. Due to the non-stationarity feature of the model, dynamic bias-variance decomposition of the estimator is obtained. With a bias-correction procedure, the local null distribution of the estimator of the time-varying coefficient vector is characterized for iid Gaussian and heavy-tailed errors. The limiting null distribution is also established for Gaussian process errors, and we show that the asymptotic properties differ between short-range and long-range dependent errors. Here, p-values are adjusted by a Bonferroni-type correction procedure to control the familywise error rate (FWER) in the asymptotic sense at each time point. The finite sample size performance of the proposed inference algorithm is illustrated with synthetic data and an application to learn brain connectivity by using the resting-state fMRI data for Parkinson's disease.

Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk.

Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role, it also forms an integral part of estimation of functionals such as the density-ratio or "relative risk" surface. Originally developed with the epidemiological motivation of examining fluctuations in disease risk based on samples of cases and controls collected over a given geographical region, such functions have also been successfully used across a diverse range of disciplines where a relative comparison of spatial density functions has been of interest. This versatility has demanded ongoing developments and improvements to the relevant methodology, including use spatially adaptive smoothers; tests of significantly elevated risk based on asymptotic theory; extension to the spatiotemporal domain; and novel computational methods for their evaluation. In this tutorial paper, we review the current methodology, including the most recent developments in estimation, computation, and inference. All techniques are implemented in the new software package sparr, publicly available for the R language, and we illustrate its use with a pair of epidemiological examples.

Determining optimum wavelengths for leaf water content estimation from reflectance: A distance correlation approach

This paper proposes a method to estimate leaf water content from reflectance in four commercial vineyard varieties by estimating the local maxima of a distance correlation function. First, it applies four different functional regression models to the data and compares the models to test the viability of estimating water content from reflectance. It then applies our methodology to select a small number of wavelengths (optimum wavelengths) from the continuous spectrum, which simplifies the regression problem. Finally, it compares the results to those obtained by means of two different methods: a nonparametric kernel smoothing for variable selection in functional data and a wavelet-based weighted LASSO functional linear regression. Our approach proved to have some advantages over these two testing approaches, mainly in terms of the computing time and the lack of assumption of an underlying model. Finally, the paper concludes that estimating water content from a few wavelengths is almost equivalent to doing so using larger wavelength intervals.

Estimation of spot volatility with superposed noisy data

By using high frequency financial data, we nonparametrically estimate the spot volatility at any given time point, while the simultaneous presence of multiple transactions and market microstructure noise in the observation procedure are considered. Our estimator is based on the summation of the locally ranged increments, while kernel smoothing give us spot volatility. Besides, the microstructure noise can be estimated and removed, if it is modeled as bid-ask spread, which is a frequently used assumption. The consistency and asymptotic normality of the estimator are established. We do some simulation studies to assess the finite sample performance of our estimator. The estimator is also applied to some real data sets, further, the relationship between multiple records and spot volatility is also explored.

Discretization of a New Method for Localizing Discontinuity Lines of a Noisy Two-Variable Function

We consider the ill-posed problem of localizing (finding the position of) discontinuity lines of a noisy function of two variables. New regularizing methods of localization are constructed in a discrete form. In these methods, the smoothing kernel is varying, which simplifies the implementation of the algorithms. We obtain bounds for the localization error of the methods and for their separability threshold, which is another important characteristic.

A two-step estimation of diffusion processes using noisy observations

ABSTRACTThis paper considers the estimation of unknown drift and diffusion functions of a one-dimensional diffusion process when the observation is a discrete sampling of with an additive noise, at times , . In order to reduce the noise effect, a two-step estimation method is proposed based on the joint use of the pre-averaging technique and kernel smoothing. Under some suitable conditions, the proposed estimators are consistent and asymptotically normal. A simulation study and a real data application are given to evaluate the finite sample performance of the proposed method in comparison with alternative methods.

Testing normality for unconditionally heteroscedastic macroeconomic variables

In this paper the testing of normality for unconditionally heteroscedastic macroeconomic time series is studied. It is underlined that the classical Jarque-Bera test (JB hereafter) for normality is inadequate in our framework. On the other hand it is found that the approach which consists in correcting the heteroscedasticity by kernel smoothing for testing normality is justified asymptotically. Nevertheless it appears from Monte Carlo experiments that such a methodology can noticeably suffer from size distortion for samples that are typical for macroeconomic variables. As a consequence a parametric bootstrap methodology for correcting the problem is proposed. The innovations distribution of a set of inflation measures for the U.S., Korea and Australia are analyzed.

