Pub Date : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01043.X
M. O'Neill
{"title":"Distributional Expansions for Canonical Correlations from Contingency Tables","authors":"M. O'Neill","doi":"10.1111/J.2517-6161.1978.TB01043.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01043.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"34 1","pages":"303-312"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80030455","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 : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01042.X
A. McLeod
{"title":"On the Distribution of Residual Autocorrelations in Box–Jenkins Models","authors":"A. McLeod","doi":"10.1111/J.2517-6161.1978.TB01042.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01042.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"68 1","pages":"296-302"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77353742","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 : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01051.X
R. Farebrother
{"title":"An Historical Note on Recursive Residuals","authors":"R. Farebrother","doi":"10.1111/J.2517-6161.1978.TB01051.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01051.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"8 1","pages":"373-375"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84602099","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 : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01046.X
A. Whittemore
{"title":"Collapsibility of Multidimensional Contingency Tables","authors":"A. Whittemore","doi":"10.1111/J.2517-6161.1978.TB01046.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01046.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"50 1","pages":"328-340"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82085298","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 : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01049.X
M. Berman
SUMMARY The likelihood function for each of k independent sets of data is assumed to belong to the two-parameter exponential family, the two parameters for the ith data set being si, which is a nuisance parameter, and 0, which is common to all the data sets and is the parameter of interest. The theory of similar tests suggests that the appropriate method for testing 0 is to condition on the statistic which is minimal sufficient for * = (b1, ..., a/4) when 0 is known. This minimal sufficient statistic will be different depending on whether or not the .s's are known to be equal. The effect of assuming that the as's are not equal when in fact they are (and vice versa) is investigated and some examples are given. The broad conclusion is that, provided the k samples are balanced in a certain sense, no great harm is done by conditioning on the incorrect statistic.
{"title":"Exponential Families and Conditioning on Statistics which are not Minimal Sufficient","authors":"M. Berman","doi":"10.1111/J.2517-6161.1978.TB01049.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01049.X","url":null,"abstract":"SUMMARY The likelihood function for each of k independent sets of data is assumed to belong to the two-parameter exponential family, the two parameters for the ith data set being si, which is a nuisance parameter, and 0, which is common to all the data sets and is the parameter of interest. The theory of similar tests suggests that the appropriate method for testing 0 is to condition on the statistic which is minimal sufficient for * = (b1, ..., a/4) when 0 is known. This minimal sufficient statistic will be different depending on whether or not the .s's are known to be equal. The effect of assuming that the as's are not equal when in fact they are (and vice versa) is investigated and some examples are given. The broad conclusion is that, provided the k samples are balanced in a certain sense, no great harm is done by conditioning on the incorrect statistic.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"43 1","pages":"358-363"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74722006","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 : 1978-07-01DOI: 10.1111/J.2517-6161.1978.TB01041.X
E. Godolphin
{"title":"A Large‐Sample Test for Detecting Gaps in Moving Average Models","authors":"E. Godolphin","doi":"10.1111/J.2517-6161.1978.TB01041.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1978.TB01041.X","url":null,"abstract":"","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"129 1","pages":"290-295"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73761926","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 : 1976-09-01DOI: 10.1111/J.2517-6161.1976.TB01562.X
T. W. Anderson
When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this lineand of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of simultaneous equations in econometrics.
{"title":"Estimation of Linear Functional Relationships: Approximate Distributions and Connections with Simultaneous Equations in Econometrics","authors":"T. W. Anderson","doi":"10.1111/J.2517-6161.1976.TB01562.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1976.TB01562.X","url":null,"abstract":"When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this lineand of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of simultaneous equations in econometrics.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"47 1","pages":"1-20"},"PeriodicalIF":0.0,"publicationDate":"1976-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79691765","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 : 1975-07-01DOI: 10.1111/J.2517-6161.1975.TB01548.X
A. Cliff, J. Ord
It is the purpose of this paper to determine how far various statistical models and methods of statistical inference have enabled the aims of geographical research to be met in the problem areas to which they have been applied. In so doing, we hope we can indicate to the statistician questions of geo graphical interest which cannot readily be answered by existing statistical methods; and to the geographer, some of the insights into geographical processes which may be gained from a statistical and model building approach. We would stress that we have not tried to be all inclusive in our coverage. Instead, we have tried to select some topics which best seem to convey the flavour of the kinds of things human geographers have been doing, and which will, at the same time, be of interest to statisticians on either theoretical or empirical grounds. In addition, our own interests mean that we have concentrated upon examples in human (economic and urban), rather than physical, geography, although similar approaches have been used there to a lesser degree. More general reviews are provided by Gould (1969), Berry (1971) and Wilson (1972).
