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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.

We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between “locally randomized” RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.

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 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.

Land value varies at a micro level depending on the location’s economic, geographical and political determinants. The purpose of this study is to present a comprehensive assessment of the determinants affecting land value in the Indian city of Thiruvananthapuram in the state of Kerala.

The global influence of the identified 20 explanatory variables on land value is measured using the traditional hedonic price modeling approach. The localized spatial variations of the influencing parameters are examined using the non-parametric regression method, geographically weighted regression. This study used advertised land value prices collected from Web sources and screened through field surveys.

Global regression results indicate that access to transportation facilities, commercial establishments, crime sources, wetland classification and disaster history has the strongest influence on land value in the study area. Local regression results demonstrate that the factors influencing land value are not stationary in the study area. Most variables have a different influence in Kazhakootam and the residential areas than in the central business district region.

This study confirms findings from previous studies and provides additional evidence in the spatial dynamics of land value creation. It is to be noted that advanced modeling approaches used in the research have not received much attention in Indian property valuation studies. The outcomes of this study have important implications for the property value fixation of urban Kerala. The regional variation of land value within an urban agglomeration shows the need for a localized method for land value calculation.

This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.

Based 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.

The 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%.

Studies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.

The 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.

This paper aims to determine the regression rate using wax fuels for three different grain configurations and find a suitable grain port design for hybrid rocket application.

The design methodology of this work includes different grain port designs and subsequent selection of solid fuels for a suitable hybrid rocket application. A square, a cylindrical and a five-point star grained were designed and prepared using paraffin and beeswax fuels. They were tested in a laboratory-scale rocket with gaseous oxygen to study the effectiveness of solid fuels on these grain structures. The regression rate by static fire testing of these wax fuels was analyzed.

Beeswax performance is better than that of paraffin wax fuel for all three designs, and the five-slotted star fuel port grain attained the best performance. Beeswax fuel attained an average regression rate ≈of 1.35 mm/s as a function of oxidizer mass flux Gox ≈ 111.8 kg/m² s and for paraffin wax 1.199 mm/s at Gox ≈ 121 kg/m² s with gaseous oxygen. The local regression rates of fuels increased in the range of 0.93–1.194 mm/s at oxidizer mass flux range of 98–131 kg/m² s for cylindrical grain, 0.99–1.21 mm/s at oxidizer mass flux range of 96–129 kg/m2s for square grain and 1.12–1.35 mm/s at oxidizer mass flux range of 91–126 kg/m² s for a star grain. A complete set of the regression rate formulas is obtained for all three-grain designs as a function of oxidizer flux rate.

The experiment has been performed for a lower chamber pressure up to 10 bar.

Different grain configurations were designed according to the required dimension of the combustion chamber, injector and exhaust nozzle of the design of a lab-scale hybrid rocket, and input parameters were selected and analyzed.

In the literature on determinants of disclosure, scholars generally tend to investigate the existence of relations in “global” terms by considering the whole range of observed values pertaining to both dependent and independent variables involved in the descriptive model. Despite the different methodologies used coherently to this approach, a hypothesis can be only accepted or rejected entirely. This paper aims to contribute to the literature by proposing a data-driven method based on smooth curves, which allow scholars to detect the existence of local relations, significant in a limited interval of the dependent variable.

The employment of smooth curves is simplified by conducting a study on goodwill disclosure. The model derived by the adoption of the locally weighted scatterplot smoothing (LOWESS) curves may provide an accurate description about complex relations between the extent of disclosure and its expected determinants, whose shape is not completely captured by traditional statistic techniques.

The model based on LOWESS curves provided a comprehensive description about the complexities characterizing the relationship between disclosure and its determinants. The results show that in some cases, the extent of disclosure is influenced by multi-faceted local relations.

The exemplificative study provides evidences useful for standard setters to improve their comprehension about the inclination of companies in disclosing information on goodwill impairment.

The adoption of smooth curves is coherent with an inductive research approach, where empirical evidence is generalized and evolves into theoretical explanations. The method proposed is replicable in all the field of studies, when extant studies come to unclear and contradicting results as a consequence of the complex relations investigated.

Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods, and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader, and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.

Regression discontinuity designs have become popular in empirical studies due to their attractive properties for estimating causal effects under transparent assumptions. Nonetheless, most popular procedures assume i.i.d. data, which is unreasonable in many common applications. To fill this gap, we derive the properties of traditional local polynomial estimators in a fixed- G setting that allows for cluster dependence in the error term. Simulation results demonstrate that accounting for clustering in the data while selecting bandwidths may lead to lower MSE while maintaining proper coverage. We then apply our cluster-robust procedure to an application examining the impact of Low-Income Housing Tax Credits on neighborhood characteristics and low-income housing supply.