Local Linear Kernel Research Articles

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables.

Generalized single index modeling of longitudinal data with multiple binary responses.

In health and clinical research, medical indices (eg, BMI) are commonly used for monitoring and/or predicting health outcomes of interest. While single-index modeling can be used to construct such indices, methods to use single-index models for analyzing longitudinal data with multiple correlated binary responses are underdeveloped, although there are abundant applications with such data (eg, prediction of multiple medical conditions based on longitudinally observed disease risk factors). This article aims to fill the gap by proposing a generalized single-index model that can incorporate multiple single indices and mixed effects for describing observed longitudinal data of multiple binary responses. Compared to the existing methods focusing on constructing marginal models for each response, the proposed method can make use of the correlation information in the observed data about different responses when estimating different single indices for predicting response variables. Estimation of the proposed model is achieved by using a local linear kernel smoothing procedure, together with methods designed specifically for estimating single-index models and traditional methods for estimating generalized linear mixed models. Numerical studies show that the proposed method is effective in various cases considered. It is also demonstrated using a dataset from the English Longitudinal Study of Aging project.

Golden eagle based improved Att-BiLSTM model for big data classification with hybrid feature extraction and feature selection techniques

ABSTRACT The remarkable development in technology has led to the increase of massive big data. Machine learning processes provide a way for investigators to examine and particularly classify big data. Besides, several machine learning models rely on powerful feature extraction and feature selection techniques for their success. In this paper, a big data classification approach is developed using an optimized deep learning classifier integrated with hybrid feature extraction and feature selection approaches. The proposed technique uses local linear embedding-based kernel principal component analysis and perturbation theory, respectively, to extract more representative data and select the appropriate features from the big data environment. In addition, the feature selection task is fine-tuned by using perturbation theory through heuristic search based on their output accuracy. This feature selection heuristic search method is analysed with five recent heuristic optimization algorithms for deciding the final feature subset. Finally, the data are categorized through an attention-based bidirectional long short-term memory classifier that is optimized with a golden eagle-inspired algorithm. The performance of the proposed model is experimentally verified on publicly accessible datasets. From the experimental outcomes, it is demonstrated that the proposed framework is capable of classifying large datasets with more than 90% accuracy.

Abstract 073: Thrombectomy Alone Versus Bridging Intravenous Alteplase in A US Population: Regression Discontinuity Analysis

Introduction Recent randomized controlled trials (RCT) failed to demonstrate the non‐inferiority of skipping IV tPA in patients with planned endovascular therapy (EVT). None of these studies included patients from the US due to regulatory challenges. Given that practice patterns vary relative to Asia, Australia, and Europe, we sought to address this topic using a validated alternative to RCTs, regression discontinuity (RD). Methods From the prospectively collected SVIN Registry encompassing all consecutive patients treated with EVT from 12 centers across the US, we identified patients from 12/2010 – 12/2021. RD design achieves quasi‐randomization and can determine causal effects by analyzing subjects on immediately adjacent sides of a cutoff. Here, we take advantage of the sharp drop in the likelihood of IV tPA treatment at the 4.5‐hour mark from the patients’ last known well time. Subjects immediately on either side of the cutoff have markedly different probabilities of receiving the treatment while sharing similar characteristics in other relevant aspects. Patients were excluded if they underwent EVT after inter‐hospital transfer, were inpatient at the time of acute ischemic stroke (AIS), received IV tPA outside the 4.5‐hour window, or were treated with EVT after the 10‐hour window, as these patients would not contribute to the RD analysis. The primary outcome was a good functional outcome defined as 90‐day mRS 0‐2 and was analyzed using validated RD analysis methods with local linear regressions and triangular kernel weights. Secondary endpoints included rates of symptomatic intracranial hemorrhage and substantial reperfusion. Results Among 961 patients who met inclusion criteria, all 12 EVT centers within the SVIN Registry were represented. The median age was 70 [IQR 58‐79], 48% were female, NIHSS was 17, and the most common occlusion location was M1 MCA (45%). There were no substantial differences in presentation characteristics between patients treated with IV tPA and without. We observed a significant fall (30%) in the probability of tPA around the cutoff time of 235 minutes from the last known well to hospital arrival (allowing 35 minutes for in‐hospital evaluation from the 4.5‐hour cutoff), while there were no significant differences in other relevant features including age, NIHSS, ASPECTS, and final reperfusion grade at the cutoff, validating the underlying RD assumptions (Figure A). In RD analysis, we observed no association between IV tPA treatment and functional independence at 90‐days in patients undergoing EVT (risk difference ‐0.29 (95% CI [‐2.75 to 2.15]) (Figure B), nor in the secondary outcomes of excellent outcomes (mRS 0‐1) at 90 days, mortality, symptomatic ICH or first pass reperfusion. Conclusion Here, we perform what we believe to be the strongest study to date examining the benefit of IV tPA in patients undergoing EVT for LVO AIS in a US‐based cohort, and we find no evidence of association with 90‐day functional independence, consistent with findings of RCTs performed outside the US.

