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新产品市场渗透预测：贝叶斯方法AI 解读

We adopt a Bayesian approach to forecast the penetration of a new product into a market. We incorporate prior information from an existing product and/or management judgments into the data analysis. The penetration curve is assumed to be a nondecreasing function of time and may be under shape constraints. Markov-chain Monte Carlo methods are proposed and used to compute the Bayesian forecasts. An example on forecasting the penetration of color television using the…

新产品市场渗透率预测：贝叶斯方法AI 解读

We adopt a Bayesian approach to forecast the penetration of a new product into a market. We incorporate prior information from an existing product and/or management judgments into the data analysis. The penetration curve is assumed to be a nondecreasing function of time and may be under shape constraints. Markov-chain Monte Carlo methods are proposed and used to compute the Bayesian forecasts. An example on forecasting the penetration of color television using the…

不平衡析因设计的非参数假设与秩统计量AI 解读

Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testing the nonparametric hypotheses of no main effects, no interaction, and no factor effects in unbalanced crossed classifications. The formulation of all results includes tied…

析因设计的完全非参数假设（一）：多元重复测量设计AI 解读

We introduce nonparametric versions for many of the hypotheses tested in analysis of variance and repeated measures models, such as the hypotheses of no main effects, no interaction effects, and no factor effects. These natural extensions of the nonparametric hypothesis of equality of the k distributions in the k sample problem have appealing practical interpretations. We concentrate on multivariate repeated measures designs and obtain simple rank statistics for testing…

非平稳自回归模型下的多元均值推断AI 解读

Inference about multivariate means is investigated for the case in which the covariance matrix is assumed to follow an antedependence model, which is a general first-order autoregressive model. We present two test statistics that offer alternatives to Hotelling's T 2 test for testing whether a vector mean is equal to some specified value. These antedependence statistics have simple representations in terms of Hotelling's T 2 statistics computed for certain bivariate and…

摘要暂缺

普通线性模型与复相关模型中 F 检验的渐近有效性AI 解读

In this article we establish under fairly general conditions that the F tests used in the linear model and the correlation model are asymptotically valid in the presence of nonnormality, in that their sizes are unaffected, asymptotically, by this nonnormality. Similar results could be derived for Scheffé-type simultaneous confidence intervals as well as the one-sided t tests used in these models. Finally, we find the asymptotic distribution of the sample variance and show…

摘要暂缺

广义组检验程序AI 解读

A person wishes to determine which, if any, of $n = \Pi^k_{j=1} a_j$ i.i.d. random variables, $X(i_1,\cdots, i_k), i_j = 1,\cdots, a_j$, lie in some specified set $A$. Such observations will be called unsafe. It is assumed that the density of the $X$'s is known and that $Y_j(i_1,\cdots, i_j)$, the sum of all the $X$'s whose first $j$ indices are $i_1,\cdots, i_j$, can be measured as easily as the individual $X$'s. In this paper, search procedures of the following form are…

乘积方法在广义复合对称问题中的应用AI 解读

Arnold (1973) studied testing problems where the covariance matrix is assumed to have the generalized correlation structure under both hypotheses. That paper showed how to transform such problems to "products" of unpatterned problems. This paper extends those results to testing problems where the covariance matrix is assumed to have Geisser's (1963) generalization of the pattern of compound symmetry. We prove theorems indicating how to transform such problems to products of…

问题乘积理论在具有特定结构的协方差矩阵中的应用AI 解读

This paper describes a general method for deriving optimal procedures for problems where the covariance matrices are patterned under both null and alternative hypotheses. The pattern considered in this paper was first suggested by Olkin (1970) and is a generalization of the intraclass correlation model of Wilks (1946) and arises in the study of interchangeable random variables. We prove a theorem showing how we can transform most such problems to products of problems where…