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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.

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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.

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

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Book part
Publication date: 23 June 2016

Liangjun Su and Yonghui Zhang

In this paper, we study a partially linear dynamic panel data model with fixed effects, where either exogenous or endogenous variables or both enter the linear part, and…

Abstract

In this paper, we study a partially linear dynamic panel data model with fixed effects, where either exogenous or endogenous variables or both enter the linear part, and the lagged-dependent variable together with some other exogenous variables enter the nonparametric part. Two types of estimation methods are proposed for the first-differenced model. One is composed of a semiparametric GMM estimator for the finite-dimensional parameter θ and a local polynomial estimator for the infinite-dimensional parameter m based on the empirical solutions to Fredholm integral equations of the second kind, and the other is a sieve IV estimate of the parametric and nonparametric components jointly. We study the asymptotic properties for these two types of estimates when the number of individuals N tends to and the time period T is fixed. We also propose a specification test for the linearity of the nonparametric component based on a weighted square distance between the parametric estimate under the linear restriction and the semiparametric estimate under the alternative. Monte Carlo simulations suggest that the proposed estimators and tests perform well in finite samples. We apply the model to study the relationship between intellectual property right (IPR) protection and economic growth, and find that IPR has a non-linear positive effect on the economic growth rate.

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Book part
Publication date: 13 May 2017

Jasjeet S. Sekhon and Rocío Titiunik

We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the…

Abstract

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.

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

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Book part
Publication date: 13 May 2017

Abstract

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

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Book part
Publication date: 23 November 2011

Francesco Bravo, Kim P. Huynh and David T. Jacho-Chávez

This chapter proposes a simple procedure to estimate average derivatives in nonparametric regression models with incomplete responses. The method consists of replacing the…

Abstract

This chapter proposes a simple procedure to estimate average derivatives in nonparametric regression models with incomplete responses. The method consists of replacing the responses with an appropriately weighted version and then use local polynomial estimation for the average derivatives. The resulting estimator is shown to be asymptotically normal, and an estimator of its asymptotic variance–covariance matrix is also shown to be consistent. Monte Carlo experiments show that the proposed estimator has desirable finite sample properties.

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Missing Data Methods: Cross-sectional Methods and Applications
Type: Book
ISBN: 978-1-78052-525-9

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Article
Publication date: 10 July 2019

Meihua Zuo, Hongwei Liu, Hui Zhu and Hongming Gao

The purpose of this paper is to identify potential competitive relationships among brands by analyzing the dynamic clicking behavior of consumers.

Abstract

Purpose

The purpose of this paper is to identify potential competitive relationships among brands by analyzing the dynamic clicking behavior of consumers.

Design/methodology/approach

Consumer sequential online click data, collected from JD.com, is used to analyze the dynamic competitive relationship between brands. It is found that the competition intensity across categories of products can differ considerably. Consumers exhibit big differences in purchasing time of durable-like goods, that is, the purchasing probability of such products changes considerably over time. The local polynomial regression model (LPRM) is used to analyze the relationship between brand competition of durable-like goods and the purchasing probability of a particular brand.

Findings

The statistical results of collective behaviors show that there is a 90/10 rule for the category durable-like goods, implying that ten percent of the brands account for 90 percent market share in terms of both clicking and purchasing behavior. The dynamic brand cognitive process of impulsive consumers displays an inverted V shape, while cautious consumers display a double V shaped cognitive process. The dynamic consumers’ cognition illustrates that when the brands capture a half of the click volume, the brands’ competitiveness reaches to its peak and makes no significant different from brands accounting for 100 percent of the click volume in terms of the purchasing probability.

Research limitations/implications

There are some limitations to the research, including the limitations imposed by the data set. One of the most serious problems in the data set is that the collected click-stream is desensitized severely, restricting the richness of the conclusions of this study. Second, the data set consists of many other consumer behavioral data, but only the consumer’s clicking behavior is analyzed in this study. Therefore, in future research, the parameters brand browsing by consumers and the time of browsing in each brand should be added as indicators of brand competitive intensity.

Practical implications

The authors study brand competitiveness by analyzing the relationship between the click rate and the purchase likelihood of individual brands for durable-like products. When the brand competitiveness is less than 50 percent, consumers tend to seek a variety of new brands, and their purchase likelihood is positively correlated with the brand competitiveness. Once consumers learn about a particular brand excessively among all other brands at a period of time, the purchase likelihood of its products decreases due to the thinner consumer’s short-term loyalty the brand. Till the brand competitiveness runs up to 100 percent, consumers are most likely to purchase a brand and its product. That indicates brand competitiveness maintain 50 percent of the whole market is most efficient to be profitable, and the performance of costing more to improve the brand competitiveness might make no difference.

Originality/value

There are many studies on brand competition, but most of these research works analyze the brand’s marketing strategy from the perspective of the company. The limitation of this research is that the data are historical and failure to reflect time-variant competition. Some researchers have studied brand competition through consumer behavior, but the shortcoming of these studies is that it does not consider sequentiality of consumer behavior as this study does. Therefore, this study contributes to the literature by using consumers’ sequential clicking behavior and expands the perspective of brand competition research from the angle of consumers. Simultaneously, this paper uses the LPRM to analyze the relationship between consumer clicking behavior and brand competition for the first time, and expands the methodology accordingly.

Details

Industrial Management & Data Systems, vol. 119 no. 6
Type: Research Article
ISSN: 0263-5577

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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.

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

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Book part
Publication date: 23 June 2016

Daniel J. Henderson and Christopher F. Parmeter

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…

Abstract

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.

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

Keywords

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Book part
Publication date: 23 June 2016

Abstract

Details

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

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