Smoothing histograms by means of lattice-and continuous distributions

Gawronski, Wolfgang; Stadtmüller, Ulrich

doi:10.1007/bf01902889

Cited by 33 publications

(26 citation statements)

References 10 publications

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“…Marron and Ruppert (1994) give a three-step transformation method. An older method with favorable properties is the smoothed histogram approach developed by Gawronski andStadtmüller (1980, 1981) and recently explored by Bouezmarni and Scaillet (2005). These last authors also discuss the use of asymmetric kernels for circumventing the boundary bias of kernel estimators.…”

Section: A Estimationmentioning

confidence: 99%

Manipulation of the running variable in the regression discontinuity design: A density test

McCrary

2008

Journal of Econometrics

2,868

532

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Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll-call voting in the House, where sorting is both expected and found. * I thank two anonymous referees for comments, the editors for multiple suggestions that substantially improved the paper, Jack Porter, John DiNardo, and Serena Ng for discussion, Jonah Gelbach for computing improvements, and Ming-Yen Cheng for manuscripts. Any errors are my own.

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Section: A Estimationmentioning

confidence: 99%

Manipulation of the running variable in the regression discontinuity design: A density test

McCrary

2008

Journal of Econometrics

2,868

532

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“…and mj~ is the number of Xl's in n + 1' n + ' j = 1 ..... n. Our estimator is a special case of the so-called smoothed histogram estimators introduced by Grawronski and Stadtmiiller [5]. Theorem 1 of U. Stadtmiiller [15] shows the uniform convergence in measure for the one-dimensional case.…”

Section: Remarkmentioning

confidence: 99%

“…Starting with the classical theorem of WeierstraB on approximation of continuous functions by means of Bernstein polynomials, Vitale [19] by Grawronski and Stadtmiiller [5]. The aim of this paper is to introduce a Bernstein polynomial estimator for two-dimensional density functions.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Bernstein polynomial density estimators

Tenbusch

1994

Metrika

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A Bernstein polynomial estimator for f. N(x, y) for an unknown probability density function f(x, y) concentrated on the triangle ,d = {(x, y): 0 _< x, y < l, x + y < 1} or on the square [] = {(x, y): 0 < x, y < 1} is developed. As a measure ofquality the exact order of magnitude for the pointwise mean squared error is established. It is seen that the quality of these Bernstein polynomial estimators is comparable with the quality of the so-called kernel estimators. Further for such estimators uniform weak consistency results and central limit theorems are developed.

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“….., N we obtain for the bias B g and variance V N of ~nN(t) (see [28], or [11], [12]) In the following we consider only the "stochastic deviation", that is ~nnN(t ) --E(~nnN(t)) and define…”

Section: Local Consistencymentioning

confidence: 99%