Pub Date : 1972-01-01DOI: 10.1007/978-1-4612-4380-9_37
D. Cox
{"title":"Regression Models and Life-Tables","authors":"D. Cox","doi":"10.1007/978-1-4612-4380-9_37","DOIUrl":"https://doi.org/10.1007/978-1-4612-4380-9_37","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"17 1","pages":"187-220"},"PeriodicalIF":0.0,"publicationDate":"1972-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88776731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1971-10-01DOI: 10.1111/J.2517-6161.1971.TB01523.X
V. P. Godambe, M. Thompson
In this paperan attempt ismadeto showhowthe regression analysisgenerally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.
{"title":"Bayes, Fiducial and Frequency Aspects of Statistical Inference in Regression Analysis in Survey‐Sampling","authors":"V. P. Godambe, M. Thompson","doi":"10.1111/J.2517-6161.1971.TB01523.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1971.TB01523.X","url":null,"abstract":"In this paperan attempt ismadeto showhowthe regression analysisgenerally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"25 1","pages":"361-376"},"PeriodicalIF":0.0,"publicationDate":"1971-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81770676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1971-10-01DOI: 10.1111/J.2517-6161.1971.TB01521.X
K. Kemp
The paper describes a number of formal expressions which can be used to determine properties of cumulative sum schemes. Formulae given only depend upon very general assumptions with regard to the distribution of the cumulated statistic. Numerical as well as algebraic procedures are described which permit calculation of the average sample run length to a specified degree of accuracy for almost any statistic likely to arise in practice. Methods for generating the sample run length distribution are also given.
{"title":"Formal Expressions Which Can be Applied to Cusum Charts","authors":"K. Kemp","doi":"10.1111/J.2517-6161.1971.TB01521.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1971.TB01521.X","url":null,"abstract":"The paper describes a number of formal expressions which can be used to determine properties of cumulative sum schemes. Formulae given only depend upon very general assumptions with regard to the distribution of the cumulated statistic. Numerical as well as algebraic procedures are described which permit calculation of the average sample run length to a specified degree of accuracy for almost any statistic likely to arise in practice. Methods for generating the sample run length distribution are also given.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"1 1","pages":"331-355"},"PeriodicalIF":0.0,"publicationDate":"1971-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75104496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1971-10-01DOI: 10.1111/J.2517-6161.1971.TB01525.X
E. Foreman, K. Brewer
SUMMARY Use is made of a well-known heteroscedastic super-population model to obtain comparisons of the efficiencies of six methods of sampling in common use. These are simple random sampling with unbiased estimators, simple random sampling with ratio estimators, and sampling with probability proportional to size with unbiased estimators; each with and without replacement. The resulting comparisons are readily interpretable, thus affording simple criteria for comparing the efficiencies of these widely used sample plans. They also provide heuristic explanations of their properties.
{"title":"The Efficient Use of Supplementary Information in Standard Sampling Procedures","authors":"E. Foreman, K. Brewer","doi":"10.1111/J.2517-6161.1971.TB01525.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1971.TB01525.X","url":null,"abstract":"SUMMARY Use is made of a well-known heteroscedastic super-population model to obtain comparisons of the efficiencies of six methods of sampling in common use. These are simple random sampling with unbiased estimators, simple random sampling with ratio estimators, and sampling with probability proportional to size with unbiased estimators; each with and without replacement. The resulting comparisons are readily interpretable, thus affording simple criteria for comparing the efficiencies of these widely used sample plans. They also provide heuristic explanations of their properties.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"9 1","pages":"391-400"},"PeriodicalIF":0.0,"publicationDate":"1971-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74865918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1970-07-01DOI: 10.1111/J.2517-6161.1970.TB00832.X
W. Fuller
FOR populations arranged in natural order, say in increasing values of a concomitant variable, one common sampling scheme is to divide the population into strata and sample proportionately from each stratum. Variance of the sample mean is minimized (with the possible exception of finite corrections) if the population is divided into n strata and one unit selected from each. A second common procedure, particularly if the sampling is with unequal probabilities, is to sample systematically.t It is well known that if the y characteristic is composed of a linear trend plus random elements the 1-per-stratum design is more efficient than systematic sampling of the population in natural order. The disadvantage of both of these sampling schemes is, of course, that no unbiased estimator of variance is available. In this paper we develop a sampling procedure which for n > 4 and a linear trend has a smaller variance for the sample mean than 1 per stratum and for which an unbiased estimator of the variance is available.
