Kernel Regression Estimator Research Articles

Kernel regression estimation with errors-in-variables for random fields

In this paper, we investigate kernel regression estimation when the data are contaminated by measurement errors in the context of random fields. We establish sharp rate of weak and strong convergence of the kernel regression estimator under both the ordinary smooth and super-smooth assumptions. Numerical studies were carried out in order to illustrate the performance of the estimator with simulated data.

A Method of Opportunity Prediction in Mobile Ad Hoc Network

The mobility of nodes in mobile ad hoc network (MANET) makes great changes in network topology. And limited knowledge of the future encounter opportunity leads to a blind and unpredictable packet forwarding behavior in routing decisions. Finding the regularity in topology changes and makes efficient opportunity prediction is the key to routing in mobile ad hoc network. To this end, this thesis proposed KROP, a kernel regression opportunity prediction method in MANET. In KROP, we first extract Adamic-Adar metric and contact frequency metric to form features of node pairs, and use these features to capture the evolution of the local network topology over time. Then, we use kernel regression estimation method to model the historical evolution of the topology and output the probability of a future encounter. According to the given sequence of the probability, we make opportunity prediction of the future. In the comparsion experiments on world datasets, we eventually proved KROP outperforms on prediction accuracy.

Kernel-based methods for combining information of several frame surveys

A sample selected from a single sampling frame may not represent adequatly the entire population. Multiple frame surveys are becoming increasingly used and popular among statistical agencies and private organizations, in particular in situations where several sampling frames may provide better coverage or can reduce sampling costs for estimating population quantities of interest. Auxiliary information available at the population level is often categorical in nature, so that incorporating categorical and continuous information can improve the efficiency of the method of estimation. Nonparametric regression methods represent a widely used and flexible estimation approach in the survey context. We propose a kernel regression estimator for dual frame surveys that can handle both continuous and categorical data. This methodology is extended to multiple frame surveys. We derive theoretical properties of the proposed methods and numerical experiments indicate that the proposed estimator perform well in practical settings under different scenarios.

APPROXIMATELY SINGULAR WAVELET

The problem of approximation is relevant for most engineering applications. In this connection, the universal methods of approximation are of interest. The method of nonparametric approximation is developing in the paper – the method of singular wavelets. The method includes an effective numerical algorithm based on the summation of a recursive sequence of functions. The universal algorithm of approximation makes it possible to apply it to approximate one-dimensional and multidimensional functions, in decision support systems, in the processing of stochastic information, pattern recognition, and solution of boundary-value problems.The introduction explain the idea of the method of singular wavelets – to combine the theory of wavelets with the Nadaraya-Watson kernel regression estimator. Usually, Nadaraya-Watson kernel regression are considered as an example of non- parametric estimation. However, one parameter, the smoothing parameter, is still present in the traditional kernel regression algorithm. The choice of the optimal value of this parameter is a complex mathematical problem, and numerous studies have been devoted to this question. In the approximation by the method of singular wavelets, summation of Nadaraya-Watson kernel regression estimates with the smoothing parameter takes place, which solves the problem of the optimal choice of this parameter.In the main part of the paper theorems are formulated that determine the properties of the regularized wavelet transform. Sufficient conditions for uniform convergence of the wavelet series are obtained for the first time. To illustrate the effectiveness of the numerical approximation algorithm, we consider an example of the quasi-interpolation of the Runge function by wavelets with a uniform distribution of interpolation nodes.

On the strong universal consistency of local averaging regression estimates

A general result concerning the strong universal consistency of local averaging regression estimates is presented, which is used to extend previously known results on the strong universal consistency of kernel and partitioning regression estimates. The proof is based on ideas from Etemadi’s proof of the strong law of large numbers, which shows that these ideas are also useful in the context of strong laws of large numbers for conditional expectations in $$L_2$$ .

A Lattice-Based Smoother for Regions With Irregular Boundaries and Holes

ABSTRACTWe consider the problem of estimating a smooth function over a spatial region that is delineated by an irregular boundary and potentially contains holes within the boundary. Methods commonly used for spatial function estimation are well-known to suffer from bias along such boundaries. The estimator we propose is a kernel regression estimator, where the kernel is an approximation to a two-dimensional diffusion process contained within the region of interest. The diffusion process is approximated by the distribution of length-k random walks originating from each observation location and constrained to stay within the domain boundaries. We propose using a cross-validation criterion to find the optimal walk length k, which controls the smoothness of the resulting estimate. Simulations show that the method outperforms the soap film smoother of Wood, Bravington, and Hedley in many realistic scenarios, when data are noisy and borders are highly irregular. We illustrate the practical use of the estimator using measurements of soil manganese concentration around Port Moller, Alaska. Supplementary materials for this article are available online.

A secondary market metaphor for content delivery networks

A Secondary Market (SM) mechanism is used to allow the exchange of unused resources between Origin Servers (content-generating entities) that claim and reserve resources from Content Delivery Networks (CDNs). Using a Predictive Reservation Scheme, network and disk resources are being monitored through well-established techniques (Kernel Regression Estimators) in a given time frame. We show that the SM mechanism significantly improves the efficiency and robustness of our Predictive Reservation Scheme by allowing fast exchange of unused resources between the Origin Servers (CDN Clients), either by implementing socially optimal practices or by allowing automatic electronic auctions at the end of day (EOD) or at shorter time intervals. Therefore, all the involved players (including the CDN itself) benefit from the rationalized use of CDN resources.

Feature Screening for Nonparametric and Semiparametric Models with Ultrahigh-Dimensional Covariates

This paper considers the feature screening and variable selection for ultrahigh dimensional covariates. The new feature screening procedure base on conditional expectation which is used to differentiate whether an explanatory variable contributes to a response variable or not, without requiring a specific parametric form of the underlying data model. The authors estimate the marginal conditional expectation by kernel regression estimator. The proposed method is showed to have sure screen property. The authors propose an iterative kernel estimator algorithm to reduce the ultrahigh dimensionality to an appropriate scale. Simulation results and real data analysis demonstrate the proposed method works well and performs better than competing methods.

Strong consistency of non parametric kernel regression estimator for strong mixing samples

ABSTRACTFor α-mixing samples, we study Priestley–Chao kernel estimator for non parametric regression model. By using the moment inequality and the exponential inequality, the strong consistency and the uniformly strong consistency of the estimator are obtained for some weak conditions.

Identification of Insurance Models with Multidimensional Types

In this paper we address the identification and estimation of insurance models where insurees have private information about their risk and risk aversion. The model includes random damage and allows for several claims, while insurees choose from a finite number of coverages. We show that the joint distribution of risk and risk aversion is nonparametrically identified despite bunching due to multidimensional types and a finite number of coverage. Our identification strategy exploits the observed number of claims as well as an exclusion restriction and a support assumption. Our results apply to any form of competition. We propose a novel and computationally friendly estimation method combining kernel regression and density estimation as well as inverse Fourier transforms.

UNIFORM CONVERGENCE RATES OVER MAXIMAL DOMAINS IN STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

On the $$L_p$$ norms of kernel regression estimators for incomplete data with applications to classification

We consider kernel methods to construct nonparametric estimators of a regression function based on incomplete data. To tackle the presence of incomplete covariates, we employ Horvitz–Thompson-type inverse weighting techniques, where the weights are the selection probabilities. The unknown selection probabilities are themselves estimated using (1) kernel regression, when the functional form of these probabilities are completely unknown, and (2) the least-squares method, when the selection probabilities belong to a known class of candidate functions. To assess the overall performance of the proposed estimators, we establish exponential upper bounds on the $$L_p$$ norms, $$1\le p<\infty $$ , of our estimators; these bounds immediately yield various strong convergence results. We also apply our results to deal with the important problem of statistical classification with partially observed covariates.

Modified kernel regression estimation with functional time series data

This paper derives the asymptotic distribution of a modified kernel regression estimator for strong mixing functional time series data. As a direct consequence, the approximate pointwise confidence interval of regression operator is presented.

Kernel regression estimates of time delays between gravitationally lensed fluxes

Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. A number of methods have been proposed to address this problem. In this paper, we explore in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several datasets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test of performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results.

Disability Among Veterans: Analysis of the National Survey of Veterans (1997-2001).

This manuscript assesses whether the Veterans Administration Rating System (VADR) correlates with self-reported activities of daily living (ADL) used in the National Survey of Veterans and likelihood of employment. Veterans' disability benefits are determined based on a single-index standardized rating scheme, measured at time of discharge. The primary aim of this study was to assess how this single-index rating of disability for veterans compares to multidimensional measures of disability (ADL and instrumental activities of daily living [IADL]). The relationship between disability ratings and labor market outcomes such as job search behavior and the likelihood of being employed was assessed. Successful labor market reintegration requires both physical/mental well-being, we examined the extent that VADR can capture the relationship between job market behavior and measures of mental/physical health. Kernel regression estimates were obtained of the likelihood of working/looking for work. Mean numbers of IADL and ADL difficulties and medical conditions were positively associated with VADR (p-trend < 0.001). An inverse relationship was observed with VADR and predicted probability of working (p-trend < 0.001). The combination of >4 ADL/IADL deficits and mental health diagnosis increased the likelihood of not working. The probability of not working correlated with VADR when VADR was greater than 40%.

Nonparametric relative error regression for spatial random variables

Let \(\displaystyle Z_{\mathbf {i}}=\left( X_{\mathbf {i}},\ Y_{\mathbf {i}}\right) _{\mathbf {i}\in \mathbb {N}^{N}\, N \ge 1}\), be a \( \mathbb {R}^d\times \mathbb {R}\)-valued measurable strictly stationary spatial process. We consider the problem of estimating the regression function of \(Y_{\mathbf {i}}\) given \(X_{\mathbf {i}}\). We construct an alternative kernel estimate of the regression function based on the minimization of the mean squared relative error. Under some general mixing assumptions, the almost complete consistency and the asymptotic normality of this estimator are obtained. Its finite-sample performance is compared with a standard kernel regression estimator via a Monte Carlo study and real data example.

General method of boundary correction in kernel regression estimation

Kernel estimators of both density and regression functions are not consistent near the nite end points of their supports. In other words, boundary eects seriously aect the performance of these estimators. In this paper, we combine the transformation and the reflection methods in order to introduce a new general method of boundary correction when estimating the mean function. The asymptotic mean squared error of the proposed estimator is obtained. Simulations show that our method performes quite well with respect to some other existing methods. Keywords: Boundary; Kernel estimation; Mean squared error; Regression; Estimation

Kernel regression estimation of fiber orientation mixtures in diffusion MRI

We present and evaluate a method for kernel regression estimation of fiber orientations and associated volume fractions for diffusion MR tractography and population-based atlas construction in clinical imaging studies of brain white matter. This is a model-based image processing technique in which representative fiber models are estimated from collections of component fiber models in model-valued image data. This extends prior work in nonparametric image processing and multi-compartment processing to provide computational tools for image interpolation, smoothing, and fusion with fiber orientation mixtures. In contrast to related work on multi-compartment processing, this approach is based on directional measures of divergence and includes data-adaptive extensions for model selection and bilateral filtering. This is useful for reconstructing complex anatomical features in clinical datasets analyzed with the ball-and-sticks model, and our framework's data-adaptive extensions are potentially useful for general multi-compartment image processing. We experimentally evaluate our approach with both synthetic data from computational phantoms and in vivo clinical data from human subjects. With synthetic data experiments, we evaluate performance based on errors in fiber orientation, volume fraction, compartment count, and tractography-based connectivity. With in vivo data experiments, we first show improved scan–rescan reproducibility and reliability of quantitative fiber bundle metrics, including mean length, volume, streamline count, and mean volume fraction. We then demonstrate the creation of a multi-fiber tractography atlas from a population of 80 human subjects. In comparison to single tensor atlasing, our multi-fiber atlas shows more complete features of known fiber bundles and includes reconstructions of the lateral projections of the corpus callosum and complex fronto-parietal connections of the superior longitudinal fasciculus I, II, and III.

Fast and accurate computation for kernel estimators

Standard kernel density and regression estimators are well-known to be computationally very slow when analyzing large data sets, and algorithms that achieve considerable computational savings are highly desirable. With this goal in mind, two fast and accurate computational methods are proposed in this paper for computation of univariate and multivariate local polynomial estimators defined on an equally spaced grid. Compared to direct implementation, the proposed algorithms lead to substantial computational savings. For the case in which the evaluation points are not the grid points, a fast algorithm is also proposed. It is shown that the proposed method is asymptotically superior to the general binning method. Numerical comparisons are also made to compare computational speeds and error bounds of the proposed methods with those of the linear binning and the direct implementation.

Kernel regression estimation for incomplete data with applications

Methods are proposed to construct kernel estimators of a regression function in the presence of incomplete data. Furthermore, exponential upper bounds are derived on the performance of the \(L_p\) norms of the proposed estimators, which can then be used to establish various strong convergence results. The presence of incomplete data points are handled by a Horvitz–Thompson-type inverse weighting approach, where the unknown selection probabilities are estimated by both kernel regression and least-squares methods. As an immediate application of these results, the problem of nonparametric classification with partially observed data will be studied.