摘要:

This note examines the experiment performed by Beaton, Rubin, and Barone (1976) to study the effect of rounding errors in published figures, when these data are used in regression analysis. The experiment could be vitiated by the fact that the error introduced in the trend variable is by no means trivial when one measures the data in deviation from the mean. For this reason, the results presented in Beaton, Rubin, and Barone (1976) do not contain enough evidence to suggest “that it is extremely unlikely that the unperturbed solution” (p. 161) of the Longley model is the correct one.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480622

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The limiting distribution of the chi-square goodness-of-fit statisticTnunder alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate asn→ ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn− μn)/σnis standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two approximations indicate that for large values of the true power, the normal approximation is best, but for moderate values of power, the chi-square approximation is best.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480623

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Three classes ofMestimates for robust linear regression are investigated for various contaminated normal distributions, sample sizes, and distributions of the independent variable. These are theLpestimates, the amt estimate, and a new class of estimates (Ea) with bounded influence function. It is found that theEaclass consistently outperforms theLpclass, performs about as well as the amt estimate, and solutions forEaestimates can be obtained rapidly and reliably. Results are also reported on a robust scale estimate in theEaclass which has negligible bias for normal distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480624

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A mean squared error criterion is used to compare five estimators of the coefficients in a linear regression model: least squares, principal components, ridge regression, latent root, and a shrunken estimator. Each of the biased estimators is shown to offer improvement in mean squared error over least squares for a wide range of choices of the parameters of the model. The results of a simulation involving all five estimators indicate that the principal components and latent root estimators perform best overall, but the ridge regression estimator has the potential of a smaller mean squared error than either of these.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480625

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The approach of Grizzle, Starmer, and Koch (1969) to analyzing categorical data using linear and loglinear transformations is applied to the analysis of univariate paired and triple comparison experiments. This method of analysis produces noniterative weighted least-squares estimates of the preference ratings corresponding to the treatments under test and allows for testing hypotheses relative to their values within the framework of the general linear hypothesis. Further, the technique produces estimates of the preference ratings which are linear on the log scale within which Bradley (1965) defined his model. Examples with and without ties or order effects for paired comparison experiments and an example of a triple comparison experiment are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480626

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This article considers the test reset which is intended to detect a nonzero mean of the disturbance in a linear regression model. Analysis of an approximation to the test statistic's distribution and Monte Carlo experiments reveal that the power of the test may decline as the size of the disturbance mean increases. However, the possibility is remote and declines with increasing sample size. Alternative sets of test variables are considered, and their effect on the power of the test is studied in Monte Carlo experiments. The best set seems to be composed of powers of the explanatory variables.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480627

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A family of concepts of stochastic dependence for bivariate distribution functions is introduced. Each concept gives rise to a family of bivariate distribution functions. We show the equivalence of some of these families with families of positively dependent distribution functions, which are known in the literature, and characterize some of them by notions from reliability theory. Interrelations among the various families are studied, and some moment inequalities are derived. Some examples and applications are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480628

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

An invariance principle is used to show that λ−1is the prior density representing ignorance concerning the parameter λ of a Poisson process, and a compatibility principle is applied to find an ignorance prior for the probabilitiespiof the categories in a multinomial model. It is shown that IIpi−1is the only positive and exchangeable prior that satisfies the compatibility condition.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480629

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The linear regression superpopulation model for survey sampling allows a formulation of the survey design problem which is close to optimum experimental design theory. This article introduces an alternative criterion to that of Royall (1970). A sampling design can be chosen to minimize the maximum mean squared error (mse) of “prediction” over the unsampled units. An upper bound for this maximum mse is derived and an algorithm given for obtaining samples satisfying the bound. The efficiency of these minimax designs for estimation of the population total is compared with the best designs in this case—namely the balanced designs of Royall.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480630

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The asymptotic distribution of Cochran'sQstatistic is obtained under the null hypothesisH0for comparing proportions in matched samples under the multinomial model. Simulation studies show that a Satterthwaithe-type approximation provides a better approximation to the limiting distribution than does the chi-square distribution. Also, if by the nature of the problem,H0implies the side conditionH, which is necessary forQto have a limiting chi-square distribution, thenQhas the same Pitman efficiency as a Wald statistic that is known to have some optimal asymptotic properties and that has the χ2distribution in the limit underH0whether or notHholds.

ISSN:0162-1459    

DOI:10.1080/01621459.1977.10480631

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor