Nearest-neighbor Estimators Research Articles

Complete moment convergence for m-END random variables with application to non-parametric regression models

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result.

The consistency and convergence rate for the nearest neighbor density estimator based on -mixing random samples

In this work, we mainly investigate the consistency and strong convergence rate for the nearest neighbor density estimator based on -mixing random samples. The weak consistency, complete consistency, the rates of complete consistency and strong consistency for the nearest neighbor estimator of density function based on -mixing random samples are established. The results obtained in the article extend some corresponding ones for independent samples.

Complete f-moment Convergence for Widely Orthant Dependent Random Variables and Its Application in Nonparametric Models

In this paper, we study the complete f-moment convergence for widely orthant dependent (WOD, for short) random variables. A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained. As applications, we present some new results on complete f-moment convergence for WOD random variables. We also give an application to nonparametric regression models based onWOD errors by using the complete convergence that we established. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed, and a numerical simulation is provided to verify the validity of the theoretical result.

Virtual Statistics in Simulation via k Nearest Neighbors

“Virtual statistics,” as we define them, are estimators of performance measures that are conditional on the occurrence of an event; virtual waiting time of a customer arriving to a queue at time [Formula: see text] is one example of virtual performance. In this paper, we describe a [Formula: see text]-nearest-neighbor method for estimating virtual performance postsimulation from the retained sample paths, examining both its small-sample and asymptotic properties and providing two approaches for measuring the error of the [Formula: see text]-nearest-neighbor estimator. We implement leave-one-replication-out cross-validation for tuning a single parameter [Formula: see text] to use for any time (or times) of interest and evaluate the prediction performance of the [Formula: see text]-nearest-neighbor estimator via controlled studies. As a by-product, this paper motivates a different way of thinking about how to process the output from dynamic, discrete-event simulation.

On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency, strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.

On complete consistency for the weighted estimator of nonparametric regression models

In this paper, we consider the following nonparametric regression model: $$\begin{aligned} Y_{ni} = f\left( x_{ni}\right) + \varepsilon _{ni},\quad i = 1, 2, \ldots , n,\quad n\ge 1, \end{aligned}$$ where $$x_{ni}$$ are known fixed design points from A, where $$A\subset {\mathbb {R}}^d$$ is a given compact set for some $$d\ge 1$$ , $$f(\cdot )$$ is an unknown regression function defined on A and $$\varepsilon _{ni}$$ are random errors, which are assumed to widely orthant dependent (WOD, for short). Firstly, a general result on complete convergence for partial sums of WOD random variables is obtained, which has some interest itself. Based on some mild conditions and the complete convergence result that we established, we further establish the complete consistency of the weighted estimator in the nonparametric regression model, which improves the corresponding one of Wang et al. (TEST 20:607–629, 2014). As an application, the complete consistency of the nearest neighbor estimator is obtained. Finally we provide a numerical simulation to verify the validity of our result.

Demystifying Fixed <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math> </inline-formula>-Nearest Neighbor Information Estimators

Estimating mutual information from independent identically distributed samples drawn from an unknown joint density function is a basic statistical problem of broad interest with multitudinous applications. The most popular estimator is the one proposed by Kraskov, Stogbauer, and Grassberger (KSG) in 2004 and is nonparametric and based on the distances of each sample to its $k^{\mathrm{ th}}$ nearest neighboring sample, where $k$ is a fixed small integer. Despite of its widespread use (part of scientific software packages), theoretical properties of this estimator have been largely unexplored. In this paper, we demonstrate that the estimator is consistent and also identify an upper bound on the rate of convergence of the $\ell _{2}$ error as a function of a number of samples. We argue that the performance benefits of the KSG estimator stems from a curious “correlation boosting” effect and build on this intuition to modify the KSG estimator in novel ways to construct a superior estimator. As a by-product of our investigations, we obtain nearly tight rates of convergence of the $\ell _{2}$ error of the well-known fixed $k$ -nearest neighbor estimator of differential entropy by Kozachenko and Leonenko.

