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长程依赖正态误差下的非参数回归AI 解读

We consider the fixed-design regression model with long-range dependent normal errors and show that the finite-dimensional distributions of the properly normalized Gasser-Muller and Priestley-Chao estimators of the regression function converge to those of a white noise process. Furthermore, the distributions of the suitably renormalized maximal deviations over an increasingly finer grid converge to the Gumbel distribution. These results contrast with our previous findings…

长程依赖下的密度估计AI 解读

Dehling and Taqqu established the weak convergence of the empirical process for a long-range dependent stationary sequence under Gaussian subordination. We show that the corresponding density process, based on kernel estimators of the marginal density, converges weakly with the same normalization to the derivative of their limiting process. The phenomenon, which carries on for higher derivatives and for functional laws of the iterated logarithm, is in contrast with…

经验函数的自助法AI 解读

We develop the complete bootstrapped parallel to the asymptotic theory of weighted empirical and quantile processes. Utilizing this parallel theory, we present a general body of techniques to establish the asymptotic validity of the bootstrap method of constructing confidence bands for statistical functions. These techniques are demonstrated to be applicable to the construction of asymptotic bootstrap confidence bands for a variety of concrete functions.

任意维度下的正态性检验AI 解读

The univariate weak convergence theorem of Murota and Takeuchi (1981) is extended for the Mahalanobis transform of the $d$-variate empirical characteristic function, $d \geq 1$. Then a maximal deviation statistic is proposed for testing the composite hypothesis of $d$-variate normality. Fernique's inequality is used in conjunction with a combination of analytic, numerical analytic, and computer techniques to derive exact upper bounds for the asymptotic percentage points of…

分布尾指数的核估计AI 解读

We introduce a new estimate of the exponent of a distribution whose tail varies regularly at infinity. This estimate is expressed as the convolution of a kernel with the logarithm of the quantile function, and includes as particular cases the estimates introduced by Hill and by De Haan. Under very weak conditions, we prove asymptotic normality, consistency and discuss the optimal choices of the kernel and of the bandwidth parameter.