In tissue engineering, biodegradable polymer materials with both high biocompatibility and high strength are very important as scaffolds for long term use. Therefore, in this research, we tried to prepare the three types of poly(L-lactic acid) (PLLA)/calcium phosphate (CP) hybrid composite for a scaffold biomaterial. The effects of addition of different CP on both biocompatibility and mechanical properties were evaluated. CP powders and voids were three-dimensionally and uniformly distributed in the solid samples and porous composite samples. These compositions of CP and PLLA greatly improved the cellular adhesiveness, which increased as the volume fraction of CP in the composite increased. For the porous samples, cells migrated into the pores. This study demonstrated that a composite of PLLA and CP is an effective new scaffold material that results in better osteoconductivity, bone regeneration, and mineralization and has moderately high strength.

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The MSE-minimizing local variable bandwidth for the univariate local linear estimator (the LL) is well-known. This bandwidth does not stabilize variance over the domain. Moreover, in regions where a regression function has zero curvature, the LL estimator is discontinuous. In this paper, we propose a variance-stabilizing (VS) local variable diagonal bandwidth matrix for the multivariate LL estimator. Theoretically, the VS bandwidth can outperform the multivariate extension of the MSE-minimizing local variable scalar bandwidth in terms of asymptotic MISE and can avoid discontinuity created by the MSE-minimizing bandwidth. We present an algorithm for estimating the VS bandwidth and simulation studies.

In linear regression under heteroscedastic variances, Aitken estimator is employed to account for the differences in variances. Employing the same principle, we propose the Nadaraya-Watson regression estimator with variable variancestabilizing bandwidth (VS bandwidth) that minimizes asymptotic MISE (AMISE) while maintaining asymptotic homoscedasticity. We examine its local and global properties relative to the MISE minimizing fixed bandwidth. The proposed VS bandwidth produces the asymptotic variance smaller on some part of the support than the fixed bandwidth and may in some cases achieve smaller AMISE than its fixed counterpart. In numerical examples, we find that the proposed VS bandwidth is more serviceable when the distribution of X's are flatter.

It is well-known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall (1998) proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of one LL estimator and two SK estimators that are symmetrically placed on both sides of the LL estimator (the convex combination (CC) estimator) to eliminate higher-order terms in its asymptotic bias. To obtain a CC estimator with a constant estimator variance without employing the VS local variable bandwidth, the weight in the convex combination must be determined locally to produce a constant estimator variance. In this study, we compare the performances of two VS methods for a CC estimator and find cases in which the weighting method can superior to the VS bandwidth method in terms of the degree of variance stabilization.