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Book part
Publication date: 23 June 2016

Yangin Fan and Emmanuel Guerre

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

Abstract

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.

Book part
Publication date: 23 June 2016

Jeffrey S. Racine

Local polynomial regression is extremely popular in applied settings. Recent developments in shape-constrained nonparametric regression allow practitioners to impose…

Abstract

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.

Details

Essays in Honor of Aman Ullah
Type: Book
ISBN: 978-1-78560-786-8

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Book part
Publication date: 10 April 2019

Luc Clair

Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and…

Abstract

Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. The purpose of this paper is to derive the asymptotic properties of a design-based nonparametric regression estimator under a combined inference framework. The nonparametric regression estimator considered is the local constant estimator. This work contributes to the literature in two ways. First, it derives the asymptotic properties for the multivariate mixed-data case, including the asymptotic normality of the estimator. Second, I use least squares cross-validation for selecting the bandwidths for both continuous and discrete variables. I run Monte Carlo simulations designed to assess the finite-sample performance of the design-based local constant estimator versus the traditional local constant estimator for three sampling methods, namely, simple random sampling, exogenous stratification and endogenous stratification. Simulation results show that the estimator is consistent and that efficiency gains can be achieved by weighting observations by the inverse of their inclusion probabilities if the sampling is endogenous.

Details

The Econometrics of Complex Survey Data
Type: Book
ISBN: 978-1-78756-726-9

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Book part
Publication date: 16 December 2009

Zongwu Cai, Jingping Gu and Qi Li

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent…

Abstract

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

Details

Nonparametric Econometric Methods
Type: Book
ISBN: 978-1-84950-624-3

Article
Publication date: 24 December 2020

Xuesong Cao, Xican Li, Wenjing Ren, Yanan Wu and Jieya Liu

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

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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%.

Practical implications

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.

Originality/value

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.

Details

Grey Systems: Theory and Application, vol. 11 no. 4
Type: Research Article
ISSN: 2043-9377

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Book part
Publication date: 13 May 2017

Otávio Bartalotti, Gray Calhoun and Yang He

This chapter develops a novel bootstrap procedure to obtain robust bias-corrected confidence intervals in regression discontinuity (RD) designs. The procedure uses a wild…

Abstract

This chapter develops a novel bootstrap procedure to obtain robust bias-corrected confidence intervals in regression discontinuity (RD) designs. The procedure uses a wild bootstrap from a second-order local polynomial to estimate the bias of the local linear RD estimator; the bias is then subtracted from the original estimator. The bias-corrected estimator is then bootstrapped itself to generate valid confidence intervals (CIs). The CIs generated by this procedure are valid under conditions similar to Calonico, Cattaneo, and Titiunik’s (2014) analytical correction – that is, when the bias of the naive RD estimator would otherwise prevent valid inference. This chapter also provides simulation evidence that our method is as accurate as the analytical corrections and we demonstrate its use through a reanalysis of Ludwig and Miller’s (2007) Head Start dataset.

Details

Regression Discontinuity Designs
Type: Book
ISBN: 978-1-78714-390-6

Keywords

Article
Publication date: 22 February 2011

A. Can Inci, H.C. Li and Joseph McCarthy

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…

1217

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

Review of Accounting and Finance, vol. 10 no. 1
Type: Research Article
ISSN: 1475-7702

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Book part
Publication date: 13 May 2017

Hugo Jales and Zhengfei Yu

This chapter reviews recent developments in the density discontinuity approach. It is well known that agents having perfect control of the forcing variable will invalidate…

Abstract

This chapter reviews recent developments in the density discontinuity approach. It is well known that agents having perfect control of the forcing variable will invalidate the popular regression discontinuity designs (RDDs). To detect the manipulation of the forcing variable, McCrary (2008) developed a test based on the discontinuity in the density around the threshold. Recent papers have noted that the sorting patterns around the threshold are often either the researcher’s object of interest or may relate to structural parameters such as tax elasticities through known functions. This, in turn, implies that the behavior of the distribution around the threshold is not only informative of the validity of a standard RDD; it can also be used to recover policy-relevant parameters and perform counterfactual exercises.

Details

Regression Discontinuity Designs
Type: Book
ISBN: 978-1-78714-390-6

Keywords

Book part
Publication date: 13 May 2017

Yang Tang, Thomas D. Cook, Yasemin Kisbu-Sakarya, Heinrich Hock and Hanley Chiang

Relative to the randomized controlled trial (RCT), the basic regression discontinuity (RD) design suffers from lower statistical power and lesser ability to generalize…

Abstract

Relative to the randomized controlled trial (RCT), the basic regression discontinuity (RD) design suffers from lower statistical power and lesser ability to generalize causal estimates away from the treatment eligibility cutoff. This chapter seeks to mitigate these limitations by adding an untreated outcome comparison function that is measured along all or most of the assignment variable. When added to the usual treated and untreated outcomes observed in the basic RD, a comparative RD (CRD) design results. One version of CRD adds a pretest measure of the study outcome (CRD-Pre); another adds posttest outcomes from a nonequivalent comparison group (CRD-CG). We describe how these designs can be used to identify unbiased causal effects away from the cutoff under the assumption that a common, stable functional form describes how untreated outcomes vary with the assignment variable, both in the basic RD and in the added outcomes data (pretests or a comparison group’s posttest). We then create the two CRD designs using data from the National Head Start Impact Study, a large-scale RCT. For both designs, we find that all untreated outcome functions are parallel, which lends support to CRD’s identifying assumptions. Our results also indicate that CRD-Pre and CRD-CG both yield impact estimates at the cutoff that have a similarly small bias as, but are more precise than, the basic RD’s impact estimates. In addition, both CRD designs produce estimates of impacts away from the cutoff that have relatively little bias compared to estimates of the same parameter from the RCT design. This common finding appears to be driven by two different mechanisms. In this instance of CRD-CG, potential untreated outcomes were likely independent of the assignment variable from the start. This was not the case with CRD-Pre. However, fitting a model using the observed pretests and untreated posttests to account for the initial dependence generated an accurate prediction of the missing counterfactual. The result was an unbiased causal estimate away from the cutoff, conditional on this successful prediction of the untreated outcomes of the treated.

Article
Publication date: 5 January 2015

Islam Hassouneh, Teresa Serra and Štefan Bojnec

– The purpose of this paper is to assess price linkages and patterns of transmission among producer and consumer markets for apple in Slovenia.

Abstract

Purpose

The purpose of this paper is to assess price linkages and patterns of transmission among producer and consumer markets for apple in Slovenia.

Design/methodology/approach

Non-linear error correction models are applied. Non-linearities are allowed by means of threshold and multivariate local linear regression estimation techniques. Monthly prices over the period 2000-2011 are used in the empirical application.

Findings

Both techniques provide evidence of non-linearities in price adjustments. Findings suggest that producer and consumer prices tend to increase rather than decrease. Results also indicate that parametric threshold approaches may have difficulties in adequately representing price behavior dynamics.

Originality/value

The main contribution of this work to the literature relies on the fact that this is the first attempt to assess vertical price transmission in the apple sector in Central and Eastern European Country markets. Further, it is the first attempt to use multivariate local linear regression techniques in this context.

Details

British Food Journal, vol. 117 no. 1
Type: Research Article
ISSN: 0007-070X

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