Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points

Double-smoothing for bias reduction in local linear regression

Local linear regression with nonparametrically generated covariates for weakly dependent data

The quality of object proposal plays an important role in boosting the performance of many computer vision tasks, such as, object detection and recognition. Due to the absence of manually annotated bounding-box in practice, the quality metric towards blind assessment of object proposal is highly desirable for singling out the optimal proposals. In this paper, we propose a blind proposal quality assessment algorithm based on the Deep Objectness Representation and Local Linear Regression (DORLLR). Inspired by the hierarchy model of the human vision system, a deep convolutional neural network is developed to extract the objectness-aware image feature. Then, the local linear regression method is utilized to map the image feature to a quality score, which tries to evaluate each individual test window based on its k-nearest-neighbors. Experimental results on a large-scale IoU labeled dataset verify that the proposed method significantly outperforms the state-of-the-art blind proposal evaluation metrics.

Local polynomial regression is a useful nonparametric regression tool to explore fine data structures and has been widely used in practice. In this paper, we propose a new nonparametric regression technique called local composite-quantile-regression (CQR) smoothing in order to further improve local polynomial regression. Sampling properties of the proposed estimation procedure are studied. We derive the asymptotic bias, variance and normality of the proposed estimate. Asymptotic relative efficiency of the proposed estimate with respect to the local polynomial regression is investigated. It is shown that the proposed estimate can be much more efficient than the local polynomial regression estimate for various non-normal errors, while being almost as efficient as the local polynomial regression estimate for normal errors. Simulation is conducted to examine the performance of the proposed estimates. The simulation results are consistent with our theoretical findings. A real data example is used to illustrate the proposed method.

In the case of the random design nonparametric regression, the double smoothing technique is applied to estimate the multivariate regression function. The proposed estimator has desirable properties in both the finite sample and the asymptotic cases. In the finite sample case, it has bounded conditional (and unconditional) bias and variance. On the other hand, in the asymptotic case, it has the same mean square error as the local linear estimator in Fan (Design-Adaptive Nonparametric Regression. Journal of the American Statistical Association 1992, 87, 998–1004; Local Linear Regression Smoothers and Their Minimax Efficiencies. Annals of Statistics 1993, 21, 196–216). Simulation studies demonstrate that the proposed estimator is better than the local linear estimator, because it has a smaller sample mean integrated square error and gives smoother estimates.

Asymptotic normality for a local composite quantile regression estimator of regression function with truncated data

The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.

Crown profile of loblolly pine (Pinus taeda L.) was modeled by nonparametric regression analysis. Nonparametric regression may be applicable when an underlying parametric model cannot be identified and uses only the data to fit a curve. A class of local-polynomial estimators which contains the popular kernel estimator as a special case was investigated. Kernel regression appears to fit closely to the interior data points but often possesses bias problems at the boundaries of the data, a feature less exhibited by local linear or local quadratic regression. A selection of trees was used to show that nonparametric regression captures more variation in crown shape than multiple linear regression. When using nonparametric regression, decisions must be made regarding polynomial order and bandwidth. Such decisions depend on the presence of local curvature, desired degree of smoothing, and for bandwidth in particular, the minimization of some global error criterion. In the present study, a penalized PRESS criterion (PRESS*) was selected as the global error criterion. For. Sci. 44(3):445-453.

Introduction: Macroeconomic problems such as inflation and exchange rates are often highlighted as benchmarks for achieving economic progress. The stability of both must be monitored by the government in order to control the inflation rate and exchange rate. This instability is a phenomenon of fluctuation, namely the phenomenon of the rise and fall of the exchange rate of a currency based on demand and supply. Given the large impact of exchange rate fluctuations on the economy, the prediction of the wage exchange rate against the US dollar is considered necessary because it is useful to anticipate and minimize bad possibilities that arise. Method: Methods that can be used to analyze fluctuating currency exchange rate data are nonparametric regression, Nadaraya-Watson estimator, Gaussian kernel function, and Local Polynomial Regression. Results and Discussion: The results of a nonparametric regression comparison between the Nadaraya-Watson estimator, Gaussian kernel function, and local polynomial regression were obtained by MAPE of 2.508% and 0.179%, respectively. This shows that the best model uses the local polynomial regression method and predicted USD exchange rate data against IDR using the best model, namely Local polynomial Regression where the MAPE value is less than 10%, which means the prediction rate is very good. Conclusion: The nonparametric regression method of the Nadaraya-Watrson estimator, Gaussian kernel function, and local polynomial regression shows that the best model uses the local polynomial regression method.

A novel approach for real-time monitoring of long-term voltage stability using local linear regression and adaptive training database is proposed in this paper. Comparing to previous methods, the proposed local predictive regression model could properly balance the simplicity/transparency and accuracy, and it is also adaptive to the changes of system and operating conditions. The approach is tested on IEEE 30-bus system. Preliminary results show that it can be successfully employed in online voltage stability monitoring.

In this paper we study a statistical method of implementing quasi-Bayes estimators for nonlinear and nonseparable GMM models, that is motivated by the ideas proposed in Chernozhukov and Hong (2003) and Creel and Kristensen (2011) and that combines simulation with nonparametric regression in the computation of GMM models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of the use of posterior quantiles. We also show that in this setting, local linear regression methods have theoretical advantages over kernel methods that are also reected in nite sample simulation results. Our results also apply to both exactly and over identied models. These estimators do not need to rely on numerical optimization or Markov Chain Monte Carlo simulations. They provide an eective compliment to the classical M-estimators and to MCMC methods, and can be applied to both likelihood based models and method of moment based models.

Event detection has an important role in detecting the switching of the state of the appliance in the residential environment. This paper proposed a robust smoothing method for cepstrum estimation using double smoothing i.e. the cepstrum smoothing and local linear regression method. The main problem is to reduce the variance of the home appliance peak signal. In the first step, the cepstrum smoothing method removed the unnecessary quefrency by applying a rectangular window to the cepstrum of the current signal. In the next step, the local regression smoothing weighted data points to be smoothed using robust least squares regression. The result of this research shows the variance of the peak signal is decreased and has a good performance with better accuracy. In noise enviromment, performance prediction quite good with values greater than 0.6 and relatively stable at values above 0.9 on SNR> 25 for single appliances. Furthermore, in multiple appliances, performance prediction quite good at SNR> 20 and begins to decrease in SNR <20 and SNR> 25.

Watershed delineation is a process to compute the drainage area for a point on the land surface, which is a critical step in hydrologic and water resources analysis. However, existing watershed delineation tools are still insufficient to support hydrologists and watershed researchers due to the lack of essential capabilities such as fully leveraging scalable and high performance computing infrastructure (public cloud), and providing predictable performance for the delineation tasks. To solve these problems, this paper reports on WDCloud, which is a system for large-scale watershed delineation on public cloud. For the design and implementation of WDCloud, we employ three main approaches: 1) an automated catchment search mechanism for a public data set, 2) three performance improvement strategies (Data-reuse, parallel-union, and MapReduce), and 3) local linear regression-based execution time estimator for watershed delineation. Moreover, WDCloud extensively utilizes several compute and storage capabilities from Amazon Web Services in order to maximize the performance, scalability, and elasticity of watershed delineation system. Our evaluations on WDCloud focus on two main aspects of WDCloud; the performance improvement for watershed delineation via three strategies and the estimation accuracy for watershed delineation time by local linear regression. The evaluation results show that WDCloud can achieve 18x–111x of speed-ups for delineating any scale of watersheds in the contiguous United States as compared to commodity laptop environments, and accurately predict execution time for watershed delineation with 85.6% of prediction accuracy, which is 23%–13% higher than other state-of-the-art approaches.

To learn things incrementally without the catastrophic interference, we have proposed Resource Allocating Network with Long-Term Memory (RAN-LTM). In RAN-LTM, not only training data but also memory items stored in long-term memory are trained. In this paper, we propose an extended RAN-LTM called Resource Allocating Network by Local Linear Regression (RAN-LLR), in which its centers are not trained but selected based on output errors and the connections are updated by solving a linear regression problem. To reduce the computation and memory costs, the modified connections are restricted based on RBF activity. In the experiments, we first apply RAN-LLR to a one-dimensional function approximation problem to see how the negative interference is effectively suppressed. Then, the performance of RAN-LLR is evaluated for a real-world prediction problem. The experimental results demonstrate that the proposed RAN-LLR can learn fast and accurately with less memory costs compared with the conventional models.

This report extends earlier work by Brailovsky on regression theory and methodology, giving particular emphasis to function approximation for incompletely specified models. The interest here is with situations where the form of the regression relation is not known in advance. We discuss several difficulties that arise in using local approximation and linear regression methods, and propose ways to overcome these problems. To aid the data analyst in developing a suitable model, an illustrative table is derived for determining the number of initial explanatory functions justifiable for a given prespecified confidence level. The general approach formulated here is illustrated with an application to medical data. Relevance to classification and possible extensions are discussed.