• 
    

    
    

      99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

      ANewTestforaNormalCovarianceMatrix

      2015-05-19 13:13:27禹建奇
      校園英語·中旬 2015年2期
      關(guān)鍵詞:校級(jí)理工大學(xué)桂林

      禹建奇

      【Abstract】The problem of testing the normal covariance matrix equal to a specified matrix is considered.A new Chi-Square test statistic is derived for multivariate normal population.Unlike the likelihood ratio test,the new test is an exact one.

      【Key words】exact test; Chi-Square test; likelihood ratio test

      1.Introduction of the Problem

      Suppose we have a sampleand we want to test the problemvs,whereis a known matrix.It is easy to see that the problem is invariant under the changeswhere T is nonsingular.Therefore,without loss of generality,we can assume that,the identity matrix.

      2.The Test Procedure

      Letbe the sample means and sample covariance,and the -th component of S,where.The null becomes .let .It is easy to see that H0 is equivalent to.

      For testing,there is a well known test statistics nS11and under .

      For testing,we regressonand get

      where

      Letthenandunder H0,and they can be used for testing respectively.Moreover,the three statistics above are independent under H0,so we combine them together and get a new statistics:

      Let ,and then under H0,.

      Finally,we get an exact test which is totally different from the ones we have already:

      If or,reject the null H0 at level .

      3.The Generalization

      At the end,we point out that the test can be easily extended to the p-variate normal cases where p>2.but the notation will become very complicated.So,we just point out this and do not show the results.

      4.Concluding Remarks

      In this article,we have developed a Chi-Square test procedure for testing a normal covariance matrix equal to a given matrix.Unlike the usual likelihood ratio test,the Chi-Square test is an exact one and easy to apply.Moreover,the powers of the Chi-Square test are always higher than are those of LRT,especially for small samples.In a word,the Chi-Square test is superior to the LRT.

      References:

      [1]Das Gupta,S.,1969.Properties of power functions of some tests concerning dispersion matrices of multivariate normal distributions.Ann.Math.Statist.40,697-701.

      [2]Muirhead,R.J.,1982.Aspects of Multivariate Statistical Theory.Wiley,New York.

      [3]Seber,G.A.F.,1984.Multivariate Observations,Wiley,New York.

      【資助項(xiàng)目】本文獲“桂林理工大學(xué)博士科研啟動(dòng)基金(2014)”及“桂林理工大學(xué)校級(jí)教改項(xiàng)目(2014B06)”支持。

      猜你喜歡
      校級(jí)理工大學(xué)桂林
      桂林六漫之歌
      歌海(2024年2期)2024-06-06 05:54:00
      桂林,美
      昆明理工大學(xué)
      黃山學(xué)院校級(jí)重點(diǎn)學(xué)科簡(jiǎn)介
      ——生態(tài)學(xué)
      我校黨委榮獲“陜西省高校先進(jìn)校級(jí)黨委”稱號(hào)
      黃山學(xué)院校級(jí)重點(diǎn)學(xué)科簡(jiǎn)介
      ——馬克思主義學(xué)科
      昆明理工大學(xué)
      昆明理工大學(xué)
      浙江理工大學(xué)
      桂林游
      雷山县| 凭祥市| 白银市| 南投市| 福安市| 长丰县| 东山县| 临沂市| 淅川县| 安阳县| 远安县| 黄龙县| 镇安县| 洛川县| 旬阳县| 文山县| 呈贡县| 康定县| 六枝特区| 黔西县| 南部县| 韶山市| 洛川县| 万年县| 东宁县| 中西区| 渝中区| 铅山县| 剑河县| 和平区| 湖州市| 泸水县| 云霄县| 阳山县| 东光县| 湄潭县| 沈阳市| 张家口市| 华容县| 宁陕县| 志丹县|