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简单线性模型百分位数曲线的紧置信带与容忍带AI 解读

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

摘要暂缺

一般线性模型中百分位数线的同时置信带AI 解读

This article is a generalization of the procedures developed by Steinhorst and Bowden (1971) for constructing confidence bands for the 100βth percentiles in the general linear model. Since the original procedure built these bands about a biased estimator of the 100βth precentile line, some other estimators were tried. While some improvement was noted, the results are not conclusive, suggesting that the best procedure has not been found yet.

百分位数的同时置信带与判别集合AI 解读

Using the general linear model, y = Xβ+e, where e∼N(0, σ2/): simultaneous confidence bonds are found for the 100 pth percentile, x′β+kpσ, of the normal population with mean x′β and variance σ2 (kp is the 100 pth percentile of the standard normal distribution). The bands are simultaneous in x or in x and p. In the simple linear regression case these bands are used to define simultaneous discrimination sets for any fixed values, yP, of the dependent variable.

判别与百分位数置信带AI 解读

Using the general linear model, y = Xβ+e, where e∼N(0, σ2/): simultaneous confidence bonds are found for the 100 pth percentile, x′β+kpσ, of the normal population with mean x′β and variance σ2 (kp is the 100 pth percentile of the standard normal distribution). The bands are simultaneous in x or in x and p. In the simple linear regression case these bands are used to define simultaneous discrimination sets for any fixed values, yP, of the dependent variable.

线性回归模型的同时置信带AI 解读

In this article a procedure is given for constructing confidence bands of various forms for linear regression models. Application of the procedure yields, as special cases, hyperbolic, straight line segment, uniform width and trapezoidal confidence bands.

简单线性模型的线段置信带AI 解读

In this paper confidence bands are given for the entire line for simple linear regressions. The conventional bands that have been given in the past are curvilinear. In this paper we consider confidence bands that are straight lines. It is shown that under certain conditions the “width” of these straight line bands is less than the width of the conventional curvilinear bands.

线性模型中等宽与比例宽度的置信带AI 解读

In this paper confidence bands are given for simple linear models. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval.