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The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

Local polynomial regression is extremely popular in applied settings. Recent developments in shape-constrained nonparametric regression allow practitioners to impose constraints on local polynomial estimators thereby ensuring that the resulting estimates are consistent with underlying theory. However, it turns out that local polynomial derivative estimates may fail to coincide with the analytic derivative of the local polynomial regression estimate which can be problematic, particularly in the context of shape-constrained estimation. In such cases, practitioners might prefer to instead use analytic derivatives along the lines of those proposed in the local constant setting by Rilstone and Ullah (1989). Demonstrations and applications are considered.

The purpose of this paper is to use the local correlation technique to measure flight to quality, which is defined as a pronounced and generally rapid increase in risk aversion. Flight to quality between American, British, German, Japanese, and Hong Kong spot equity indices and index futures is examined.

The technique of non‐linear local correlation is employed to detect flight to quality in both spot and futures markets. The use of this methodology allows us to properly process both normally or non‐normally distributed time series. In addition, the estimation of local correlation minimizes the theoretical restrictions resulting from the selection of conditional events and the use of linear regression.

As market risk grows, an increase in flight to quality is documented. For example, a crash in the US stock market results in the flight of capital to the Treasury bond market. Evidence of flight to quality from domestic and foreign spot equity markets to US Treasury bonds is provided. Furthermore, flights to quality from domestic and foreign index futures to US bond futures are revealed. The strength of the reaction from one market to the other is measured and reported. Surprisingly, the authors observe that when market risk becomes extremely high, flight to quality diminishes.

To the best of the authors' knowledge, this is the first study that examines flight to quality in the futures markets by applying local correlation analysis. This study broadens the application of local polynomial regression and local correlation analysis.

It is known that model averaging estimators are useful when there is uncertainty governing which covariates should enter the model. We argue that in applied research there is also uncertainty as to which method one should deploy, prompting model averaging over user-defined choices. Specifically, we propose, and detail, a nonparametric regression estimator averaged over choice of kernel, bandwidth selection mechanism and local-polynomial order. Simulations and an empirical application are provided to highlight the potential benefits of the method.

The purpose of this paper is to propose an improved optimization methodology of information granulation‐based fuzzy radial basis function neural networks (IG‐FRBFNN). In the IG‐FRBFNN, the membership functions of the premise part of fuzzy rules are determined by means of fuzzy c‐means (FCM) clustering. Also, high‐order polynomial is considered as the consequent part of fuzzy rules which represent input‐output relation characteristic of sub‐space and weighted least squares learning is used to estimate the coefficients of polynomial. Since the performance of IG‐RBFNN is affected by some parameters such as a specific subset of input variables, the fuzzification coefficient of FCM, the number of rules and the order of polynomial of consequent part of fuzzy rules, we need the structural as well as parametric optimization of the network. The proposed model is demonstrated with the use of two kinds of examples such as nonlinear function approximation problem and Mackey‐Glass time‐series data.

The type of polynomial of each fuzzy rule is determined by selection algorithm by considering the local error as performance index. In addition, the combined local error is introduced as a performance index considered by two kinds of parameters such as the polynomial type of each rule and the number of polynomial coefficients of each rule. Besides this, other structural and parametric factors of the IG‐FRBFNN are optimized to minimize the global error of model by means of the hierarchical fair competition‐based parallel genetic algorithm.

The performance of the proposed model is illustrated with the aid of two examples. The proposed optimization method leads to an accurate and highly interpretable fuzzy model.

The proposed hybrid optimization methodology is interesting for designing an accurate and highly interpretable fuzzy model. Hybrid optimization algorithm comes in the form of the combination of the combined local error and the global error.

This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

We provide straightforward new nonparametric methods for testing conditional independence using local polynomial quantile regression, allowing weakly dependent data. Inspired by Hausman's (1978) specification testing ideas, our methods essentially compare two collections of estimators that converge to the same limits under correct specification (conditional independence) and that diverge under the alternative. To establish the properties of our estimators, we generalize the existing nonparametric quantile literature not only by allowing for dependent heterogeneous data but also by establishing a weak consistency rate for the local Bahadur representation that is uniform in both the conditioning variables and the quantile index. We also show that, despite our nonparametric approach, our tests can detect local alternatives to conditional independence that decay to zero at the parametric rate. Our approach gives the first nonparametric tests for time-series conditional independence that can detect local alternatives at the parametric rate. Monte Carlo simulations suggest that our tests perform well in finite samples. We apply our test to test for a key identifying assumption in the literature on nonparametric, nonseparable models by studying the returns to schooling.

The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation (IG‐FRBFNN) and their optimization realized by means of the Multiobjective Particle Swarm Optimization (MOPSO).

In fuzzy modeling, complexity, interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. Since the performance of the IG‐RBFNN model is directly affected by some parameters, such as the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials in the consequent parts of the rules, the authors carry out both structural as well as parametric optimization of the network. A multi‐objective Particle Swarm Optimization using Crowding Distance (MOPSO‐CD) as well as O/WLS learning‐based optimization are exploited to carry out the structural and parametric optimization of the model, respectively, while the optimization is of multiobjective character as it is aimed at the simultaneous minimization of complexity and maximization of accuracy.

The performance of the proposed model is illustrated with the aid of three examples. The proposed optimization method leads to an accurate and highly interpretable fuzzy model.

A MOPSO‐CD as well as O/WLS learning‐based optimization are exploited, respectively, to carry out the structural and parametric optimization of the model. As a result, the proposed methodology is interesting for designing an accurate and highly interpretable fuzzy model.