Nonparametric Statistical Model Research Articles

Nonparametric efficient causal mediation with intermediate confounders

SummaryInterventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two asymptotically optimal nonparametric estimators that leverage data-adaptive regression for the estimation of nuisance parameters: a one-step estimator and a targeted minimum loss estimator. We further present results establishing the conditions under which these estimators are consistent, multiply robust, $n^{1/2}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on risky behaviour in adolescent girls.

Direct Volume Rendering with Nonparametric Models of Uncertainty.

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.

Assessing the effect of snowfall and cold temperature on a commuter highway traffic volume using several layers of statistical methods

Presented in this paper is an application of the parametric and non-parametric statistical modelling technique to assess and diagnosis the impact of snowfall and cold temperature on classified vehicle volume variations with five years of Weigh-in-Motion (WIM) data recorded at the commuter type highway nearby the City of Leduc in Alberta, Canada. The influence of the winter driving conditions on classified vehicle volumes travelling in mixed traffic stream is examined. The first phase involves developing parametric dummy-variable regression models to relate and then quantify the variations of daily traffic volumes associated with snowfall and temperature. The second phase involves utilizing a non-parametric Chi-square test combined with the Binomial and the Friedman test. Two levels of statistical tests commonly revealed that the total traffic and passenger car volumes are influenced by both snowfall and temperature, but the truck traffic volumes are not affected significantly. The results of this study may contribute to presenting a new statistical methodology for observing changes in highway traffic in winter. It can also provide important insights for highway agencies to develop efficient traffic monitoring programs throughout the year.

A Data-Driven Approach to Prediction and Optimal Bucket-Filling Control for Autonomous Excavators

We develop a data-driven, statistical control method for autonomous excavators. Interactions between soil and an excavator bucket are highly complex and nonlinear, making traditional physical modeling difficult to use for real-time control. Here, we propose a data-driven method, exploiting data obtained from laboratory tests. We use the data to construct a nonlinear, non-parametric statistical model for predicting the behavior of soil scooped by an excavator bucket. The prediction model is built for controlling the amount of soil collected with a bucket. An excavator collects soil by dragging the bucket along the soil surface and scooping the soil by rotating the bucket. It is important to switch from the drag phase to the scoop phase with the correct timing to ensure an appropriate amount of soil has accumulated in front of the bucket. We model the process as a heteroscedastic Gaussian process (GP) based on the observation that the variance of the collected soil mass depends on the scooping trajectory, i.e., the input, as well as the shape of the soil surface immediately prior to scooping. We develop an optimal control algorithm for switching from the drag phase to the scoop phase at an appropriate time and for generating a scoop trajectory to capture a desired amount of soil with high confidence. We implement the method on a robotic excavator and collect experimental data. Experiments show promising results in terms of being able to achieve a desired bucket fill factor with low variance.

Estimation Combining Unbiased and Possibly Biased Estimators

Statisticians often face a dilemma, namely how to decide between choosing a parametric versus a nonparametric statistical model. Parametric statistical models can be asymptotically efficient if the model assumptions hold but biased under model misspecification. Nonparametric models, on the other hand, are often asymptotically unbiased but likely to be less efficient than parametric models if the parametric model is correctly specified. In this work, we propose a new estimator, which combines parametric and nonparametric estimators into a single estimating procedure. In contrast to previously suggested combined estimators, the new estimator ensures that it is asymptotically equivalent to the efficient parametric estimator if parametric assumptions hold. If the assumptions are violated, the combined estimator converges to the nonparametric estimator. The new combined estimator is illustrated with quantile regressions which estimate individualized prediction intervals. Through simulation studies, we explored the MSE of the proposed and competing estimators when data came from parametric distributions and, alternatively, when parametric assumptions were violated. The development of this approach was motivated by the real-data problem of predicting realistic hemoglobin A1C ranges in type 2 diabetes (T2DM) patients. A cross-validation confirmed that the proposed estimator shows better or similar prediction properties in comparison with several competing approaches.

Classification and prediction of milk yield level for Holstein Friesian cattle using parametric and non-parametric statistical classification models.