On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators

On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators

Ebct: Using entropy balancing for continuous treatments to estimate dose–response functions and their derivatives

Interest in evaluating dose–response functions of continuous treatments has been increasing recently. To facilitate the estimation of causal effects in this setting, I introduce the ebct command for the estimation of dose–response functions and their derivatives using entropy balancing for continuous treatments. First, balancing weights are estimated by numerically solving a globally convex optimization problem. These weights eradicate Pearson correlations between covariates and the treatment variable. Because simple uncorrelatedness may be insufficient to yield consistent estimates in the next step, higher moments of the treatment variable can be rendered uncorrelated with covariates. Second, the weights are used in local linear kernel regressions to estimate the dose–response function or its derivative. To perform statistical inference, I use a bootstrap procedure. The command also provides the option of producing publication-quality graphs for the estimated relationships.

On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators

Доказана состоятельность классических локально-линейных ядерных оценок в непараметрической регрессии при более слабых ограничениях на элементы дизайна (регрессоры), чем были известны ранее. Полученные в работе условия универсальны относительно стохастической природы дизайна, который может быть как фиксированным регулярным, так и случайным, при этом не обязательно состоящим из независимых или слабо зависимых случайных величин. Достаточные условия как поточечной, так и равномерной состоятельности классических локально-линейных оценок формулируются в терминах асимптотического поведения числа элементов дизайна, попавших в ту или иную окрестность точек из области задания регрессионной функции. Библиография: 57 названий.

Range-free localization for GWSN using k-NN algorithm with local linear Gaussian kernel regression (KGR)

Range-free localization for GWSN using k-NN algorithm with local linear Gaussian kernel regression (KGR)

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.

A Nonparametric Approach to Estimating Growth Determinants in Sub-Saharan Africa

This paper provides a contribution to the growth empirics in sub-Saharan Africa with a focus on identifying the major determinants of long run economic growth among SSA countries. Being aware of the overwhelming dominance of parametric regression methodology in the extant literature and its associated numerous setbacks, we specifically employ the local linear kernel estimator which does not assume any functional form for the underlying growth model. At the end of the study, the findings suggest that there is a positive and nonlinear relationship between economic growth on one hand as well as investment in physical capital, population and democracy on the other hand. Again, while we find that human capital and inflation have no significant effect on economic growth over the study period, foreign aid was found to have negative effect on economic growth in SSA. The findings obtained in the paper have important implications for growth policy in SSA. Growth policies should thus consider population control, expanding and improving the quality of education and enrolment especially at the higher levels and strengthen democratic institutions. For research, the findings imply that researchers should be cautious in specifying the functional form of growth models when investigating the determinants of economic growth. Keywords: Bandwidth, economic growth, local linear kernel regression, nonparametric, sub-Saharan Africa DOI: 10.7176/JESD/12-16-02 Publication date: August 31 st 2021

Debt-by-Price Ratio, End-of-Year Economic Growth, and Long-Term Prediction of Stock Returns

With the prominent role of government debt in economic growth in recent decades, one would expect that government debt alongside economic growth to be a risk factor priced in the time series of stock returns. In this paper, this idea is investigated by applying a nonparametric model, namely, a local-linear kernel smoother with the aim of forecasting long-term stock returns where the model and smoothing parameters are chosen by cross-validation. While a wide range of predictive variables are examined, we find that our newly introduced debt-by-price ratio and the third to fourth quarter economic growth are robust predictors of stock returns, beating the well-known predictive variables in the literature by a significant difference. The combination of these two covariates can explain almost 30% variation of stock returns at a one-year horizon. This is very crucial considering the difficulty in capturing even a small proportion of movements in stock returns.

Recognition of interface and category of roadway roof strata based on drilling parameters

Measurement while drilling is an important part of the intelligent development of coal mines and the development trend of roof formation detection. The main purpose of this paper is to study the best identification method of rock interface and category based on drilling parameters. Firstly, the borehole drilling device was independently developed; Secondly, 4 concrete blocks were poured to simulate the different rock formations; Thirdly, displacement, rotational speed, torque, and sound pressure level data were collected during drilling the concrete blocks, and the original data was processed by the local linear kernel estimation method; Finally, K-means clustering and change points detection method, was used to identify the rock formation interface respectively, and BP neural network and support vector machine method was used to identify the rock category respectively. Experimental results show that the local linear kernel estimation method based on exponentially weighted loss function can better reflect the response characteristics of drilling parameters. The change point detection method based on the penetration rate is better for the rock interface prediction (the sum of the two interface errors is 10.25 mm). Besides, with the penetration rate and sound pressure level as input parameters, BP neural network and support vector machine can achieve the operational classification of rock formations. This research is of great significance for understanding the prediction of the interface and category of rock formation in coal mines, which can not only promote safe mining but also reflect efficient coal production.

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.