Bias Reduction and Metric Learning for Nearest-Neighbor Estimation of Kullback-Leibler Divergence.

Nearest-neighbor estimators for the Kullback-Leiber (KL) divergence that are asymptotically unbiased have recently been proposed and demonstrated in a number of applications. However, with a small number of samples, nonparametric methods typically suffer from large estimation bias due to the nonlocality of information derived from nearest-neighbor statistics. In this letter, we show that this estimation bias can be mitigated by modifying the metric function, and we propose a novel method for learning a locally optimal Mahalanobis distance function from parametric generative models of the underlying density distributions. Using both simulations and experiments on a variety of data sets, we demonstrate that this interplay between approximate generative models and nonparametric techniques can significantly improve the accuracy of nearest-neighbor-based estimation of the KL divergence.

Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation

Estimators of information theoretic measures, such as entropy and mutual information, are a basic workhorse for many downstream applications in modern data science. State-of-the-art approaches have been either geometric [nearest neighbor (NN)-based] or kernel-based (with a globally chosen bandwidth). In this paper, we combine both these approaches to design new estimators of entropy and mutual information that outperform the state-of-the-art methods. Our estimator uses local bandwidth choices of $k$ -NN distances with a finite $k$ , independent of the sample size. Such a local and data dependent choice ameliorates boundary bias and improves performance in practice, but the bandwidth is vanishing at a fast rate, leading to a non-vanishing bias. We show that the asymptotic bias of the proposed estimator is universal ; it is independent of the underlying distribution. Hence, it can be precomputed and subtracted from the estimate. As a byproduct, we obtain a unified way of obtaining both the kernel and NN estimators. The corresponding theoretical contribution relating the asymptotic geometry of nearest neighbors to order statistics is of independent mathematical interest.

Correction: Renzaho, A.M.N., et al. The Synergetic Effect of Targeted Resource Transfers for Families, Child Sensitive Social Protection Programs, and Capacity Building for Effective Social Protection on Children's Nutritional Status in Nepal. Int. J. Environ. Res. Public Health 2017, 14, 1502.

The authors wish to add the following corrections to their paper published in the International Journal of Environmental Research and Public Health [1]. [...]

Nearest Neighbor Method to Estimate Internal Target for Real-Time Tumor Tracking.

Purpose:This work proposed a nearest neighbor estimation method to track the respiration-induced tumor motion.Methods:Based on the simultaneously collected motion traces of external surrogate and internal target during the modeling phase prior to treatment, we first obtain the nearest neighbors of the current surrogate in external space. Subsequently, the concurrent targets in internal space are determined and used to estimate the current target position. The method was validated on 71 cases that were from 3 open access databases. In addition, to evaluate the method’s estimation and prediction accuracy, we compared the method with other works.Results:Except for 2 cases, the nearest neighbor estimation achieved the root-mean-square error of <3 mm. The comparison indicated that the method had better estimation accuracy than polynomial model and good prediction performance.Discussion:The 2 exceptive cases were further analyzed for failure causes. We inferred that one was because of the lack of estimating new target in our method, and the other one was because of the mistake during data collection. Accordingly, the potential solutions were suggested. Besides, the method’s estimation for surrogate outliers, effects of modeling length, calibration, and extension were discussed.Conclusion:The results demonstrated nearest neighbor estimation’s effectiveness. Except for this, the method imposes no restrictions on the modality of the pretreatment target images and does not assume a specific correspondence function between the surrogate and the target. With only 1 critical parameter, this nearest neighbor estimation method is easy to implement in clinical setting and thus has potential for broad applications.