Objective:The objective of this study was to assess the veracities of most admired strategy discriminant analysis (DA), in comparison to the artificial neural network (ANN) for the anticipation and classification of milk production level in Holstein Friesian cattle using their performances.Materials and Methods:A total of 3,460 performance records of imported and locally born Holstein Friesian cows were gathered during the period from 2000 to 2016 to compare two alternative techniques for predicting the level of production based on performance traits in dairy cattle with the use of statistical software (Statistical Package for the Social Sciences, version 20.0).Results:The findings of the comparison indicated that ANN was more impressive in the expectancy of milk production level than did an imitator statistical method based on DA. The accuracy of the ANN model was high for the winter season (79.5%), whereas it was 47.3% for DA. The current findings were assured via the areas under receiver operating characteristic curves (AUROC) for DA and ANN. AUROC curves were smaller in the condition of the DA model across different calving seasons compared with the ANN model. The inaccuracies of variations were significant at a 5% significance level utilizing paired sample t-test.Conclusion:ANN model can be used efficiently to predict the level of production across the different calving seasons compared to the DA model.

MODEL DEBIT DAERAH ALIRAN SUNGAI JANGKOK BERDASARKAN HASIL PREDIKSI MODEL STATISTICAL DOWNSCALING NONPARAMETRIK KERNEL CURAH HUJAN DAN TEMPERATUR

River water discharge is important information for water resources management planning, so it is necessary to develop river water discharge model as basis of its predictions. In order to get the result of predictions of river water discharge with high accuracy, it is developed a model of river water discharge based on the predictions of local climate (local rainfall and temperature) that are influenced by global climate conditions. Prediction of local climate is based on the Kernel nonparametric statistical downscaling model by utilizing GCM data. GCM data is a high dimensional global data, so data pre-processing is needed to reduce data dimension. It is done by CART algorithm. Statistical downscaling model is used to predict local rainfall and temperature. The prediction results are quite good with relatively small RMSE value. They are used to develop model of river water discharge. Modeling river water discharge is carried out using the Kernel nonparametric approach. The model of river water discharge produced is quite good because it can be used to predict river water discharge with relatively small RMSE.

Prior distribution-based statistical active contour model

Employing prior information can greatly improve the segmentation result of many image segmentation problems. For example, a commonly used prior information is the shape of the object. In this paper, we introduce a different kind of prior information called the prior distribution. On the basis of non-parametric statistical active contour model, we add prior distribution energy to build a novel prior active contour model. During the convergence of contour curve, distribution difference between the inside and outside of the active contour is maximized while the distribution difference between the inside/outside of contour and the prior object/background is minimized. Furthermore, in order to improve the computation speed, a method to accelerate the computation speed is also proposed, which significantly relieves the burden of estimating probability density functions. As the experimental results suggest, satisfactory effects can be achieved in the segmentation of synthetic images and natural images via the our algorithm. Compared with the traditional non-parametric statistical active contour model without prior information, our method achieves a distinct improvement in both accuracy and computation efficiency.

Integrated statistical modeling method: part I—statistical simulations for symmetric distributions

The use of parametric and nonparametric statistical modeling methods differs depending on data sufficiency. For sufficient data, the parametric statistical modeling method is preferred owing to its high convergence to the population distribution. Conversely, for insufficient data, the nonparametric method is preferred owing to its high flexibility and conservative modeling of the given data. However, it is difficult for users to select either a parametric or nonparametric modeling method because the adequacy of using one of these methods depends on how well the given data represent the population model, which is unknown to users. For insufficient data or limited prior information on random variables, the interval approach, which uses interval information of data or random variables, can be used. However, it is still difficult to be used in uncertainty analysis and design, owing to imprecise probabilities. In this study, to overcome this problem, an integrated statistical modeling (ISM) method, which combines the parametric, nonparametric, and interval approaches, is proposed. The ISM method uses the two-sample Kolmogorov–Smirnov (K–S) test to determine whether to use either the parametric or nonparametric method according to data sufficiency. The sequential statistical modeling (SSM) and kernel density estimation with estimated bounded data (KDE-ebd) are used as the parametric and nonparametric methods combined with the interval approach, respectively. To verify the modeling accuracy, conservativeness, and convergence of the proposed method, it is compared with the original SSM and KDE-ebd according to various sample sizes and distribution types in simulation tests. Through an engineering and reliability analysis example, it is shown that the proposed ISM method has the highest accuracy and reliability in the statistical modeling, regardless of data sufficiency. The ISM method is applicable to real engineering data and is conservative in the reliability analysis for insufficient data, unlike the SSM, and converges to an exact probability of failure more rapidly than KDE-ebd as data increase.

