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图像数据离散薄板平滑样条的快速计算AI 解读

This paper describes a fast method of computation for a discretized version of the thin-plate spline for image data. This method uses the Discrete Cosine Transform and is contrasted with a similar approach based on the Discrete Fourier Transform. The two methods are similar from the point of view of speed, but the errors introduced near the edge of the image by use of the Discrete Fourier Transform are significantly reduced when the Discrete Cosine Transform is used. This is…

平滑信号检测：基于累积和程序的最优性AI 解读

Cox et al. (1988) show that under a random smooth function model with signal covariance matrix V, a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic yTVy. We show that if a well-known difference-based roughness measure is used to derive a natural choice for V then this statistic is the sum of squares of a residual cusum sequence. Thus we confirm theoretically the long-held impression that the residual cusum sequence is powerful…

平滑信号检测：基于累积和程序的最优性AI 解读

Cox et al. (1988) show that under a random smooth function model with signal covariance matrix V, a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic yTVy. We show that if a well-known difference-based roughness measure is used to derive a natural choice for V then this statistic is the sum of squares of a residual cusum sequence. Thus we confirm theoretically the long-held impression that the residual cusum sequence is powerful…

非参数回归中残差方差估计的图方法AI 解读

If one wishes to make inferences about a regression, then an accurate estimator of the residual variance is required. However, except in the simplest cases, all estimators of variance are biased by an amount which depends on the unknown regression. Here, a graphical procedure is proposed which indicates whether the bias in a particular estimate is small. This procedure is studied in some detail for estimators which are weighted sums of squares of divided differences of the…

非参数回归残差方差估计的图形方法AI 解读

If one wishes to make inferences about a regression, then an accurate estimator of the residual variance is required. However, except in the simplest cases, all estimators of variance are biased by an amount which depends on the unknown regression. Here, a graphical procedure is proposed which indicates whether the bias in a particular estimate is small. This procedure is studied in some detail for estimators which are weighted sums of squares of divided differences of the…

非参数回归中的残差方差估计AI 解读

A wide class of estimators of the residual variance in nonparametric regression is considered, namely those that are quadratic in the data, unbiased for linear regression, and always nonnegative. The minimax mean squared error estimator over a natural class of regression functions is derived. This optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself.

非参数回归中残差方差的估计AI 解读

A wide class of estimators of the residual variance in nonparametric regression is considered, namely those that are quadratic in the data, unbiased for linear regression, and always nonnegative. The minimax mean squared error estimator over a natural class of regression functions is derived. This optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself.

大规模秩相关系数集合的评估AI 解读

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large…

大量秩相关系数的显著性评估AI 解读

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large…