International Real Estate Review

A special type of spatial dependence model has been developed for the valuation of residential property by using a Bayesian approach which takes into account the unique attributes of Hong Kong property. Inspired by an approach that bases transactions on nearest neighbor estimation, the current model has fine-tuned the spatial dependence method of deriving value from the transactions of the real estate closest in proximity by factoring in differences in structural and auxiliary attributes for more precise property valuation. The model is established on a dataset that covers all residential real estate transactions in a new town in Hong Kong during a given period of time. This model excels other valuation methods with its unique reference to attribute differences, which may impact the valuation results of properties in close vicinity. With this calibration method, we hope to improve the accuracy of real estate appraisals, thus enabling potential homeowners, lenders and investors to make better informed decisions.

Nearest neighbor estimates of regression

New nearest neighbor estimators of the nonparametric regression function and its derivatives are developed. Asymptotic normality is obtained for the proposed estimators over the interior points and the boundary region. Connections with other estimators such as local polynomial smoothers are established. The proposed estimators are boundary adaptive and extensions of the Stute estimators. Asymptotic minimax risk properties are also established for the proposed estimators. Simulations are conducted to compare the performance of the proposed estimators with others.

Fusing multiple existing space‐time land cover products

AbstractLand cover (LC) is a critical variable driving many environmental processes, so its assessment, monitoring, and characterization are essential. However, existing LC products, derived primarily from satellite spectral imagery, each have different temporal and spatial resolutions and different LC classes. Most effort is focused on either fusing a pair of LC products over a small space‐time region or on interpolating missing values in an individual LC product. Here, we review the complexities of LC identification and propose a method for fusing multiple existing LC products to produce a single LC record for a large spatial‐temporal grid, referred to as spatiotemporal categorical map fusion. We first reconcile the LC classes of different LC products and then present a probabilistic weighted nearest neighbor estimator of LC class. This estimator depends on three unknown parameters that are estimated using numerical optimization to maximize an agreement criterion that we define. We illustrate the method using six LC products over the Rocky Mountains and show the improvement gained by supplying the optimization with data‐driven information describing the spatial‐temporal behavior of each LC class. Given the massive size of the LC products, we show how the optimal parameters for a given year are often optimal for other years, leading to shorter computing times.

Data-driven kNN estimation in nonparametric functional data analysis

Kernel nearest-neighbor ( k NN) estimators are introduced for the nonparametric analysis of statistical samples involving functional data. Asymptotic theory is provided for several different target operators including regression, conditional density, conditional distribution and hazard operators. The main point of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed methods fully automatic. As a by-product of our proofs we state consistency results for k NN functional estimators which are uniform in the number of neighbors (UINN). Some simulated experiences illustrate the feasibility and the finite-sample behavior of the method.

Bilateral Internal Thoracic Artery Grafting Increases Mediastinitis: Myth or Fact?

There is controversy about the risk of mediastinitis associated with the use of both internal thoracic arteries (ITA). We performed a case-control study of patients operated on at a single institution from January 2003 to December 2014. A total of 3,118 consecutive patients undergoing isolated coronary artery bypass graft surgery were included; 81.3% (n= 2,533) underwent bilateral ITA (BITA) grafts exclusively and constitute the BITA group, and 18.7% (n= 585) constitute the single ITA (SITA) group. Mediastinitis was defined as deep tissue mediastinal infection, with clinical or microbiologic evidence. Continuous variables were expressed as mean ± SD, and categoric variables as percentage (range). Student's t test and Fisher's exact test were used, as appropriate. Propensity score matching analysis was performed according to the nearest neighbor estimation method (n= 1,040). The incidence of diabetes mellitus was similar in both groups (29%, p= 0.9). The BITA patients were more like to be younger (p < 0.001), men (p < 0.001), had a higher prevalence of hypertension (p < 0.01), higher body mass index (p < 0.001), lower prevalence of left ventricular dysfunction (p < 0.001) and of previous myocardial infarction (p < 0.01), and greater use of off-pump coronary artery bypass graft surgery (p < 0.01). The BITA patients had lower unadjusted hospital mortality (1.6%, versus 5.3% for SITA, p < 0.0001). The total incidence of mediastinitis was 1.8% (BITA 1.9% versus SITA 1.5%, p= 0.6). Diabetes (p < 0.01) and nonelective surgery (p= 0.004) were the only predictors of mediastinitis in the entire population. Propensity score matching showed no differences in mediastinitis: BITA 2.5% versus SITA 1.3% (p= 0.17). In this series of patients, BITA did not increase the risk of mediastinitis in the total population or in the propensity score matched subgroups.