Senior citizens’ requirements of services provided by community-based care facilities: a China study

Purpose This study aims to identify senior citizens’ requirements related to “embedded retirement facilities (ERFs)”, which are small-scale, multi-functional and community-based care facilities for senior citizens in mainland China, and to discuss whether senior citizens’ perceptions are influenced by their backgrounds. Design/methodology/approach A questionnaire type of research was administrated to gain senior citizens’ rankings of services that should be provided by ERFs. Non-parametric statistical models were applied to analyse the collected data. Findings Results reveal that health care services for senior citizens are considered the most important. Requirements regarding rehabilitation and entertainment and daily life assistance are ranked second and third, respectively. Culture-related activities are the least important. Differences in the senior citizens’ background also influence their choices. Research limitations/implications This research is based on a questionnaire survey completed in northeast China. Opinions from other areas of mainland China will be collected in the future study. Furthermore, the key items identified in this research, which was completed by participants from the built environment discipline, can be further elaborated by combining interdisciplinary feedback. Practical implications This study explores services that are supposedly provided by ERFs. Findings will provide useful perceptions from senior citizens and will enable decision makers to prioritise services for senior citizens. Social implications Although senior citizens are the end users of ERFs, their needs are easily overlooked. This study calls attention to their needs from ERFs, and the results are likely to serve as references for stakeholders in building improved facilities. Originality/value ERFs have been provided in mainland China to cater to senior citizens’ needs since 2014. However, few studies have identified senior citizens’ requirements for provided services. The survey-based results of this work will serve as references for various stakeholders in making enhanced decisions.

Nonparametric Statistical and Clustering Based RGB-D Dense Visual Odometry in a Dynamic Environment

The robustness of dense-visual-odometry is still a challenging problem if moving objects appear in the scene. In this paper, we propose a form of dense-visual-odometry to handle a highly dynamic environment by using RGB-D data. Firstly, to find dynamic objects, we propose a multi-frame based residual computing model, which takes a far time difference frame into consideration to achieve the temporal consistency motion segmentation. Then the proposed method combines a scene clustering model and a nonparametric statistical model to obtain weighted cluster-wise residuals, as the weight describes how importantly a cluster residual is considered. Afterward, the motion segmentation labeling and clusters’ weights are added to the energy function optimization of dense-visual-odometry to reduce the influence of moving objects. Finally, the experimental results demonstrate that the proposed method has better performance than the state-of-the-art methods on many challenging sequences from a benchmark dataset, especially on highly dynamic sequences.

Two-step semiparametric empirical likelihood inference

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.

A Machine Learning Metasystem for Robust Probabilistic Nonlinear Regression-Based Forecasting of Seasonal Water Availability in the US West

Hydroelectric power generation, water supplies for municipal, agricultural, manufacturing, and service industry uses including technology-sector requirements, dam safety, flood control, recreational uses, and ecological and legal constraints, all place simultaneous, competing demands on the heavily stressed water management infrastructure of the mostly arid American West. Optimally managing these resources depends on predicting water availability. We built a probabilistic nonlinear regression water supply forecast (WSF) technique for the US Department of Agriculture, which runs the largest stand-alone WSF system in the US West. Design criteria included improved accuracy over the existing system; uncertainty estimates that seamlessly handle complex (heteroscedastic, non-Gaussian) prediction errors; integration of physical hydrometeorological process knowledge and domain-specific expert experience; ability to accommodate nonlinearity, model selection uncertainty and equifinality, and predictor multicollinearity and high dimensionality; and relatively easy, low-cost implementation. Some methods satisfied some of these requirements but none met all, leading us to develop a novel, interdisciplinary, and pragmatic prediction metasystem through a carefully considered synthesis of well-established, off-the-shelf components and approaches, spanning supervised and unsupervised machine learning, nonparametric statistical modeling, ensemble learning, and evolutionary optimization, focusing on maintaining but radically updating the principal components regression framework widely used for WSF. Testing this integrated multi-method prediction engine demonstrated its value for river forecasting; USDA adoption is a landmark for transitioning machine learning from research into practice in this field. Its ability to handle all the foregoing design criteria and requirements, which are not unique to WSF, suggests potential for extension to complex probabilistic prediction problems in other fields.

