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空间场稀疏记录的补全AI 解读

Historical records of weather, such as monthly precipitation and temperatures from the last century, are an invaluable database to use in studying changes and variability in climate. These data also provide the starting point for understanding and modeling the relationship among climate, ecological processes, and human activities. However, these data are observed irregularly over space and time. The basic statistical problem is to create a complete data record that is…

非参数曲线估计的置信区间AI 解读

Numerous nonparametric regression methods exist that yield consistent estimators of function curves. Often, one is also interested in constructing confidence intervals for the unknown function. When a function estimate is based on a single global smoothing parameter the resulting confidence intervals may hold their desired confidence level 1 – α on average but because bias in nonparametric estimation is not uniform, they do not hold the desired level uniformly at all design…

回归模型两侧的非参数变换AI 解读

SUMMARY One way to model heteroscedasticity and skewness of the error distribution in regression is to transform both sides of the regression equation. If it is possible to transform the regression equation to result in normally distributed errors, then we can obtain more efficient parameter estimates and valid prediction intervals. One problem with this approach is that the choice of transformation is usually restricted to the power or shifted power family. Often there is…

作为局部平滑器的样条AI 解读

A smoothing spline is a nonparametric curve estimate that is defined as the solution to a minimization problem. One problem with this representation is that it obscures the fact that a spline, like most other nonparametric estimates, is a local, weighted average of the observed data. This property has been used extensively to study the limiting properties of kernel estimates and it is advantageous to apply similar techniques to spline estimates. Although equivalent kernels…

营养吸收速率方程的非参数估计AI 解读

Knowledge of the rate of a biological process is important for characterizing the system and is necessary for gaining a deeper understanding of the process. Consider measurements, Y, made over time on a system following the model Y = f(t) + e, where f is a smooth, unknown function and e is measurement error. Although most statistical methodology has focused on estimating f(t) or f′(t), in some applications what is of real biological interest is the relationship between f and…

非参数回归中平滑程度范围的选择AI 解读

Most nonparametric regression estimates smooth the observed data in the process of generating a suitable estimate. The resulting curve estimate is sensitive to the amount of smoothing introduced, and it is important to examine the estimate over a range of smoothing choices. An objective way to specify such a range is to estimate the optimal value of the smoothing parameter (bandwidth) with respect to some loss function and then report a confidence interval for this parameter…

平滑样条的平均后验方差与平均平方误差的一致估计AI 解读

A smoothing spline estimator can be interpreted in two ways: either as the solution to a variational problem or as the posterior mean when a particular Gaussian prior is placed on the unknown regression function. In order to explain the remarkable performance of her Bayesian "confidence intervals" in a simulation study, Wahba conjectured that the average posterior variance of a spline estimate evaluated at the observation points will be close to the expected average squared…

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平滑样条的贝叶斯置信区间AI 解读

The frequency properties of Wahba's Bayesian confidence intervals for smoothing splines are investigated by a large-sample approximation and by a simulation study. When the coverage probabilities for these pointwise confidence intervals are averaged across the observation points, the average coverage probability (ACP) should be close to the nominal level. From a frequency point of view, this agreement occurs because the average posterior variance for the spline is similar to…

由二维截面估计三维肿瘤尺寸分布的交叉验证样条方法AI 解读

We study the problem of estimating the distribution of the three-dimensional radiuses of a collection of spheres, given measurements of the two-dimensional radiuses of a sample of planar cross sections. This problem arises in the estimation of the tumor size distribution of spherical microtumors induced in mouse livers following injection of a carcinogen. We first convert this problem to a form suitable for the application of cross-validated spline methods for the solution…