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Hellinger 邻域上的稳健模型判别设计AI 解读

To aid in the discrimination between two, possibly nonlinear, regression models, we study the construction of experimental designs. Considering that each of these two models might be only approximately specified, robust “maximin” designs are proposed. The rough idea is as follows. We impose neighbourhood structures on each regression response, to describe the uncertainty in the specifications of the true underlying models. We determine the least favourable—in terms of…

分位数回归的模型稳健设计AI 解读

We give methods for the construction of designs for regression models, when the purpose of the investigation is the estimation of the conditional quantile function, and the estimation method is quantile regression. The designs are robust against misspecified response functions, and against unanticipated heteroscedasticity. The methods are illustrated by example, and in a case study in which they are applied to growth charts.

剂量—反应研究中实验设计的稳健性AI 解读

Summary We construct experimental designs for dose–response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum mean-squared error of the estimated dose required to attain a response in 100p% of the target population. Here p might be one particular value—p = 0.5 corresponds to ED50-estimation—or it might range over an interval of values of interest. The maximum of the mean-squared error is evaluated over a…

问题 02.3.2：不当加权最小二乘——解答AI 解读

Badly weighted least squares—solution.An excellent solution was independently proposed by Geert Dhaene. A proof for the case p = 1 based on the convexity of Laplace transforms was also provided by Koenker and Portnoy, the posers of the problem.

异方差近似线性模型中用于估计与外推的整数值极小极大稳健设计AI 解读

We present our findings on a new approach to robust regression design. This approach differs from previous investigations into this area in three respects: The use of a finite design space, the use of simulated annealing to carry out the numerical minimization problems, and in our search for integer-valued, rather than continuous, designs. We present designs for the situation in which the response is thought to be approximately polynomial. We also discuss the cases of…

异方差与回归模型近似设定下的极小极大稳健设计及权重AI 解读

This article addresses the problem of constructing designs for regression models in the presence of both possible heteroscedasticity and an approximately and possibly incorrectly specified response function. Working with very general models for both types of departure from the classical assumptions, I exhibit minimax designs and correspondingly optimal weights. Simulation studies and a case study accompanying the theoretical results lead to the conclusions that the robust…

基于无穷小方法的稳健设计AI 解读

We introduce an infinitesimal approach to the construction of robust designs for linear models. The resulting designs are robust against small departures from the assumed linear regression response and/or small departures from the assumption of uncorrelated errors. Subject to satisfying a robustness constraint, they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model. The robustness constraint is quantified in terms of…

ε 污染模型中的极小极大方差 M 估计量AI 解读

In the framework of Huber's theory of robust estimation of a location parameter, minimax variance M-estimators are studied for error distributions with densities of the form $f(x) = (1 - \varepsilon)h(x) + \varepsilon g(x)$, where $g$ is unknown. A well-known result of Huber (1964) is that when $h$ is strongly unimodal, the least informative density $f_0 = (1 - \varepsilon)h + \varepsilon g_0$ has exponential tails. We study the minimax variance solutions when the known…