Methodology of Complex Evaluation of Sustainable Development of Socio-Environmental-Economic Systems

This feasibility study proposes a new approach to the classification of data array concerning sustainable development of socio-environmental-economic systems (hereinafter referred to as SEES) in the area of large river basins. The developed methodology allows carrying out the integrated assessment and forecasting the principal results of the territorial entities functioning and is based on the socio-environmental-economic conditions and the use of multidimensional comparative analysis of the development of individual territories, which, in its turn, allows considering the regional characteristics of their development. The aim of the study is to determine the conceptual and methodological foundations of integrated assessment of SEES sustainable development in the area of a large river basin. The methods of logical analysis (deduction), non-parametric statistical multidimensional estimation (PATTERN method) and econometric modeling were used in this work. The novelty of the proposed approaches consists in the development of theoretical and methodological guidelines for further improvement of the mechanism of integrated assessment of SEES formation, forecasting its development and sustainable functioning at the regional level. The obtained results allow to rank the territories according to integrated assessment, as well as to develop regional strategic programs.

Exploring factors associated with commute mode choice: An application of city-level general social survey data

Developing sustainable transportation systems in a city can be substantially assisted by promoting environmentally friendly transportation modes such as walking, cycling, and public transit rather than private cars. Strategies for promoting these desirable transportation modes can be effectively identified based on a sound understanding of how citizens choose a travel mode. In this study, we sought to enhance this understanding by exploring factors associated with commute mode choice utilizing data from a general social survey in Seoul, South Korea. Based on the data, parametric and non-parametric statistical models based on classification tree and multilevel logistic regression approaches, respectively, were developed as a way to capture influential factors associated with the mode choice decision. The models illustrate that commuters' socio-demographic characteristics such as income, occupation, gender, and residence duration tend to significantly influence mode choice. In addition, they showed that respondents' attitudes and behaviors, including the amount of time spent on the internet and self-assessed social status, can be strongly associated with mode choice. This study is also meaningful in that it demonstrates the potential applicability of general social survey data for investigating travel behavior considering various factors that are rarely included in general transportation surveys.

Does left ventricular hypertrophy by electrocardiogram predict adverse outcomes in pregnancies with chronic hypertension?

Objectives: The American College of Obstetricians and Gynecologists Task Force on Hypertension in Pregnancy recommends assessing left ventricular function with echocardiogram or electrocardiogram (ECG) in women with severe hypertension of long duration. We aim to compare the rates of superimposed preeclampsia (SIP) and other obstetrical outcomes in pregnancies with chronic hypertension (CHTN) and left ventricular hypertrophy (LVH) by ECG criteria with mothers without LVH. Study design: After IRB approval, we performed a retrospective chart review from January 2015 to December 2016. Singleton pregnancies with CHTN who carried the pregnancy beyond 20 weeks and planned to deliver at our institution were included for analysis. Patients with insufficient data, multiple gestations, and those with systemic lupus erythematosus were excluded from this study. Rates of SIP and other obstetrical outcomes were compared among those with LVH and those without LVH. Univariate parametric and nonparametric statistical models were applied as appropriate. Associations were considered statistically significant at an alpha level of 0.05. Results: We included 218 pregnancies. Nineteen (8.7%) had LVH. The rate of SIP was higher in pregnancies with LVH than in those without it (68 versus 41%; OR = 3.01; 95% CI 1.1–8.5; p = .022). The birthweight was lower in the LVH group (2432 g [2120–2990] versus 2870 g [2430–3440]; p = .016). Other obstetrical outcomes were not significantly different between those patients with LVH and those without. Conclusions: LVH by ECG criteria may be associated with higher rates of SIP and with lower birthweight in pregnancies with CHTN. ECG may be a cost-effective tool to identify patients with CHTN at risk of adverse outcomes. Larger trials are necessary to corroborate our findings.

