Tests for serial correlation in regression analysis based on the periodogram of least-squares residualsDURBIN,, J.
doi: 10.1093/biomet/56.1.1pmid: N/A
Abstract A well-known procedure for testing for serial correlation is to plot out the sample path of the cumulated periodogram and to compare the resulting graph with the Kolmogorov-Smirnov limits. The paper considers small-sample aspects of this procedure when the periodogram is calculated from the residuals from least-squares regression. It is shown that for a test against an excess of low-frequency relative to high-frequency variation in the errors of the regression model, a pair of lines can be drawn on the graph such that if the path crosses the upper line the hypothesis of serial independence is definitely rejected, while if the path fails to cross the lower line the hypothesis is definitely accepted. In the intermediate case the test is inconclusive. Similar procedures are given for tests against an excess of high-frequency variation and for two-sided tests. To facilitate the tests a table of significance values of the appropriate modified Kolmogorov-Smirnov statistics is given. A further test based on the mean of the ordinates of the cumulated periodogram is considered. It is shown that bounding significance values are easily obtainable from significance values of the mean of a uniform distribution. This content is only available as a PDF. © Oxford University Press
The use of residuals as a concomitant variableATKINSON, ANTHONY, C.
doi: 10.1093/biomet/56.1.33pmid: N/A
Abstract Suppose that there is correlation between the yields of successive or adjacent experimental units. An estimator of treatment effects using the residuals of adjacent plots as a concomitant variable is investigated. It is shown to be very close to the maximum likelihood estimator when the errors form a first-order autoregressive series. This content is only available as a PDF. © Oxford University Press
The analysis of variance of some non-orthogonal designs with split plotsREES, D., H.
doi: 10.1093/biomet/56.1.43pmid: N/A
Abstract The paper describes the analysis of variance of some experimental designs in which there may be several levels of splitting of plots, and in which the treatments at any level may be non-orthogonal to blocks. The construction of the designs, based on the Kronecker product method as used by Kurkjian & Zelen (1962), is discussed first. Then the method of analysis, based on the ideas developed by Nelder (1965a, b), is outlined. The paper shows that some potentially useful designs, not previously discussed in any detail, can be analysed quite simply using these ideas. The combination of information from several sources, and the derivation of unbiased estimates of error, are also mentioned. This content is only available as a PDF. © Oxford University Press
The choice of variables in the design of experiments for linear regressionDAVIES,, P.
doi: 10.1093/biomet/56.1.55pmid: N/A
Abstract In this paper, a procedure is developed which can be used to decide if a doubtful variable should be included in an experiment to fit a linear model to a set of yields. The criterion of success of the experiment is based on the mean square error of the fitted linear model, averaged over a specified region of the independent variables. A study is made of the gains to be expected when a variable is correctly excluded. This content is only available as a PDF. © Oxford University Press
Multivariate paired comparisons: The extension of a univariate model and associated estimation and test proceduresDAVIDSON, ROGER, R.;BRADLEY, RALPH, A.
doi: 10.1093/biomet/56.1.81pmid: N/A
Abstract This study is concerned with the development of an extension of the Bradley-Terry model for paired comparisons to situations in which responses to paired comparisons are obtained on each of several characteristics. At the outset a probability model for multivariate paired comparisons is proposed that may be represented in several distinct ways. An iterative procedure for obtaining maximum-likelihood estimates of the parameters introduced into the model is given and its behaviour examined in some detail. It is observed that the procedure generally performed well, the key to this conclusion being the relative stability of the initial estimates of the preference parameters. On the basis of some initial applications of the test of the appropriateness of the multivariate paired comparisons procedure, one might surmise that the model yields a reasonable representation of actual experimentation. However, further applications of the model to actual data are required before a realistic evaluation of its utility can be made. This content is only available as a PDF. Author notes * Now at University of Victoria Victoria, B.C. © Oxford University Press
Bayesian estimation of latent roots and vectors with special reference to the bivariate normal distributionTIAO, G., C.;FIENBERG,, S.
doi: 10.1093/biomet/56.1.97pmid: N/A
Abstract This paper discusses from a Bayesian viewpoint some aspects of the estimation of latent roots and vectors of the covariance matrix of the bivariate normal distribution. The joint distribution of (i) the angle of the canonical transformation, and (ii) the ratio of the larger root to the total variance is considered in detail and illustrated by an example. Also discussed is the problem of making inferences about the larger roots, and several simple approximations to the distribution are considered. Finally, a generalization is given of one of the approximation methods to latent roots of higher dimensional covariance matrices. This content is only available as a PDF. Author notes †Now at the University of Chicago © Oxford University Press
On the exact distribution of Wilks's criterionPILLAI, K. C., SREEDHARAN;GUPTA, ARJUN, K.
doi: 10.1093/biomet/56.1.109pmid: N/A
Abstract In this paper, the exact distribution of Wilks's likelihood ratio criterion, Λ, is obtained, and explicit expressions for Λ are given for p = 3, 4, 5 and 6, where p is the number of variables. The distribution is expressed as a finite series except where p and f2, the degrees of freedom, are both odd, in which case it is given in infinite series form. Lower percentage points are tabulated for selected values of f2 > 10, extending the tabulations of Schatzoff (1966) for the above values of p. This content is only available as a PDF. © Oxford University Press