Gaku Igarashi

In regression discontinuity design (RDD), the continuity of the density of a running variable is required. Hence, a discontinuity test of density is used for RDD. In previous studies, tests using difference estimators between the left- and right-hand limits of a density at a (potential) discontinuity point were suggested. In the present paper, a new discontinuity test based on direct density ratio estimation using a beta kernel is proposed. By using the ratio estimator in the proposed test statistic, rather than a difference estimator, the characteristic form of the asymptotic variance of the test statistic is obtained. Consequently, the power of the proposed test is shown to increase when used as a one-tailed test. Simulation studies illustrate the larger power of the proposed test when used as a one-tailed test.

A new nonparametric density ratio estimator using the beta kernel is proposed. It is shown that the beta kernel density ratio estimator (KDRE) is free of boundary or tail bias, and the asymptotic properties of the beta KDRE are derived. Simulation studies are conducted to illustrate the finite sample performance of the beta KDRE.

Multiplicative bias correction technique is revisited for asymmetric kernel density estimators (KDEs) when the data is nonnegative or bounded. It is crucial to classify the recently developed asymmetric KDEs into two types. The multiplicative bias correction applied to the non two-regime type is shown to effectively reduce the order of the bias, at the expense of a constant-factor inflation of the variance. However, it is revealed that, in common with other bias corrections, the multiplicative bias correction applied to the two-regime type fails in reducing the bias near the boundary, unless the density to be estimated satisfies the shoulder condition. (C) 2019 Elsevier B.V. All rights reserved.

The Amoroso kernel density estimator (Igarashi and Kakizawa 2017) for non-negative data is boundary-bias-free and has the mean integrated squared error (MISE) of order O(n(- 4/5)), where n is the sample size. In this paper, we construct a linear combination of the Amoroso kernel density estimator and its derivative with respect to the smoothing parameter. Also, we propose a related multiplicative estimator. We show that the MISEs of these bias-reduced estimators achieve the convergence rates n(- 8/9), if the underlying density is four times continuously differentiable. We illustrate the finite sample performance of the proposed estimators, through the simulations.

We consider density estimation for nonnegative data using generalised gamma density. What is being emphasised here is that a negative exponent is allowed. We show that, for each positive or negative exponent, (i) generalised gamma kernel density estimator, without bias reduction, has the mean integrated squared error (MISE) of order O(n-4/5), as in other boundary-bias-free density estimators from the existing literature, and that (ii) the bias-reduced versions have the MISEs of order O(n-4/5), where n is the sample size. We illustrate the finite sample performance of the proposed estimators through the simulations.

This paper suggests a multivariate asymmetric kernel density estimation using a multivariate weighted log-normal (LN) kernel for non-negative multivariate data. Asymptotic properties of the multivariate weighted LN kernel density estimator are studied. Simulation studies are also conducted in the bivariate situation.

This paper considers a varying asymmetric kernel estimation of the density f for non negative data. Regardless of f(0) = 0 or f (0) > 0, it is important to give a good varying shape/scale parameter for the inverse gamma (IGam) kernel, due to the problem of (f) over cap (0) = 0 in some existing literature. After reformulating the IGam kernel density estimator, asymptotic properties like mean, integrated squared error, mean integrated absolute error, strong consistency, and asymptotic normality are investigated in detail, under some conditions on the target density f. Simulation studies are conducted to compare the proposed IGam kernel density estimators with the existing gamma kernel density estimators. (C) 2016 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

The beta kernel estimator for a density with support [GRAPHICS] was discussed by Chen [(1999) 'Beta Kernel Estimators for Density Functions', Computational Statistics and Data Analysis, 31, 131-145]. In this paper, when the underlying density has a fourth-order derivative, we improve the beta kernel estimator using the bias correction techniques based on two beta kernel estimators with different smoothing parameters. As a result, we propose new bias corrected beta kernel estimators involving the digamma functions, and then establish their asymptotic properties. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.

The log-normal (LN) kernel estimator of a density with support [0, ) was discussed by Jin and Kawczak (2003). The contribution of this paper is to suggest a new class of LN kernel estimators using the idea of weighted distribution. The asymptotic properties of the new class of estimators are studied. Also, numerical studies based on both simulated and real data set are presented.

Several asymmetric kernel (AK) estimators of a density with support [0, infinity) have been suggested in the recent fifteen years. In this paper, additive and nonnegative bias correction techniques, originally developed for the standard kernel estimator, are applied to some AK estimators when the underlying density has a fourth order derivative. The major contribution is to study asymptotic properties of new AK estimators corresponding to the limits of improved estimators. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators. (C) 2014 Elsevier B.V. All rights reserved.

We reveal the boundary bias problem of Birnbaum-Saunders, inverse Gaussian, and reciprocal inverse Gaussian kernel estimators (Jin and Kawczak, 2003; Scaillet, 2004) and re-formulate these estimators to solve the problem. We investigate asymptotic properties of a new class of asymmetric kernel estimators. (C) 2013 Elsevier B.V. All rights reserved.