Exponential models by Orlicz spaces and applications

AbstractThe geometric structure of the nonparametric statistical model of all positive densities connected by an open exponential arc and its intimate relation to Orlicz spaces give new insights to well-known financial objects which arise in exponential utility maximization problems.

Appraisal of groundwater with special reference to nitrate using statistical index approach

Nitrate pollution is a serious groundwater problem, a statistical index called Normalized Difference Dispersal Index (NDDI) and nonparametric spatial statistical model have been used for appraisal of groundwater samples. The groundwater monitoring data of period (2005–2013) of Kanchipuram district of state Tamil Nadu, country India has been used in this study. Maximum NDDI value enrichment is exhibited by NO3- (+ 1.0) at many locations in studied period and it shows absolute accretion (increment of NO3-) and at few locations NO3- (− 1.0) shows its absolute dilution (decrement of NO3-). Mean index values of NO3- are + 0.01, − 0.20, − 0.19, − 0.09, − 0.11, 0.00, − 0.04 and − 0.17, respectively in year 2006, 2007, 2008, 2009, 2010, 2011, 2012 and 2013. In order to quantify the site-specific variations through index, map of NO3- a environmentally sensitive species was generated by ArcGIS ver. 10. Statistical index based mapping is an appraisal method for evaluation and comparative assessment of NO3- ion at different sites. The elevated index values shows that the sampling locations are not safe for consumptive use. This statistical index has potential to identify the ion specific risk zones.

Probability of bivariate superiority: A non-parametric common-language statistic for detecting bivariate relationships

Researchers often focus on bivariate normal correlation (r) to evaluate bivariate relationships. However, these techniques assume linearity and depend on parametric assumptions. We propose a new nonparametric statistical model that can be more intuitively understood than the conventional r: probability of bivariate superiority (PBS). Our development of Bp, the estimator of a PBS relationship, extends Dunlap's (1994) common-language transformation of r (CLr) by providing a method to directly estimate PBS-the probability that when x is above (or below) the mean of all X, its paired y score will also be above (or below) the mean of all Y. Probability of superiority is an important form of bivariate relationship that until now could only be accurately estimated when data met the parametric assumptions for r. We specify the copula that forms the theoretical basis for PBS, provide an algorithm for estimating PBS from a sample, and describe the results of a Monte Carlo experiment that evaluated our algorithm across 448 data conditions. The PBS estimate, Bp, is robust to violations of parametric assumptions and offers a useful method for evaluating the significance of probability-of-superiority relationships in bivariate data. It is critical to note that Bp estimates a different form of bivariate relationship than does r. Our working examples show that a PBS effect can be significant in the absence of a significant correlation, and vice versa. In addition to utilizing the PBS model in future research, we suggest that this new statistical procedure be used to find theoretically important but previously overlooked effects from past studies.

Spatially Dependent Multiple Testing Under Model Misspecification, With Application to Detection of Anthropogenic Influence on Extreme Climate Events

ABSTRACTThe Weather Risk Attribution Forecast (WRAF) is a forecasting tool that uses output from global climate models to make simultaneous attribution statements about whether and how greenhouse gas emissions have contributed to extreme weather across the globe. However, in conducting a large number of simultaneous hypothesis tests, the WRAF is prone to identifying false “discoveries.” A common technique for addressing this multiple testing problem is to adjust the procedure in a way that controls the proportion of true null hypotheses that are incorrectly rejected, or the false discovery rate (FDR). Unfortunately, generic FDR procedures suffer from low power when the hypotheses are dependent, and techniques designed to account for dependence are sensitive to misspecification of the underlying statistical model. In this article, we develop a Bayesian decision-theoretical approach for dependent multiple testing and a nonparametric hierarchical statistical model that flexibly controls false discovery and is robust to model misspecification. We illustrate the robustness of our procedure to model error with a simulation study, using a framework that accounts for generic spatial dependence and allows the practitioner to flexibly specify the decision criteria. Finally, we apply our procedure to several seasonal forecasts and discuss implementation for the WRAF workflow. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.