{"title":"Sampling with Random Stratum Boundaries","authors":"W. Fuller","doi":"10.1111/J.2517-6161.1970.TB00832.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1970.TB00832.X","url":null,"abstract":"FOR populations arranged in natural order, say in increasing values of a concomitant variable, one common sampling scheme is to divide the population into strata and sample proportionately from each stratum. Variance of the sample mean is minimized (with the possible exception of finite corrections) if the population is divided into n strata and one unit selected from each. A second common procedure, particularly if the sampling is with unequal probabilities, is to sample systematically.t It is well known that if the y characteristic is composed of a linear trend plus random elements the 1-per-stratum design is more efficient than systematic sampling of the population in natural order. The disadvantage of both of these sampling schemes is, of course, that no unbiased estimator of variance is available. In this paper we develop a sampling procedure which for n > 4 and a linear trend has a smaller variance for the sample mean than 1 per stratum and for which an unbiased estimator of the variance is available.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"38 1","pages":"209-226"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82307502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1970-07-01DOI: 10.1111/J.2517-6161.1970.TB00828.X
Awf Edwards
A solution to the problem of estimating the positions and times of the branch points of a Brownian-motion/Yule process, given the positions of all the particles at a particular time, is outlined. A likelihood approach is used, and it is shown that the solution involves maintaining a clear distinction between likelihood and conditional probability if difficulties over mathematical singularities are to be avoided. Several unsolved mathematical problems are encountered, and it is concluded that some simulation studies may be required for a complete solution. Questions of scientific inference which the problem raises are discussed briefly.
{"title":"Estimation of the Branch Points of a Branching Diffusion Process","authors":"Awf Edwards","doi":"10.1111/J.2517-6161.1970.TB00828.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1970.TB00828.X","url":null,"abstract":"A solution to the problem of estimating the positions and times of the branch points of a Brownian-motion/Yule process, given the positions of all the particles at a particular time, is outlined. A likelihood approach is used, and it is shown that the solution involves maintaining a clear distinction between likelihood and conditional probability if difficulties over mathematical singularities are to be avoided. Several unsolved mathematical problems are encountered, and it is concluded that some simulation studies may be required for a complete solution. Questions of scientific inference which the problem raises are discussed briefly.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"25 1","pages":"155-164"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75373590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1970-07-01DOI: 10.1111/J.2517-6161.1970.TB00830.X
J. Kalbfleisch, D. A. Sprott
[Read before the ROYAL STATISTICAL SOCIETY at a meeting organized by the RESEARCH SECTION on Wednesday, March 11th, 1970, Professor J. DURBIN in the Chair] SUMMARY Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal and conditional likelihoods are dependent upon factorings of the likelihood function. They are applied to the linear functional relationship and to related models and are found to give intuitively appealing results. These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted. This gives an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach.
{"title":"Application of Likelihood Methods to Models Involving Large Numbers of Parameters","authors":"J. Kalbfleisch, D. A. Sprott","doi":"10.1111/J.2517-6161.1970.TB00830.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1970.TB00830.X","url":null,"abstract":"[Read before the ROYAL STATISTICAL SOCIETY at a meeting organized by the RESEARCH SECTION on Wednesday, March 11th, 1970, Professor J. DURBIN in the Chair] SUMMARY Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal and conditional likelihoods are dependent upon factorings of the likelihood function. They are applied to the linear functional relationship and to related models and are found to give intuitively appealing results. These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted. This gives an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"29 1","pages":"175-194"},"PeriodicalIF":0.0,"publicationDate":"1970-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79230980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1968-07-01DOI: 10.1111/J.2517-6161.1968.TB00728.X
M. J. Box
{"title":"The Occurrence of Replications in Optimal Designs of Experiments to Estimate Parameters in Non‐Linear Models","authors":"M. J. Box","doi":"10.1111/J.2517-6161.1968.TB00728.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1968.TB00728.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"77 1","pages":"290-302"},"PeriodicalIF":0.0,"publicationDate":"1968-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88560349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1968-07-01DOI: 10.1111/J.2517-6161.1968.TB00727.X
D. Cox, D. Hinkley
SUMMARY A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series, for a Pearson Type VII distribution and for a log gamma distribution.
{"title":"A Note on the Efficiency of Least-squares Estimates","authors":"D. Cox, D. Hinkley","doi":"10.1111/J.2517-6161.1968.TB00727.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1968.TB00727.X","url":null,"abstract":"SUMMARY A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series, for a Pearson Type VII distribution and for a log gamma distribution.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"3 1","pages":"284-289"},"PeriodicalIF":0.0,"publicationDate":"1968-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86980984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1968-07-01DOI: 10.1111/J.2517-6161.1968.TB00730.X
P. Sen
{"title":"Asymptotically Efficient Tests by the Method of N Rankings","authors":"P. Sen","doi":"10.1111/J.2517-6161.1968.TB00730.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1968.TB00730.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"53 1","pages":"312-317"},"PeriodicalIF":0.0,"publicationDate":"1968-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80659496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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