Nonparametric Kernel Smoothing Research Articles

Convex Robust Recovery of Corrupted Tensors via Tensor Singular Value Decomposition and Local Low-Rank Approximation

This paper discusses the recovery of tensor data corrupted by random noise. Our approach assumes that the potential structure of data is a linear combination of several low-rank tensor subspaces. The goal is to recover exactly these local low-rank tensors and remove random noise as much as possible. Non-parametric kernel smoothing technique is employed to establish an effective mathematical notion of local models. After that, each local model can be robustly separated into a low-rank tensor and a sparse tensor. The low-rank tensor can be recovered by minimizing a weighted combination of the norm and the tensor nuclear norm (TNN) obtained as the tightest convex relaxation of tensor multi-linear rank defined in Tensor Singular Value Decomposition (TSVD). Numerical simulation experiments verify that our proposed approach can effectively denoise the tensor data such as color images with random noise and has superior performance compared to the existing methods.

Exploring Seismic Hazard in the Groningen Gas Field Using Adaptive Kernel Smoothing

The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards, though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state-of-the-art rate-and-state models for the prediction of seismic hazard fail to capture inter-event interaction in the earthquake catalogue. Based on these findings, we suggest a modified rate-and-state model that also takes into account changes in gas production volumes and uncertainty in the pore pressure field.

Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models

Abstract The aim of this paper is twofold. First, a new functional representation of accelerometer data of a distributional nature is introduced to build a complete individualized profile of each subject’s physical activity levels. Second, we extend two nonparametric functional regression models, kernel smoothing and kernel ridge regression, to handle survey data and obtain reliable conclusions about the influence of physical activity. The advantages of the proposed distributional representation are demonstrated through various analyses performed on the NHANES cohort, which possesses a complex sampling design.

Generalized mean residual life models for survival data with missing censoring indicators.

The mean residual life (MRL) function is an important and attractive alternative to the hazard function for characterizing the distribution of a time-to-event variable. In this article, we study the modeling and inference of a family of generalized MRL models for right-censored survival data with censoring indicators missing at random. To estimate the model parameters, augmented inverse probability weighted estimating equation approaches are developed, in which the non-missingness probability and the conditional probability of an uncensored observation are estimated by parametric methods or nonparametric kernel smoothing techniques. Asymptotic properties of the proposed estimators are established and finite sample performance is evaluated by extensive simulation studies. An application to brain cancer data is presented to illustrate the proposed methods.

A Stepwise Algorithm for Linearly Combining Biomarkers under Youden Index Maximization

Combining multiple biomarkers to provide predictive models with a greater discriminatory ability is a discipline that has received attention in recent years. Choosing the probability threshold that corresponds to the highest combined marker accuracy is key in disease diagnosis. The Youden index is a statistical metric that provides an appropriate synthetic index for diagnostic accuracy and a good criterion for choosing a cut-off point to dichotomize a biomarker. In this study, we present a new stepwise algorithm for linearly combining continuous biomarkers to maximize the Youden index. To investigate the performance of our algorithm, we analyzed a wide range of simulated scenarios and compared its performance with that of five other linear combination methods in the literature (a stepwise approach introduced by Yin and Tian, the min-max approach, logistic regression, a parametric approach under multivariate normality and a non-parametric kernel smoothing approach). The obtained results show that our proposed stepwise approach showed similar results to other algorithms in normal simulated scenarios and outperforms all other algorithms in non-normal simulated scenarios. In scenarios of biomarkers with the same means and a different covariance matrix for the diseased and non-diseased population, the min-max approach outperforms the rest. The methods were also applied on two real datasets (to discriminate Duchenne muscular dystrophy and prostate cancer), whose results also showed a higher predictive ability in our algorithm in the prostate cancer database.

A novel nonparametric computational strategy for identifying differential methylation regions

BackgroundDNA methylation has long been known as an epigenetic gene silencing mechanism. For a motivating example, the methylomes of cancer and non-cancer cells show a number of methylation differences, indicating that certain features characteristics of cancer cells may be related to methylation characteristics. Robust methods for detecting differentially methylated regions (DMRs) could help scientists narrow down genome regions and even find biologically important regions. Although some statistical methods were developed for detecting DMR, there is no default or strongest method. Fisher’s exact test is direct, but not suitable for data with multiple replications, while regression-based methods usually come with a large number of assumptions. More complicated methods have been proposed, but those methods are often difficult to interpret.ResultsIn this paper, we propose a three-step nonparametric kernel smoothing method that is both flexible and straightforward to implement and interpret. The proposed method relies on local quadratic fitting to find the set of equilibrium points (points at which the first derivative is 0) and the corresponding set of confidence windows. Potential regions are further refined using biological criteria, and finally selected based on a Bonferroni adjusted t-test cutoff. Using a comparison of three senescent and three proliferating cell lines to illustrate our method, we were able to identify a total of 1077 DMRs on chromosome 21.ConclusionsWe proposed a completely nonparametric, statistically straightforward, and interpretable method for detecting differentially methylated regions. Compared with existing methods, the non-reliance on model assumptions and the straightforward nature of our method makes it one competitive alternative to the existing statistical methods for defining DMRs.