Afforestation and climatic niche dynamics of black locust (Robinia pseudoacacia)

Abstract Many tree species have been introduced outside their native ranges, but there is little knowledge of their niche dynamics during afforestation in different regions. Here, we test the climatic niche dynamics of a species, black locust (Robinia pseudoacacia), planted worldwide, between its native range (southeastern parts of United States) and four introduced ranges (North America, Europe, East Asia, and Australia). A principal component analysis method with kernel smoothers was applied to species’ occurrence densities to investigate the climatic niche centroid, breadth and unfilling/expansion between native and introduced ranges of black locust. The niche equivalency test, the niche similarity test, and the niche centroid/breadth shift tests were used to evaluate the conservatism and dynamics of realized niche of black locust. Niche equivalency/similarity tests show that only the European population has the same identical climatic niche as the native population and all introduced population in four areas are similar to native population than expected by chance with niche overlap between native and introduced areas ranging from 0.13 to 0.4. Niche centroid/breadth shift tests reveal that the niche centroid of black locust will significantly shift to warm or colder areas, as well as drier areas, and the niche breadth of black locust will significantly broaden both in water and heat gradients in the four introduced ranges separately. Niche partitioning shows that the proportion of niche unfilling occurred from 0 to 27% and that of niche expansion occurred in the 42–83% range. Our results imply that the internal causes of realized niche dynamics of black locust are mainly due to the release of biotic constraints and change in dispersal capability, but the relative importance of these factors is different among the four introduced ranges. Our study suggests that black locust conserves its climatic niche in the afforestation process allowing future studies to use ecological niche models to predict areas with suitable habitat for introduction and cultivation around the world and respond to climate change needs.

Independent and synergistic effects of self- and public stigmas on quality of life of HIV-infected persons

ABSTRACTStigma has a potential impact on the quality of life of HIV-infected individuals over time. There is little empirical evidence regarding the first appearance and dynamic changes among different types of stigma, self-stigma and public-stigma, and their impacts on quality of life over time in HIV-infected persons. The purpose of this study was to assess the dynamic changes in self-stigma and public-stigma along the time course and determined their independent and synergistic impacts on quality of life. A Cross-sectional study was conducted at Two HIV-designed hospitals and two branches of non-government an-AIDS organizations in Wes Java, Indonesia. Persons diagnosed with HIV completed self-report measures of stigma and the questionnaire of World Health Organization Quality of Life (WHOQOL)-HIV brief version. Kernel smoothing method and multivariate linear regression were applied for statistical analysis. Two hundred fifteen adult HIV-infected persons agreed to participate in this study, with a response rate of 85.3%. The kernel smoothing means showed that one-third of subjects developed self-stigma immediately after HIV diagnosis while a higher public-stigma felt 6 months later, and both seemed to last continually. Beginning at about 48 months after diagnosis, participants with stigma showed consistently lower scores for all domains of quality of life. After control of potential confounding through multiple linear regression analyses, we found scores of all four domains and items of mobility, fatigue, activity of daily living, positive feeling, self-esteem, social support, and physical environment of WHOQOL were independently associated with both self-stigma and public-stigma. While self-stigma also affects items related to personal psychological feelings, public stigma alone associates with lower scores of items related to social and environmental domains. Our findings underscore the need to explore and control the complex structure and possible synergistic effects of multiple stigmatizations.

Efficient adiabatic hydrodynamical simulations of the high-redshift intergalactic medium

We present a post-processing tool for GADGET-2 adiabatic simulations to model various observed properties of the Ly$\alpha$ forest at $2.5 \leq z \leq 4$ that enables an efficient parameter estimation. In particular, we model the thermal and ionization histories that are not computed self-consistently by default in GADGET-2. We capture the effect of pressure smoothing by running GADGET-2 at an elevated temperature floor and using an appropriate smoothing kernel. We validate our procedure by comparing different statistics derived from our method with those derived using self-consistent simulations with GADGET-3. These statistics are: line of sight density field power spectrum, flux probability distribution function, flux power spectrum, wavelet statistics, curvature statistics, HI column density (${\rm N_{HI}}$) distribution function, linewidth ($b$) distribution and $b$ versus $\log {\rm N_{HI}}$ scatter. For the temperature floor of $10^4$ K and typical signal-to-noise of 25, the results agree well within 20 percent of the self-consistent GADGET-3 simulation. However, this difference is smaller than the expected $1\sigma$ sample variance for an absorption path length of $\sim 5.35$ at $z=3$. Moreover for a given cosmology, we gain a factor of $\sim N$ in computing time for modelling the intergalactic medium under $N \gg 1$ different thermal histories. In addition, our method allows us to simulate the non-equilibrium evolution of thermal and ionization state of the gas and include heating due to non-standard sources like cosmic rays and high energy $\gamma$-rays from Blazars.