Disaster loss and social media: Can online information increase flood resilience?

AbstractWhen confronted with natural disasters, individuals around the world increasingly use online resources to become informed of forecasted conditions and advisable actions. This study tests the effectiveness of online information and social media in enabling households to reduce disaster losses. The 2011 Bangkok flood is utilized as a case study since it was one of the first major disasters to affect a substantial population connected to social media. The role of online information is investigated with a mixed methods approach. Both quantitative (propensity score matching) and qualitative (in‐depth interviews) techniques are employed. The study relies on two data sources—survey responses from 469 Bangkok households and in‐depth interviews with internet users who were a subset of the survey participants. Propensity score matching indicates that social media enabled households to reduce flood losses by an average of 37% (USD 3708 per household), using a nearest neighbor estimator. This reduction is substantial when considering that household flood losses for the matched sample averaged USD 8278. Social media offered information not available from other sources, such as localized and nearly real‐time updates of flood location and depth. With this knowledge, households could move belongings to higher ground before floodwaters arrived. These findings suggest that utilizing social media users as sensors could better inform populations during disasters. Overall, the study reveals that online information can enable effective disaster preparedness and reduce losses.

Bias and variance reduction in nonparametric estimation of time-dependent accuracy measures.

A new nonparametric approach is developed to estimate the time-dependent accuracy measure curves, which are defined on the cumulative cases and dynamic controls, for censored survival data. Based on an estimable survival process, the main intention of this study is to reduce the finite-sample biases of nearest neighbor estimators. The asymptotic variances of some retrospective accuracy measure estimators are further reduced by applying a smoothing technique to the underlying process of a marker. Meanwhile, practically feasible and theoretically valid procedures are proposed for bandwidth selection in the presented estimators. In addition, the proposed methodology can be reasonably extended to accommodate stratified survival data and survival data with multiple markers. As shown in the simulations, our new estimators outperform the nearest neighbor and inverse censoring weighted estimators. Data from the AIDS Clinical Trials Group study 175 and an angiographic coronary artery disease study are also used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Consistent model specification tests based on [formula omitted]-nearest-neighbor estimation method

We propose a simple consistent test for a parametric regression functional form based on k-nearest-neighbor (k-nn) method. We derive the null distribution of the test statistic and show that the test achieves the minimax rate optimality against smooth alternatives. A wild bootstrap method is used to better approximate the null distribution of the test statistic. We also propose a k-nn statistic which tests for omitted variables nonparametrically. Simulations and an empirical application using US economics new Ph.D. job market matching data show that the k-nn method is more appropriate than the kernel method to analyze unevenly distributed data.

Time related receiver operation characteristic curves and its application in clinical trials and diagnostic analysis

By using R language to deal with practical problems, we introduce two methods of obtaining time related receiver operation characteristic [ROC(t)] curves from survival data: 1) nearest-neighbor estimator of bivariate distribution (NNE) estimation: to obtain cumulative/dynamic ROC(C/D) (t) curves; 2) Cox estimation: to obtain incident/dynamic ROC(I/D) (t) curves. The areas under the ROC(t) curves (AUC) obtained from the two methods fluctuate over time. The one obtained through NNE has bigger fluctuation than that obtained through Cox, while the mean of AUC of the two methods are similar. Time related ROC (t) can be effectively used to evaluate the diagnostic capacity of the marker in clinical trials, and help to select the best diagnostic time of the marker. According to the different scientific interests, researchers should select relevant methods for more accurate evaluation.