Small area estimation and childhood obesity surveillance using electronic health records.

There is an urgent need for childhood surveillance systems to design, implement, and evaluate interventions at the local level. We estimated obesity prevalence for individuals aged 5-17 years using a southcentral Wisconsin EHR data repository, Public Health Information Exchange (PHINEX, 2007-2012). The prevalence estimates were calculated by aggregating the estimated probability of each individual being obese, which was obtained via a generalized linear mixed model. We incorporated the random effects at the area level into our model. A weighted procedure was employed to account for missingness in EHR data. A non-parametric kernel smoothing method was used to obtain the prevalence estimates for locations with no or little data (<20 individuals) from the EHR. These estimates were compared to results from newly available obesity atlas (2015-2016) developed from various EHRs with greater statewide representation. The mean of the zip code level obesity prevalence estimates for males and females aged 5-17 years is 16.2% (SD 2.72%); 17.9% (SD 2.14%) for males and 14.4% (SD 2.00%) for females. The results were comparable to the Wisconsin Health Atlas (WHA) estimates, a much larger dataset of local community EHRs in Wisconsin. On average, prevalence estimates were 2.12% lower in this process than the WHA estimates, with lower estimation occurring more frequently for zip codes without data in PHINEX. Using this approach, we can obtain estimates for local areas that lack EHRs data. Generally, lower prevalence estimates were produced for those locations not represented in the PHINEX database when compared to WHA estimates. This underscores the need to ensure that the reference EHRs database can be made sufficiently similar to the geographic areas where synthetic estimates are being created.

Nonparametric Range-Based Double Smoothing Spot Volatility Estimation for Diffusion Models

We consider nonparametric spot volatility estimation for diffusion models with discrete high frequency observations. Our estimator is carried out in two steps. First, using the local average of the range-based variance, we propose a crude estimator of the spot volatility. Second, we use usual nonparametric kernel smoothing to reconstruct the volatility function from the crude estimator. By inference, we find such a double smoothing operation can effectively reduce the estimation error.

Inference for variance risk premium

PurposeWith the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.Design/methodology/approachThe authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.FindingsThis study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.Research limitations/implicationsThis study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.Originality/valueThis study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.

Enhancing Optical Correlation Decision Performance for Face Recognition by Using a Nonparametric Kernel Smoothing Classification.

Optical correlation has a rich history in image recognition applications from a database. In practice, it is simple to implement optically using two lenses or numerically using two Fourier transforms. Even if correlation is a reliable method for image recognition, it may jeopardize decision making according to the location, height, and shape of the correlation peak within the correlation plane. Additionally, correlation is very sensitive to image rotation and scale. To overcome these issues, in this study, we propose a method of nonparametric modelling of the correlation plane. Our method is based on a kernel estimation of the regression function used to classify the individual images in the correlation plane. The basic idea is to improve the decision by taking into consideration the energy shape and distribution in the correlation plane. The method relies on the calculation of the Hausdorff distance between the target correlation plane (of the image to recognize) and the correlation planes obtained from the database (the correlation planes computed from the database images). Our method is tested for a face recognition application using the Pointing Head Pose Image Database (PHPID) database. Overall, the results demonstrate good performances of this method compared to competitive methods in terms of good detection and very low false alarm rates.

Robust inference for estimating equations with nonignorably missing data based on SIR algorithm

ABSTRACTNonresponse is a very common phenomenon in survey sampling. Nonignorable nonresponse – that is, a response mechanism that depends on the values of the variable having nonresponse – is the most difficult type of nonresponse to handle. This article develops a robust estimation approach to estimating equations (EEs) by incorporating the modelling of nonignorably missing data, the generalized method of moments (GMM) method and the imputation of EEs via the observed data rather than the imputed missing values when some responses are subject to nonignorably missingness. Based on a particular semiparametric logistic model for nonignorable missing response, this paper proposes the modified EEs to calculate the conditional expectation under nonignorably missing data. We can apply the GMM to infer the parameters. The advantage of our method is that it replaces the non-parametric kernel-smoothing with a parametric sampling importance resampling (SIR) procedure to avoid nonparametric kernel-smoothing problems with high dimensional covariates. The proposed method is shown to be more robust than some current approaches by the simulations.

SArKS: de novo discovery of gene expression regulatory motif sites and domains by suffix array kernel smoothing.

We set out to develop an algorithm that can mine differential gene expression data to identify candidate cell type-specific DNA regulatory sequences. Differential expression is usually quantified as a continuous score-fold-change, test-statistic, P-value-comparing biological classes. Unlike existing approaches, our de novo strategy, termed SArKS, applies non-parametric kernel smoothing to uncover promoter motif sites that correlate with elevated differential expression scores. SArKS detects motif k-mers by smoothing sequence scores over sequence similarity. A second round of smoothing over spatial proximity reveals multi-motif domains (MMDs). Discovered motif sites can then be merged or extended based on adjacency within MMDs. False positive rates are estimated and controlled by permutation testing. We applied SArKS to published gene expression data representing distinct neocortical neuron classes in Mus musculus and interneuron developmental states in Homo sapiens. When benchmarked against several existing algorithms using a cross-validation procedure, SArKS identified larger motif sets that formed the basis for regression models with higher correlative power. https://github.com/denniscwylie/sarks. Supplementary data are available at Bioinformatics online.

