A bandwidth selector for local linear density estimators

Cheng, Ming‐Yen

doi:10.1214/aos/1069362735

Cited by 49 publications

(16 citation statements)

References 11 publications

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“…Due to space restrictions, we omit the details of the implementation procedure (see Cheng (1997) and McCrary (2008) for more information on this topic). After θ(c) is estimated, we compute its bootstrap confidence interval (CI) with 300 repetitions.…”

Section: Testing the Continuity Of Residential Densitymentioning

confidence: 99%

The effect of seismic hazard risk information on property prices: Evidence from a spatial regression discontinuity design

Hidano

Hoshino

Sugiura³

2015

Regional Science and Urban Economics

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Section: Testing the Continuity Of Residential Densitymentioning

confidence: 99%

The effect of seismic hazard risk information on property prices: Evidence from a spatial regression discontinuity design

Hidano

Hoshino

Sugiura³

2015

Regional Science and Urban Economics

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“…The above estimators of the joint density p and its partial derivatives are similar in spirit to the local linear density estimators studied in Cheng (1997). Putting these into formula (2.2), we get the estimatorsĜ jk (x) of G jk (x), and thus the estimator of φ defined by…”

Section: Estimation Of Time Transformationmentioning

confidence: 76%

Operational time and in-sample density forecasting

Lee¹,

Mammen²,

Nielsen³

et al. 2017

Ann. Statist.

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This is the published version of the paper.This version of the publication may differ from the final published version. In this paper, we consider a new structural model for in-sample density forecasting. In-sample density forecasting is to estimate a structured density on a region where data are observed and then reuse the estimated structured density on some region where data are not observed. Our structural assumption is that the density is a product of one-dimensional functions with one function sitting on the scale of a transformed space of observations. The transformation involves another unknown one-dimensional function, so that our model is formulated via a known smooth function of three underlying unknown one-dimensional functions. We present an innovative way of estimating the one-dimensional functions and show that all the estimators of the three components achieve the optimal one-dimensional rate of convergence. We illustrate how one can use our approach by analyzing a real dataset, and also verify the tractable finite sample performance of the method via a simulation study. Permanent repository link

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“…By applying the Lagrange multiplier method, under certain regularity conditions (see, Theorem 2.2 of Newey and Smith, 2004), we can obtain the dual representation of the maximization problem in (6), that is…”

Section: Construction Of Test Statisticsmentioning

confidence: 99%

“…First, we suggest a nonparametric estimator for discontinuities of densities based on the local likelihood approach (Loader, 1996, and Hjort and Jones, 1996). In the literature, McCrary (2008) proposed to estimate discontinuities by applying a local polynomial regression method for binned data (Cheng, 1994(Cheng, , 1997). …”

Section: Introductionmentioning

confidence: 99%

Estimation and Inference of Discontinuity in Density

Otsu

Matsushita

2013

Journal of Business & Economic Statistics

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Continuity or discontinuity of probability density functions of data often plays a fundamental role in empirical economic analysis. For example, for identification and inference of causal effects in regression discontinuity designs it is typically assumed that the density function of a conditioning variable is continuous at a cutoff point that determines assignment of a treatment. Also, discontinuity in density functions can be a parameter of economic interest, such as in analysis of bunching behaviors of taxpayers. In order to facilitate researchers to conduct valid inference for these problems, this paper extends the binning and local likelihood approaches to estimate discontinuity of density functions and proposes empirical likelihood-based tests and confidence sets for the discontinuity.In contrast to the conventional Wald-type test and confidence set using the binning estimator, our empirical likelihood-based methods (i) circumvent asymptotic variance estimation to construct the test statistics and confidence sets; (ii) are invariant to nonlinear transformations of the parameters of interest; (iii) offer confidence sets whose shapes are automatically determined by data; and (iv) admit higher-order refinements, so-called Bartlett corrections. First-and second-order asymptotic theories are developed. Simulations demonstrate the superior finite sample behaviors of the proposed methods. In an empirical application, we assess the identifying assumption of no manipulation of class sizes in the regression discontinuity design studied by Angrist and Lavy (1999).

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A bandwidth selector for local linear density estimators

Cited by 49 publications

References 11 publications

The effect of seismic hazard risk information on property prices: Evidence from a spatial regression discontinuity design

The effect of seismic hazard risk information on property prices: Evidence from a spatial regression discontinuity design

Operational time and in-sample density forecasting

Estimation and Inference of Discontinuity in Density

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