A fully non-stationary linear coregionalization model for multivariate random fields

This paper introduces an extension of the traditional stationary linear coregionalization model to handle the lack of stationarity. Under the proposed model, coregionalization matrices are spatially dependent, and basic univariate spatial dependence structures are non-stationary. A parameter estimation procedure of the proposed non-stationary linear coregionalization model is developed under the local stationarity framework. The proposed estimation procedure is based on the method of moments and involves a matrix-valued local stationary variogram kernel estimator, a weighted local least squares method in combination with a kernel smoothing technique. Local parameter estimates are knitted together for prediction and simulation purposes. The proposed non-stationary multivariate spatial modeling approach is illustrated using two real bivariate data examples. Prediction performance comparison is carried out with the classical stationary multivariate spatial modeling approach. According to several criteria, the prediction performance of the proposed non-stationary multivariate spatial modeling approach appears to be significantly better.

Nonparametric kernel smoother on topology learning neural networks for incremental and ensemble regression

Incremental learning is a technique which is effective to increase the space efficiency of machine learning algorithms. Ensemble learning can combine different algorithms to form more accurate ones. The parameter selection of incremental methods is difficult because no retraining is allowed, and the combination of incremental and ensemble learning has not been fully explored. In this paper, we propose a parameter-free regression framework and it combines incremental learning and ensemble learning. First, the topology learning neural networks such as growing neural gas (GNG) and self-organizing incremental neural network (SOINN) are employed as solutions to nonlinearity. Then, the vector quantizations of GNG and SOINN are transformed into a feed-forward neural network by an improved Nadaraya–Watson estimator. A maximum likelihood process is devised for adaptive parameter selection of the estimator. Finally, a weighted training strategy is incorporated to enable the topology learning regressors for ensemble learning by AdaBoost. Experiments are carried out on 5 UCI datasets, and an application study of short-term traffic flow prediction is given. The results show that the proposed method gives comparable results to mainstream incremental and non-incremental regression methods, and better performances in the short-term traffic flow prediction.

Semi-parametric extensions of the Cairns–Blake–Dowd model: A one-dimensional kernel smoothing approach

Over the last few decades, there has been an enormous growth in mortality modeling as the field of mortality risk and longevity risk has attracted great attention from academic, government and private sectors. In this paper, we propose a time-varying coefficient (TVC) mortality model aiming to combine the good characteristics of existing models with efficient model calibration methods. Nonparametric kernel smoothing techniques have been applied in the literature of mortality modeling and based on the findings from Li et al.’s (2015) study, such techniques can significantly improve the forecasting performance of mortality models. In this study we take the same path and adopt a kernel smoothing approach along the time dimension. Since we follow the model structure of the Cairns–Blake–Dowd (CBD) model, the TVC model we propose can be seen as a semi-parametric extension of the CBD model and it gives specific model design according to different countries’ mortality experience. Our empirical study presented here includes Great Britain, the United States, and Australia amongst other developed countries. Fitting and forecasting results from the empirical study have shown superior performances of the model over a selection of well-known mortality models in the current literature.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations.

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.

A Note on Nonparametric Estimation of Conditional Hazard Quantile Function

In this paper, we study an kernel estimator of the conditional hazard quantile function (CHQF) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space and using the proposed estimator based of the kernel smoothing method. The almost complete consistency and the asymptotic normality of this estimate are obtained when the sample is an independante sequence.

Subject-specific bone attenuation correction for brain PET/MR: can ZTE-MRI substitute CT scan accurately?

In brain PET/MR applications, accurate attenuation maps are required for accurate PET image quantification. An implemented attenuation correction (AC) method for brain imaging is the single-atlas approach that estimates an AC map from an averaged CT template. As an alternative, we propose to use a zero echo time (ZTE) pulse sequence to segment bone, air and soft tissue. A linear relationship between histogram normalized ZTE intensity and measured CT density in Hounsfield units () in bone has been established thanks to a CT-MR database of 16 patients. Continuous AC maps were computed based on the segmented ZTE by setting a fixed linear attenuation coefficient (LAC) to air and soft tissue and by using the linear relationship to generate continuous μ values for the bone. Additionally, for the purpose of comparison, four other AC maps were generated: a ZTE derived AC map with a fixed LAC for the bone, an AC map based on the single-atlas approach as provided by the PET/MR manufacturer, a soft-tissue only AC map and, finally, the CT derived attenuation map used as the gold standard (CTAC). All these AC maps were used with different levels of smoothing for PET image reconstruction with and without time-of-flight (TOF). The subject-specific AC map generated by combining ZTE-based segmentation and linear scaling of the normalized ZTE signal into was found to be a good substitute for the measured CTAC map in brain PET/MR when used with a Gaussian smoothing kernel of corresponding to the PET scanner intrinsic resolution. As expected TOF reduces AC error regardless of the AC method. The continuous ZTE-AC performed better than the other alternative MR derived AC methods, reducing the quantification error between the MRAC corrected PET image and the reference CTAC corrected PET image.

