Rates of convergence for nearest neighbor estimators with the smoother regression function

In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that the regression function is $(p,C)$-smooth. It is an open problem whether the optimal rate can be achieved by some nearest neighbor estimator in case that $p$ is on (1,1.5]. We solve the problem affirmatively. This is the main result of this paper. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected $L_2$ error.Comment: 12 pages, 1 tabl

A note on retracts of polynomial rings in three variables

In Costa's paper published in 1977, he asks us whether every retract of $k^{[n]}$ is also the polynomial ring or not, where $k$ is a field. In this paper, we give an affirmative answer in the case where $k$ is a field of characteristic zero and $n = 3$.Comment: 4 page

On Jacobi Inversion Formulae for Telescopic Curves

For a hyperelliptic curve of genus $g$, it is well known that the symmetric products of $g$ points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by $y^r=f(x)$, which are special cases of $(n,s)$ curves, and derived new vanishing properties of the sigma function of the curves $y^r=f(x)$. In this paper we extend the formulae to the telescopic curves proposed by Miura and derive new vanishing properties of the sigma function of telescopic curves. The telescopic curves contain the $(n,s)$ curves as special cases

Corporate financing and product market competition: evidence from firm-level data in Japan

This paper investigates the link between external financing and product market competition by focusing on different maturity structures. Using firm-level data for Japanese manufacturing firms over the period 1990-1995, we find that long-term loans enable firms to compete aggressively at a level below profit maximization. By contrast, short-term loans are not related to product market competition. Our results suggest that long-term loans play an important role in investment in market share for long-term profits through lowering prices.debt financing, price-cost margin

Corporate Governance and the Costs of Public Debt Financing: Evidence from Japan

This paper explores the relation between corporate governance mechanisms in Japan and the costs of public debt financing. Using a sample of Japanese corporate bond issues during the period 2005-2008, we find that CEO ownership is associated with higher yield spreads after controlling for firm- and bond-specific characteristics. Founding family ownership is also positively related to yield spreads. In contrast, firms with large corporate shareholders enjoy lower yield spreads. These results are robust to various alternative specifications. Overall, our results indicate that corporate governance mechanisms in Japan are important factors affecting the costs of public debt financing.Yield spreads; Ownership structure; Corporate governance