{"title":"Model Building and the Analysis of Spatial Pattern in Human Geography","authors":"A. Cliff, J. Ord","doi":"10.1111/J.2517-6161.1975.TB01548.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1975.TB01548.X","url":null,"abstract":"It is the purpose of this paper to determine how far various statistical models and methods of statistical inference have enabled the aims of geographical research to be met in the problem areas to which they have been applied. In so doing, we hope we can indicate to the statistician questions of geo graphical interest which cannot readily be answered by existing statistical methods; and to the geographer, some of the insights into geographical processes which may be gained from a statistical and model building approach. We would stress that we have not tried to be all inclusive in our coverage. Instead, we have tried to select some topics which best seem to convey the flavour of the kinds of things human geographers have been doing, and which will, at the same time, be of interest to statisticians on either theoretical or empirical grounds. In addition, our own interests mean that we have concentrated upon examples in human (economic and urban), rather than physical, geography, although similar approaches have been used there to a lesser degree. More general reviews are provided by Gould (1969), Berry (1971) and Wilson (1972).","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"112 1","pages":"297-328"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79311566","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 : 1974-09-01DOI: 10.1111/J.2517-6161.1974.TB00983.X
J. Lindsey
OFTEN, more than one probability distribution is theoretically feasible when considering statistical models for an experiment. The problem of determination of the more plausible distribution using likelihood procedures (see, for example, Sprott and Kalbfleisch, 1969) will be discussed for the simple case where all observations are made under the same response conditions. (Lindsey, 1974, will consider this problem when independent variables are present.) To do this using likelihood inference, a base statistical model must be introduced with which all other distributions under consideration may be compared. The derivation which follows yields the multinomial model as the base model. Several approaches have been suggested in the literature to the problem of determining which of a number of possible models best describes a set of data. Cox (1961, 1962) develops asymptotic Neyman-Pearson likelihood ratio tests and suggests an alternative approach involving a combination, either additive or multiplicative, of the density functions, with estimation of additional parameters. This approach is further developed by Atkinson (1970). When prior probabilities, both for each model and for the parameters within the models, are available, Lindley (1961, p. 456) gives a posterior odds ratio of the two models using Bayes's theorem. When applicable (i.e. when prior probabilities are available), this approach may be used with the methods developed below.
通常，在考虑一个实验的统计模型时，理论上可行的概率分布不止一个。对于在相同响应条件下进行所有观测的简单情况，将讨论使用似然程序确定更合理分布的问题(例如，参见Sprott和Kalbfleisch, 1969)。(Lindsey, 1974，将在存在自变量时考虑这个问题。)要使用似然推理做到这一点，必须引入一个基本统计模型，以便与所考虑的所有其他分布进行比较。下面的推导得到多项式模型作为基本模型。文献中提出了几种方法来确定在许多可能的模型中哪一个最能描述一组数据。Cox(1961,1962)发展了渐近内曼-皮尔逊似然比检验，并提出了另一种方法，包括密度函数的加性或乘法组合，以及对附加参数的估计。Atkinson(1970)进一步发展了这种方法。当每个模型和模型内参数的先验概率可用时，Lindley (1961, p. 456)使用贝叶斯定理给出了两个模型的后验比值比。当适用时(即当先验概率可用时)，这种方法可以与下面开发的方法一起使用。
{"title":"Comparison of Probability Distributions","authors":"J. Lindsey","doi":"10.1111/J.2517-6161.1974.TB00983.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1974.TB00983.X","url":null,"abstract":"OFTEN, more than one probability distribution is theoretically feasible when considering statistical models for an experiment. The problem of determination of the more plausible distribution using likelihood procedures (see, for example, Sprott and Kalbfleisch, 1969) will be discussed for the simple case where all observations are made under the same response conditions. (Lindsey, 1974, will consider this problem when independent variables are present.) To do this using likelihood inference, a base statistical model must be introduced with which all other distributions under consideration may be compared. The derivation which follows yields the multinomial model as the base model. Several approaches have been suggested in the literature to the problem of determining which of a number of possible models best describes a set of data. Cox (1961, 1962) develops asymptotic Neyman-Pearson likelihood ratio tests and suggests an alternative approach involving a combination, either additive or multiplicative, of the density functions, with estimation of additional parameters. This approach is further developed by Atkinson (1970). When prior probabilities, both for each model and for the parameters within the models, are available, Lindley (1961, p. 456) gives a posterior odds ratio of the two models using Bayes's theorem. When applicable (i.e. when prior probabilities are available), this approach may be used with the methods developed below.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"39 1","pages":"38-47"},"PeriodicalIF":0.0,"publicationDate":"1974-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85893473","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 : 1974-09-01DOI: 10.1111/J.2517-6161.1974.TB00981.X
L. Kish, M. Frankel
The design of complex samples induces correlations between element values. In stratification negative correlation reduces the variance; but that gain is less for subclass means, and even less for their differences and for complex statistics. Clustering induces larger and positive correlations between element values. The resulting increase in variance is measured by the ratio deff, and is often severe. This is reduced but persists for subclass means, their differences, and for analytical statistics. Three methods for computing variances are compared in a large empirical study. The results are encouraging and useful.
{"title":"Inference from Complex Samples","authors":"L. Kish, M. Frankel","doi":"10.1111/J.2517-6161.1974.TB00981.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1974.TB00981.X","url":null,"abstract":"The design of complex samples induces correlations between element values. In stratification negative correlation reduces the variance; but that gain is less for subclass means, and even less for their differences and for complex statistics. Clustering induces larger and positive correlations between element values. The resulting increase in variance is measured by the ratio deff, and is often severe. This is reduced but persists for subclass means, their differences, and for analytical statistics. Three methods for computing variances are compared in a large empirical study. The results are encouraging and useful.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"132 1","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"1974-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88838961","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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