使用方差统计的假设矩阵的选择

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-01-11 DOI:10.1016/j.spl.2025.110356

Paavo Sattler , Manuel Rosenbaum

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引用次数: 0

摘要

Anova-type-statistic （ATS）最初由Brunner et al.（1997）提出，是用于检验各种不同参数向量θ∈Rd的多元假设的最常用的二次型之一。基于ATS的测试通常比基于其他二次型（如wald型统计）的测试更可取。但是，同一个原假设Hθ=y可以用不同的假设矩阵H∈Rm×d和相应的向量y∈Rm表示，从而得到不同的检验统计量值。由于这可能需要不同的测试决策，我们研究在哪些条件下使用不同假设矩阵的某些测试重合。在本文中，我们证明了对于anova类型统计的几个版本，对于每个假设Hθ=y，可以构造具有最小行数的伴侣矩阵，测试相同的假设，但也总是产生相同的测试决策。这可以大大减少计算时间，正如几个模拟所证明的那样。

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Choice of the hypothesis matrix for using the Anova-type-statistic

Initially developed in Brunner et al. (1997), the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors

θ \in R^{d}

. Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis

H θ = y

can be expressed by various hypothesis matrices

H \in R^{m \times d}

and corresponding vectors

y \in R^{m}

, yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-type-statistic, for each hypothesis

H θ = y

a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.