摘要:

Tukey's [4]T-(maximum modulus) method of multiple comparisons is applicable to homoscedastic and equally correlated normally distributed random variables. For multiple comparisons on interaction effects (in factorial experiments), the allied random variables are not equally correlated. Nevertheless, it is shown that theT-method holds in this situation. The theory is illustrated by an example on a partially balanced incomplete block (PBIB) design.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500972

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A procedure is given for the construction of a fixed-width confidence interval of the largest mean ofk(k≥1) normal populations with a common known variance, based on the largest sample mean. The sample size required to achieve the preassigned confidence coefficient can be computed by using the standard normal table only.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500973

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The asymptotic joint distribution of an arbitrary number of linear systematic statistics (that is, linear combinations of order statistics), when observations are made on a random vector, is shown to be normal under fairly general conditions. The linear systematic statistics may correspond to the same or to different components of the vector. Formulas for evaluating the parameters of the asymptotic normal distribution are derived. As an illustration, these are applied to the case of trimmed means when the distribution sampled is bivariate normal.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500974

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A progressive-censoring model arises from a life test of a sample of items in which one or more of the survivors may be removed from the test at the time of any failure. Such a model is often more realistic for actual failure data which must be analyzed by a statistician than one in which all survivors are assumed to be removed from test simultaneously. This paper deals with the situation in which the underlying failure-time distribution for the population sampled is the two-parameter Weibull distribution. The reliable life for the population is defined to be the 100 (1-R) percent point of the failure-time distribution, whereRis a specified population survival proportion, or reliability. An exact confidence bound on reliable life based on three observed ordered failure times is derived for this progressive-censoring model. The criterion used for selecting the order numbers of the three failure times upon which the bound is based depends upon computed values of the power function of the test associated with the bound. A table from which lower bounds can be obtained is given forRequal to .95, confidence level .90, sample size equal to 2, 3, …, 6, and all possible censorings.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500975

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The paper also summarizes another test due to S. M. Goldfeld and R. E. Quandt and examines the powers of the two by using Monte-Carlo simulations: the new test seems to compare favourably, except perhaps in the case of large samples.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500976

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Given a sample ofnvector observations from a multivariate normal population, Anderson and Roy-Gnanadesikan have given for the variances a set of confidence intervals which are approximate in that a lower bound only is known for the joint confidence coefficient. In the present study, exact procedures are developed in terms of multivariate Chi-Square distributions, and more general approximate procedures are given via Bonferroni's inequality. A numerical investigation suggests that the Bonferroni lower bound is fairly sharp for a variety of parameter values, and it always is superior to the Roy-Gnanadesikan procedure in the bivariate case examined. A lower bound in terms of independent statistics further is examined for a special class of one-sided intervals.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500977

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500978

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

We derive the asymptotic distribution of several estimators for the parameters of the linear regression ofyonxwhen some observations onyand onxare missing. Then, we compare estimators using a mean square error criterion. We find for example that a simple estimator of the linear regression function has asymptotic efficiency no worse than 0.95 compared with the maximum likelihood estimator (assuming bivariate normality) provided that no more than 30 per cent of they's and 30 per cent of thex's are missing. This simple estimator is defined without assuming bivariate normality in Section 8.1.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500979

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In this note we examine the bias and small sample efficiency of certain estimators for the parameters of a linear regression function when some observations are missing. The estimators studies in this paper were suggested by the large sample study reported in this issue of the Journal. We conclude that our asymptotically unbiased estimators of β andμy|xhave negligible bias in sample sizes as small asn= 20, and that our asymptotically unbiased estimator of σ2may have an 8% bias whenn= 20. The small sample and asymptotic efficiencies of these estimators are nearly the same forn= 60; whenn= 20 the difference between these two efficiencies depends on the correlation coefficient ρ and the pattern of missing observations.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500980

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

When two correlation coefficients are calculated from a single sample, rather than from two samples, they are not statistically independent, and the usual methods for testing equality of the population correlation coefficients no longer apply. This paper considers the situation when the sample is from a multivariate normal distribution. Several possible large sample testing procedures are given, all based on Fisher'sz-transformation. Power curves are given for each procedure and for seven values of the asymptotic correlation between the two sample correlation coefficients.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500981

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor