Local Linear Regression Estimator Research Articles

Asymptotic normality of local linear functional regression estimator based upon censored data

This article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0 < α < 1 . To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided.

A Comparison Between Local Linear Regression and K- Nearest Neighbor Methods in Estimating the Nonparametric Regression Model with Simulation and Application

In this paper, the nonparametric regression model was estimated using two common estimation methods (Local Linear Regression Estimator (LLRE) and K-Nearest Neighbor Estimator (KNNE). The simulation process was conducted using the statistical programming language, R, for these methods, and they were compared using the Average Root Mean Squares Error (ARMSE) criterion, with three sample sizes (50, 100, 150), three levels of error variance (0.3, 0.7, 1) and two non-linear models. The results for the first model showed the superiority of the nearest neighbor estimator (KNNE) method in most cases, and for the second model the local linear regression estimator (LLRE) was superior at all sample sizes and for all levels of variance. On the applied side, the effect of hemoglobin (Hb) on the packed cell volume (PCV) of 150 patients with chronic kidney disease was studied. The estimation process was made using the two methods, and the comparison between them was made using the root mean square error (RMSE) criterion. It was shown through the results of the applied side that the preference was for the nearest neighbor estimator (KNNE) method.

Consistency of local linear regression estimator for mixtures with varying concentrations

Finite mixtures with different regression models for different mixture components naturally arise in statistical analysis of biological and sociological data. In this paper a model of mixtures with varying concentrations is considered in which the mixing probabilities are different for different observations. A modified local linear estimation (mLLE) technique is developed to estimate the regression functions of the mixture component nonparametrically. Consistency of the mLLE is demonstrated. Performance of mLLE and a modified Nadaraya–Watson estimator (mNWE) is assessed via simulations. The results confirm that the mLLE technique overcomes the boundary effect typical to the NWE.

Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation

Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation

SUBSAMPLING INFERENCE FOR NONPARAMETRIC EXTREMAL CONDITIONAL QUANTILES

This paper proposes a subsampling inference method for extreme conditional quantiles based on a self-normalized version of a local estimator for conditional quantiles, such as the local linear quantile regression estimator. The proposed method circumvents difficulty of estimating nuisance parameters in the limiting distribution of the local estimator. A simulation study and empirical example illustrate usefulness of our subsampling inference to investigate extremal phenomena.

Uniform convergence results for the local linear regression estimation of the conditional distribution

This paper examines the local linear regression (LLR) estimate of the conditional distribution function F(y|x). We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both x and y and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. We demonstrate the usefulness of these uniform results with two examples: the stochastic equicontinuity condition in y, and the estimation of the integrated conditional distribution function.

Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment.

Regression discontinuity is popular in finding treatment/policy effects when the treatment is determined by a continuous variable crossing a cutoff. Typically, a local linear regression (LLR) estimator is used to find the effects. For binary response, however, LLR is not suitable in extrapolating the treatment, as in doubling/tripling the treatment dose/intensity. The reason is that doubling/tripling the LLR estimate can give a number out of the bound , despite that the effect should be a change in probability. We propose local maximum likelihood estimators which overcome these shortcomings, while giving almost the same estimates as the LLR estimator does for the original treatment. A simulation study and an empirical analysis for effects of an income subsidy program on religion demonstrate these points.

Nonparametric regression in nonstandard spaces

A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fréchet regression, where the value of the regression function at each point is estimated via a Fréchet mean calculated from an estimated objective function. A second approach is geodesic regression, which builds upon fitting geodesics to observations by a least squares method. These approaches are applied to transform two of the most important nonparametric regression estimators in statistics to the metric setting – the local linear regression estimator and the orthogonal series projection estimator. The resulting procedures consist of known estimators as well as new methods. We investigate their rates of convergence in a general setting and compare their performance in a simulation study on the sphere.

Local linear estimation of the trimmed regression for censored data

We introduce a non-parametric estimation of the trimmed regression by using the local linear method of a censored scalar response variable, given a functional covariate. The main result of this work is the establishment of almost complete convergence for the constructed estimator. A simulation study is carried out to compare the finite sample performance based on the mean square error between the classic local linear regression estimator and the trimmed local linear regression estimator. Moreover, a real data study is used to illustrate our methodology.

Potential Trade Vulnerability of Bangladesh: An Exploratory Analysis

Bangladesh's integration in the global economy has hitherto proven to be an important force behind its economic growth. However, exclusively trade dependent growth is also trade vulnerable growth. This paper explores the factors that may potentially affect the trade vulnerability of Bangladesh. Results of the bivariate non-parametric local linear kernel regression estimation reveal that the minimum wage of readymade garment workers, manufacturing cost, utilities cost, crude oil prices, and climate change are positively related to trade volatility, while improved political stability is negatively related to trade volatility. Multivariate kernel regressions with composite indicators show that macroeconomic factors, such as exchange rate, foreign exchange reserves and budget balance, have a statistically significant impact on the trade volatility of Bangladesh. In view of these preliminary results, a number of policy recommendations are suggested to deal with the short run and long run trade vulnerability of Bangladesh.