Delineation of an endemic tick paralysis zone in southeastern Australia

Tick paralysis has a major impact on pet dog and cat populations in southeastern Australia. It results from envenomation by Ixodes holocyclus and Ixodes cornuatus ticks, the role of Ixodes cornuatus in the epidemiology of this disease in Australia being unclear. The aim of this study was to describe the geographical distribution of tick paralysis cases in southeastern Australia using data from a national disease surveillance system and to compare characteristics of “endemic” cases with those reported outside this endemic zone (“sporadic” cases). Data were collated and a proportional symbol map of all cases by postcode was created. A 15-case isopleth was developed based on descriptive spatial statistics (directional ellipses) and then kernel smoothing to distinguish endemic from sporadic cases. During the study period (January 2010–December 2015) 12,421 cases were reported, and 10,839 of these reported by clinics located in 434 postcodes were included in the study. Endemic cases were predominantly reported from postcodes in coastal southeastern Australia, from southern Queensland to eastern Victoria. Of those cases meeting selection criteria, within the endemic zone 10,767 cases were reported from 351 (88%) postcodes and outside this zone 72 cases were reported from 48 (12%) postcodes. Of these latter 48 postcodes, 18 were in Victoria (26 cases), 16 in New South Wales (28 cases), 7 in Tasmania (9 cases), 5 in South Australia (7 cases) and 2 in Queensland (2 cases). Seasonal distribution in reporting was found: 62% of endemic and 52% of sporadic cases were reported in spring. The number of both endemic and sporadic cases reported peaked in October and November, but importantly a secondary peak in reporting of sporadic cases in April was found. In non-endemic areas, summer was the lowest risk season whilst in endemic areas, autumn was the lowest risk season. Two clusters of sporadic cases were identified, one in South Australia (P=0.022) during the period 22 May to 2 June 2012 and another in New South Wales (P=0.059) during the period 9 October to 29 November 2012. Endemic and sporadic cases did not differ with respect to neuter status (P=0.188), sex (P=0.205), case outcome (P=0.367) or method of diagnosis (P=0.413). However, sporadic cases were 4.2-times more likely to be dogs than cats (P<0.001). The endemic tick paralysis zone described is consistent with previous anecdotal reports. Sporadic cases reported outside this zone might be due to a history of pet travel to endemic areas, small foci of I. holocyclus outside of the endemic zone, or in the case of southern areas, tick paralysis caused by I. cornuatus.

Gambling-Related Cognition Scale (GRCS): Are skills-based games at a disadvantage?

The Gambling-Related Cognition Scale (GRCS; Raylu & Oei, 2004) was developed to evaluate gambling-related cognitive distortions for all types of gamblers, regardless of their gambling activities (poker, slot machine, etc.). It is therefore imperative to ascertain the validity of its interpretation across different types of gamblers; however, some skills-related items endorsed by players could be interpreted as a cognitive distortion despite the fact that they play skills-related games. Using an intergroup (168 poker players and 73 video lottery terminal [VLT] players) differential item functioning (DIF) analysis, this study examined the possible manifestation of item biases associated with the GRCS. DIF was analyzed with ordinal logistic regressions (OLRs) and Ramsay's (1991) nonparametric kernel smoothing approach with TestGraf. Results show that half of the items display at least moderate DIF between groups and, depending on the type of analysis used, 3 to 7 items displayed large DIF. The 5 items with the most DIF were more significantly endorsed by poker players (uniform DIF) and were all related to skills, knowledge, learning, or probabilities. Poker players' interpretations of some skills-related items may lead to an overestimation of their cognitive distortions due to their total score increased by measurement artifact. Findings indicate that the current structure of the GRCS contains potential biases to be considered when poker players are surveyed. The present study conveys new and important information on bias issues to ponder carefully before using and interpreting the GRCS and other similar wide-range instruments with poker players. (PsycINFO Database Record