Central limit theorem for an additive functional of the fractional Brownian motion II

We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{2+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion

Density convergence in the Breuer-Major theorem for Gaussian stationary sequences

Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a finite sum of Hermite polynomials. Then we prove that the uniform convergence of the density of $V_n$ towards the standard Gaussian density also holds true, under a mild additional assumption involving the causal representation of $X$.Comment: Published at http://dx.doi.org/10.3150/14-BEJ646 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Kernel entropy estimation for long memory linear processes with infinite variance

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process with innovations in the domain of attraction of an $\alpha$-stable law $(0<\alpha<2)$. Assume that the linear process $X$ has a bounded probability density function $f(x)$. Then, under certain conditions, we consider the estimation of the quadratic functional $\int_{\mathbb{R}} f^2(x) \,dx$ by using the kernel estimator $$T_n(h_n)=\frac{2}{n(n-1)h_n}\sum_{1\leq j<i\leq n}K\left(\frac{X_i-X_j}{h_n}\right).$$ The simulation study for long memory linear processes with symmetric $\alpha$-stable innovations is also given

Genome-Wide Association Study for Plant Height and Grain Yield in Rice under Contrasting Moisture Regimes

Drought is one of the vitally critical environmental stresses affecting both growth and yield potential in rice. Drought resistance is a complicated quantitative trait that is regulated by numerous small effect loci and hundreds of genes controlling various morphological and physiological responses to drought. For this study, 270 rice landraces and cultivars were analyzed for their drought resistance. This was done via determination of changes in plant height and grain yield under contrasting water regimes, followed by detailed identification of the underlying genetic architecture via genome-wide association study (GWAS). We controlled population structure by setting top two eigenvectors and combining kinship matrix for GWAS in this study. Eighteen, five, and six associated loci were identified for plant height, grain yield per plant, and drought resistant coefficient, respectively. Nine known functional genes were identified, including five for plant height (OsGA2ox3, OsGH3-2, sd-1, OsGNA1 and OsSAP11/OsDOG), two for grain yield per plant (OsCYP51G3 and OsRRMh) and two for drought resistant coefficient (OsPYL2 and OsGA2ox9), implying very reliable results. A previous study reported OsGNA1 to regulate root development, but this study reports additional controlling of both plant height and root length. Moreover, OsRLK5 is a new drought resistant candidate gene discovered in this study. OsRLK5 mutants showed faster water loss rates in detached leaves. This gene plays an important role in the positive regulation of yield-related traits under drought conditions. We furthermore discovered several new loci contributing to the three investigated traits (plant height, grain yield, and drought resistance). These associated loci and genes significantly improve our knowledge of the genetic control of these traits in rice. In addition, many drought resistant cultivars screened in this study can be used as parental genotypes to improve drought resistance of rice by molecular breeding