Alternatives to plotting CP in multiple regressionSPJØTVOLL,, EMIL
doi: 10.1093/biomet/64.1.1pmid: N/A
Abstract Two plotsalternative to that of CP are presented. One, which is a simple linear transformation of CP, is based on the familiar Fstatistics for testing the adequacy of subset regressions. The other is based on the significance probalities of the F statistics. It is argued that the significance probabilities give a more accurate measure of the goodness of fit of a regression function than, for example, the distance of CP from p. Problems of selecting a set of adequate regression functions are discussed. This content is only available as a PDF. © 1977 Biometrika Trust
Some inference procedures for monotonically ordered normal meansWILLIAMS, DAVID, A.
doi: 10.1093/biomet/64.1.9pmid: N/A
Abstract This paper determines a limiting distribution of the estimated maximum and range of a set of monotonically ordered normal means when all means are in fact equal. The upper percentiles of the studentized distributions are tabulated. These percentiles can be used as critical values in tests of hypotheees concerning monotonically ordered normal means, and in forming simultaneons confidence limits for contrasts between normal means when the contrast coefficients are restricted to being monotonically ordered. This content is only available as a PDF. © 1977 Biometrika Trust
Robust regression via discriminant analysisATKINSON, A., C.;COX, D., R.
doi: 10.1093/biomet/64.1.15pmid: N/A
Abstract For linear regression with grouped data, and with an equal number of observations per grouping point, linear discriminant analysis is applied to the ordered response variables to find that combination which shows strongest linear regression. After a modification to remove weights with an anomalous sign, there results a robust estimate of slope. Generalizations are outlined. This content is only available as a PDF. © 1977 Biometrika Trust
Jackknife confidence limits using Student t approximationsHINKLEY, D., V.
doi: 10.1093/biomet/64.1.21pmid: N/A
Abstract This paper presents a simplified account of the theory of jackknife confidence limits with reference to the effects of s-at-a-time omission. Both the usual and a modified Student t approximation are considered for the standardized jackknifed estimator. Monte Carlo results are given for the cases of variance and correlation parameters. This content is only available as a PDF. © 1977 Biometrika Trust
The marginal totals of a 2×2 tablePLACKETT, R., L.
doi: 10.1093/biomet/64.1.37pmid: N/A
Abstract Inferences about the odds ratio of a 2×2 contingency table are usually based on the distribution of any one frequency conditional on the observed values of the marginal totals. The reason is given that the marginal totals are ancillary statistics which contain no information about the odds ratio. We consider inferences about the odds ratio when the likelihood function is derived from the marginal totals. Standard procedures for making statements about an unknown parameter are found to be inconclusive. This content is only available as a PDF. © 1977 Biometrika Trust
A model for a binary variable with time-censored observationsFAREWELL, V., T.
doi: 10.1093/biomet/64.1.43pmid: N/A
Abstract A binary variable can specify the incidence of a particular disease, Y = 1 or a lifetime free of the disease, Y = 0. In a study, some subjects have Y = 1 recorded at specified ages. For other subjects, with Y unknown due to incomplete follow-up, the observed follow-up time compared with the ma1 incidence pattern for the disease gives some information on the possibility that Y = 0. A model for this situation is proposed which combines a logistic relationship for the probability of incidence and an exponential distribution for the time of incidence. The efficiency of the model is compared with that of a logistio model with no time censoring. The behaviour of a logistic model applied without considering the time censoring is also examined. This content is only available as a PDF. © 1977 Biometrika Trust
Optimal use of extraneous information concerning a nuisance parameterHEMON,, DENIS
doi: 10.1093/biomet/64.1.51pmid: N/A
Abstract Suppose that N experiments can be carried out. One type of experiment provides observations, Y, depending on α, the parameter of interest and β a nuisance parameter. The other type provides observations, Z, depending on β and γ. How should the N experiments be divided between the two types to estimate α optimally? The existence and uniqueness of an optimal allocation is proved and a method of calculation is provided. In the particular case of β being scalar, the optimal allocation is given explicitly, and is not necessarily the simple solution consisting of performing only experiments of the first type. In this case, an observation Z may provide additional information concerning α which is more useful than a further observation Y. An application to estimation from truncated data is described and further generalizations are considered. This content is only available as a PDF. © 1977 Biometrika Trust
The precision of different experimental designs for a random fieldDUBY,, CAMILLE;GUYON,, XAVIER;PRUM,, BERNARD
doi: 10.1093/biomet/64.1.59pmid: N/A
Abstract Various experimental designs can be used to study the effects of several treatments on a field. The variation of yield in the field will be represented by a realization of a stationary process with isotropic covariance. The variance of an estimator of a treatment effect can be divided into two parts, the first part due to experimental errors and the second part involving the process as well as randomization. This second component will be studied in order to find an optimal experimental design. This content is only available as a PDF. © 1977 Biometrika Trust