OPTIMAL BANDWIDTH SELECTION IN NONLINEAR COINTEGRATING REGRESSION

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie within a wide band of rates as the sample size $n\rightarrow \infty $ have the property that local level and local linear kernel estimates are asymptotically normal, which enables inference and conveniently corresponds to limit theory in the stationary regression case. This finding reinforces the distinctive flexibility of data-based nonparametric regression procedures for nonstationary nonparametric regression. The present results are obtained under exogenous regressor conditions, which are restrictive but which enable flexible data-based methods of practical implementation in nonparametric predictive regressions within that environment.

Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing

In two sample problems it is of interest to examine the difference between the two regression curves or to detect whether certain functions are adequate to describe the overall trend of the difference. In this paper, we propose a simultaneous confidence band (SCB) as a global inference method with asymptotically correct coverage probabilities for the difference curve based on the weighted local linear kernel regression estimates in each sample. Our procedure allows for random designs, different sample sizes, heteroscedastic errors, and especially missing covariates. Simulation studies are conducted to investigate the finite sample properties of the new SCB which support our asymptotic theory. The proposed SCB is used to analyze two data sets, one of which is concerned with human event-related potentials data which are fully observed and the other is concerned with the Canada 2010/2011 youth student survey data with partially missing covariates, leading to a number of discoveries.

Inference of Break-Points in High-Dimensional Time Series

We consider a new procedure for detecting structural breaks in mean for high-dimensional time series. We target breaks happening at unknown time points and locations. In particular, at a fixed time point our method is concerned with either the biggest break in one location or aggregating simultaneous breaks over multiple locations. We allow for both big or small sized breaks, so that we can 1), stamp the dates and the locations of the breaks, 2), estimate the break sizes and 3), make inference on the break sizes as well as the break dates. Our theoretical setup incorporates both temporal and cross-sectional dependence, and is suitable for heavy-tailed innovations. We derive the asymptotic distribution for the sizes of the breaks by extending the existing powerful theory on local linear kernel estimation and high dimensional Gaussian approximation to allow for trend stationary time series with jumps. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the US unemployment rate is considered to illustrate the usefulness of our method.

Local Linear Quantile Regression for Time Series Under Near Epoch Dependence

This paper aims to establish asymptotic normality of the local linear kernel estimator for quantile regression under near epoch dependence, a useful concept in characterising time series dependence of extensive interests in Econometrics. In particular, near epoch dependence can cover a wide range of linear or nonlinear time series models that are even not of strong or $\alpha$-mixing property (a property usually assumed in the nonlinear time series literature). Under the mild conditions, the Bahadur representation of the quantile regression estimators is established in weak convergence sense. The method provides much richer information than mean regression and covers much more processes, which do not satisfy general mixing conditions. Simulation and application to a real data set are studied, which demonstrate the usefulness of the introduced method for analysis of time series. The theoretical results of this paper will be of widely potential interest for time series econometric semiparametric quantile regression modelling.

Estimation of semi-varying coefficient error-in-variable models with surrogate data and validation sample

In this study, a semi-varying coefficient error-in-variable model with surrogate data and validation sample is proposed. Without specifying any error structure, we firstly use the local linear kernel smoothing technique to define the estimators and the proposed estimators are proved to be asymptotically normal. Then, we conduct generalized likelihood ratio (GLR) test on varying coefficient function. The data–driven bandwidth selection method is discussed. Finally, simulated studies are conducted to illustrate the finite sample properties of the proposed estimators and efficiency of the GLR methodology.

A multivariate cointegration time series model and its applications in analysing stock markets in China

This paper explores nonlinear cointegration between Chinese mainland stock markets and Hong Kong stock market in a multivariate framework for the period January, 1998 to December, 2014 by a nonparametric method. The local linear kernel smoothing method is developed to estimate the unknown function, and the practical problem of implementation is also addressed. Then, a simple nonparametric version of a bootstrap test is adapted for testing misspecification. Furthermore, Some Monte Carlo experiments are presented to examine the finite sample performance of the proposed procedure. Finally, the stock markets data set is discussed in detail by using proposed procedures, showing that Shanghai Stock Index (SHSI) and Shenzhen Component Index (SZCI) can affect Hang Seng Index (HSI), and the influence appears to be a strong nonlinear characteristics.

Bernstein conditional density estimation with application to conditional distribution and regression functions

In this paper we propose a smooth nonparametric estimation for the conditional probability density function based on a Bernstein polynomial representation. Our estimator can be written as a finite mixture of beta densities with data-driven weights. Using the Bernstein estimator of the conditional density function, we derive new estimators for the distribution function and conditional mean. We establish the asymptotic properties of the proposed estimators, by proving their asymptotic normality and by providing their asymptotic bias and variance. Simulation results suggest that the proposed estimators can outperform the Nadaraya–Watson estimator and, in some specific setups, the local linear kernel estimators. Finally, we use our estimators for modeling the income in Italy, conditional on year from 1951 to 1998, and have another look at the well known Old Faithful Geyser data.