Inference on treatment effect modification by biomarker response in a three-phase sampling design.

An objective in randomized clinical trials is the evaluation of "principal surrogates," which consists of analyzing how the treatment effect on a clinical endpoint varies over principal strata subgroups defined by an intermediate response outcome under both or one of the treatment assignments. The latter effect modification estimand has been termed the marginal causal effect predictiveness (mCEP) curve. This objective was addressed in two randomized placebo-controlled Phase 3 dengue vaccine trials for an antibody response biomarker whose sampling design rendered previously developed inferential methods highly inefficient due to a three-phase sampling design. In this design, the biomarker was measured in a case-cohort sample and a key baseline auxiliary strongly associated with the biomarker (the "baseline surrogate measure") was only measured in a further sub-sample. We propose a novel approach to estimation of the mCEP curve in such three-phase sampling designs that avoids the restrictive "placebo structural risk" modeling assumption common to past methods and that further improves robustness by the use of non-parametric kernel smoothing for biomarker density estimation. Additionally, we develop bootstrap-based procedures for pointwise and simultaneous confidence intervals and testing of four relevant hypotheses about the mCEP curve. We investigate the finite-sample properties of the proposed methods and compare them to those of an alternative method making the placebo structural risk assumption. Finally, we apply the novel and alternative procedures to the two dengue vaccine trial data sets.

Modeling arterial travel time distribution by accounting for link correlations: a copula-based approach

The estimation of urban arterial travel time distribution (TTD) is critical to help implement Intelligent Transportation Systems (ITS) and provide travelers with timely and reliable route guidance. The state-of-practice procedure for arterial TTD estimation commonly assumes that the path travel time follows a certain distribution without considering link correlations. However, this approach appears inappropriate since travel times on successive links are essentially dependent along signalized arterials. In this study, a copula-based approach is proposed to model arterial TTD by accounting for spatial link correlations. First, TTDs on consecutive links along one arterial in Hangzhou, China are investigated. Link TTDs are estimated through the nonparametric kernel smoothing method. Link correlations are analyzed in both unfavorable and favorable coordination cases. Then, Gaussian copula models are introduced to model the dependent structure between link TTDs. The parameters of Gaussian copula are obtained by Maximum-Likelihood Estimation (MLE). Next, path TTDs covering consecutive links are estimated based on the estimated copula models. The results demonstrate the advantage of the proposed copula-based approach, compared with the convolution without capturing link correlations and the empirical distribution fitting methods in both unfavorable and favorable coordination cases.

Construction of D-Optimal Experimental Designs for Nonparametric Regression Models

Under study is the problem of a D-optimal experimental design for the problem of nonparametric kernel smoothing. Modification is proposed for the process of calculating the Fisher information matrix. D-optimal designs are constructed for one and several target points for the problems of nonparametric kernel smoothing using a uniform kernel, the Gauss and Epanechnikov kernels. Comparison is performed between Fedorov’s algorithm and direct optimization methods (such as the Nelder–Mead method and the method of differential evolution). The features of the application of the optimality criterion for the experimental design of the problems with several target points were specified for the cases of various kernels and bandwidths.

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.

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.

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.

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

OA01.07 Alternative Follow-Up Methods Based on Recurrence Patterns after Surgery for Non-Small Cell Lung Cancer

There is no consensus for the appropriate follow-up of patients after complete resection of non-small cell lung cancer (NSCLC). Our study was designed to visually represent postoperative recurrence patterns for NSCLC with the use of event dynamics and to optimize postoperative follow-up schedule based on risk factors for recurrence. A total of 829 patients with NSCLC who underwent complete pulmonary resection were studied. There were 538 men and 291 women with a mean age of 69.2 at the time of operation. The majority of the patients had adenocarcinoma (62.5%), underwent lobectomy (85.9%) and pathological stage IA (47.3%). Event dynamics, based on the hazard rate, were evaluated and only first events (distant metastases or local recurrence) were considered. The effects of sex, histological type and pathological stage were studied. On non-parametric kernel smoothing, the resulting hazard rate curves indicated that the recurrence risk pattern was definitely correlated to sex, with a sharp peak in the first year for men and broad peak during the 2 to 3 years for women. This finding was also confirmed by the analysis of histological type. Although pathological stage IA patients lacked such a large peak in both sexes during the follow-up period, gender difference was shown in pathological stage IB and stage IIA to IIIB patients. The use of recurrence dynamics allows the times of peak recurrence to be visualized. The hazard rate and the peak times of recurrence differed considerably between genders in pathological stage IB or higher. Postoperative follow-up methods should be based on currently recommended follow-up guidelines, give adequate consideration to the recurrence patterns, and be modified individually.