Potential trade vulnerability of Bangladesh: an exploratory analysis

Bangladesh's integration in the global economy has hitherto proven to be an important force behind its economic growth. However, exclusively trade dependent growth is also trade vulnerable growth. This paper explores the factors that may potentially affect the trade vulnerability of Bangladesh. Results of the bivariate non-parametric local linear kernel regression estimation reveal that the minimum wage of readymade garment workers, manufacturing cost, utilities cost, crude oil prices, and climate change are positively related to trade volatility, while improved political stability is negatively related to trade volatility. Multivariate kernel regressions with composite indicators show that macroeconomic factors, such as exchange rate, foreign exchange reserves and budget balance, have a statistically significant impact on the trade volatility of Bangladesh. In view of these preliminary results, a number of policy recommendations are suggested to deal with the short run and long run trade vulnerability of Bangladesh.

Strong consistency of the nonparametric local linear regression estimation under censorship model

We introduce and study a local linear nonparametric regression estimator for censorship model. The main goal of this paper is, to establish the uniform almost sure consistency result with rate over a compact set for the new estimate. To support our theoretical result, a simulation study has been done to make comparison with the classical regression estimator.

Hyperspectral estimation of soil organic matter content using grey relational local regression model

PurposeThis study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.Design/methodology/approachBased on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.FindingsThe results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R2 = 0.924, and the average relative error is 6.608%.Practical implicationsStudies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.Originality/valueThe paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation

The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya-Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya-Watson estimator.

Bias correction for local linear regression estimation using asymmetric kernels via the skewing method

The skewing method, which has been originally proposed as a bias correction device for local linear regression estimation using standard symmetric kernels, is extended to the cases of asymmetric kernels. The method is defined as a convex combination of three local linear estimators. It is demonstrated that the skewed estimator using asymmetric kernels with properly chosen weights can accelerate the bias convergence from O(b) to O(b2) as b → 0 under sufficient smoothness of the unknown regression curve while not inflating the variance in an order of magnitude, where b is the smoothing parameter and the regressor is assumed to have at least one boundary. As a consequence, the estimator has optimal pointwise convergence of n−4/9 when best implemented, where n is the sample size. It is noteworthy that these properties are the same as those for a local cubic regression estimator. Finite-sample properties of the skewed estimator are assessed in comparison with local linear and local cubic estimators. An application of the skewed estimation to real data is also considered.

Wind speed probability density estimation using root-transformed local linear regression

Despite the many attractive features of wind-based renewables, the intermittency of wind generation stands out as a critical challenge. An accurate and reliable nonparametric wind speed probability density model is proposed in this paper based on the application of local linear regression in tandem with a root transformation method, introduced here for the first time. The proposed root-transformed local linear regression approach provides a robust estimate of wind speed distribution and produces more accurate results than kernel density estimation models. The performance of the root-transformed local linear regression estimator is assessed via comparisons with three popular parametric models (Rayleigh, Weibull and Gaussian distributions), two additional parametric models (Birnbaum–Saunders and Nakagami distributions) recently suggested for wind speed probability density estimation, and two nonparametric kernel density estimation models using two standard goodness-of-fit hypothesis tests (Chi-squared and Kolmogorov–Smirnov), coefficient of determination and two error metrics (root mean square error and mean absolute error). Results confirm the accuracy of the proposed root-transformed local linear regression estimator for modelling wind speed probability density, with substantial improvements in all error metrics over parametric and kernel density estimation models.

Skewing methods for variance-stabilizing local linear regression estimation

It is known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct the problem, Nishida and Kanazawa proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of three SK estimators (the CC estimator) to eliminate bias terms. In this study, we show the CC estimator can also produce constant estimator variance by adjusting its weighting parameter and compare the performances of the two VS methods by simulations.

Bayesian Variance-Stabilizing Kernel Density Estimation Using Conjugate Prior

Kernel-type density or regression estimator does not produce a constant estimator variance over the domain. To correct this problem, K. Nishida and Y. Kanazawa (2011, 2015) proposed a variance-stabilizing (VS) local variable bandwidth for kernel regression estimators. K. Nishida (2017) proposed another strategy to construct VS local linear regression estimator using a convex combination of three skewing estimators proposed by Choi and Hall (1998). In this study, we show that variance stabilization can be accomplished by a Bayesian approach in the case of kernel density estimator using conjugate prior.

Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator

A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact at the cut-off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the sample sizes 500, 2000, and 5000 closely match the theoretical predictions.

On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys

In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.