{"title":"Use of the bootstrap in robust estimation of location","authors":"G. E. Thomas","doi":"10.1111/1467-9884.00220","DOIUrl":"https://doi.org/10.1111/1467-9884.00220","url":null,"abstract":"Robust measures of location may be used in estimation problems to help to mitigate the possible effects of outliers or asymmetry. A practical difficulty is how to determine reliable valid estimates of the precision of the corresponding sample estimates. Commonly, precision is expressed by means of standard errors or confidence intervals. Several data sets are used to make comparisons of the performance of standard errors and confidence intervals based on both asymptotic normal results and the bootstrap for a number of robust location measures, including trimmed means with a fixed trimming level and Huber's proposal 2. Bootstrap results and asymptotic results using a winsorized standard deviation are generally comparable, but there is a tendency for the precision to be overstated with the latter both for very small data sets and for Huber's proposal 2 with skewed data sets. In addition, precision with Huber's proposal 2 is found to be marginally superior to that with the corresponding trimmed mean in the presence of extreme outliers.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"38 1","pages":"63-77"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77317629","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}
{"title":"Bayes Prediction in a Pareto Lifetime Model With Random Sample Size","authors":"A. Soliman","doi":"10.1111/1467-9884.00219","DOIUrl":"https://doi.org/10.1111/1467-9884.00219","url":null,"abstract":"The prediction of future ordered observations shows how long a sample of units might run until all fail in life testing. This paper deals with the problem of predicting the future ordered observations in a sample of size n from a Pareto distribution where the first r ordered observations have been observed. The analysis will depend mainly on assuming that the sample size n is a random variable having a Poisson or binomial distribution. Numerical examples are used to illustrate the procedure.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"12 1","pages":"51-62"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86372376","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}
{"title":"Wavelet Analysis and its Statistical Applications","authors":"F. Abramovich, T. Bailey, T. Sapatinas","doi":"10.1111/1467-9884.00216","DOIUrl":"https://doi.org/10.1111/1467-9884.00216","url":null,"abstract":"Summary. In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this paper gives a relatively accessible introduction to standard wavelet analysis and provides a review of some common uses of wavelet methods in statistical applications. It is primarily orientated towards the general statistical audience who may be involved in analysing data where the use of wavelets might be effective, rather than to researchers who are already familiar with the field. Given that objective, we do not emphasize mathematical generality or rigour in our exposition of wavelets and we restrict our discussion to the more frequently employed wavelet methods in statistics. We provide extensive references where the ideas and concepts discussed can be followed up in greater detail and generality if required. The paper first establishes some necessary basic mathematical background and terminology relating to wavelets. It then reviews the more well-established applications of wavelets in statistics including their use in nonparametric regression, density estimation, inverse problems, changepoint problems and in some specialized aspects of time series analysis. Possible extensions to the uses of wavelets in statistics are then considered. The paper concludes with a brief reference to readily available software packages for wavelet analysis.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"49 1","pages":"1-29"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77951009","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}
{"title":"Prediction Intervals Based on Autoregression Forecasts","authors":"X. Luna","doi":"10.1111/1467-9884.00222","DOIUrl":"https://doi.org/10.1111/1467-9884.00222","url":null,"abstract":"The variability of parameter estimates is commonly neglected when constructing prediction intervals based on a parametric model for a time series. This practice is due to the complexity of conditioning the inference on information such as observed values of the underlying stochastic process. In this paper, conditional prediction intervals when using autoregression forecasts are proposed whose simple implementation will hopefully enable wide use. A simulation study illustrates the improvement over classical intervals in terms of empirical coverage.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"30 3 1","pages":"87-93"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77363851","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}
{"title":"Cobweb Diagrams for Multiway Contingency Tables","authors":"G. Upton","doi":"10.1111/1467-9884.00221","DOIUrl":"https://doi.org/10.1111/1467-9884.00221","url":null,"abstract":"Cobwebs represent the categories of cross-classifying variables by nodes on the arcs of a circle. Linking two nodes by a line provides information about the corresponding two-variable marginal table. In this paper the widths of the lines are proportional to the square of the adjusted residuals corresponding to the fit of the independence model to the marginal table. Lines are shaded to indicate the signs of the residuals. The method can be used with variables of mixed types and for conditional independence models.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"28 1","pages":"79-85"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76724796","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}
{"title":"Construction of Reference Centiles Using Mean and Dispersion Additive Models","authors":"R. Rigby, D. Stasinopoulos","doi":"10.1111/1467-9884.00218","DOIUrl":"https://doi.org/10.1111/1467-9884.00218","url":null,"abstract":"Summary. A procedure for constructing 'age'-related reference centiles by flexible modelling of the mean and variance of a dependent variable, assuming normal errors, is described. Both the mean and the variance of the dependent variable are modelled by using either parametric or smooth nonparametric functions of age. This model is a submodel of the more general mean and dispersion additive model (MADAM). Maximum (penalized) likelihood estimation is used for fitting the (non)parametric model. The problem of skewness in the data is dealt with by using a Box-Cox transformation. Flexible and interactive model fitting is provided by a menu-driven GLIM4 library macro called MADAM. A method of model selection is provided which uses the deviance as a measure of the goodness of fit to the data. The method is demonstrated by an example.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"98 1","pages":"41-50"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76073785","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}
{"title":"Batting strategy in limited-overs cricket","authors":"I. Preston, Jonathan M. Thomas","doi":"10.1111/1467-9884.00223","DOIUrl":"https://doi.org/10.1111/1467-9884.00223","url":null,"abstract":"The paper attempts to understand batting strategies that are employed in limited overs cricket games. The question of the optimum batting strategy is posed in a simplified dynamic programming representation. We demonstrate that optimum strategies may be expected to differ fundamentally in the first and second innings, typically involving an increasing run rate when setting a target but a run rate which may decline over the course of an innings when chasing one. Data on English county level limited overs games are used to estimate a model of actual batting behaviour. The statistical framework takes the form of an interesting variant on conventional survival analysis models.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"54 1","pages":"95-106"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88815012","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}
{"title":"Two discordancy tests for location slippage and dispersion slippage outlier detection in agreement studies","authors":"B. Giraudeau, C. Chastang","doi":"10.1111/1467-9884.00209","DOIUrl":"https://doi.org/10.1111/1467-9884.00209","url":null,"abstract":"Summary. The agreement between quantitative replicate measures is usually assessed by using the intraclass correlation coefficient (ICC). Estimates of this coefficient can be influenced by outlying observations (the outlying mean or outlying variance of the measures). The purpose of this paper is to provide a procedure to detect these two types of outlier by means of approximate tests. These are derived from an analytical formula of the influence of a subject io on the maximum likelihood estimator of the ICC. Satterthwaite's approximation is used to derive approximate probability density functions, and Bonferroni's bound is then used to obtain two approximate tests allowing us to detect a potential outlier because of location slippage and a potential outlier because of dispersion slippage. Then, a Monte Carlo study is conducted to determine the type I error probabilities and the performance of the tests in the presence of a contaminant observation, as defined by Barnett and Lewis. The tests turn out to be rather conservative and their ability to detect a contaminant observation rapidly increases with the degree of contamination.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"34 1","pages":"517-527"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88449552","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}
{"title":"Asymptotic information and variance-covariance matrices for the linear structural model","authors":"K. Hood, B. Nix, T. Iles","doi":"10.1111/1467-9884.00206","DOIUrl":"https://doi.org/10.1111/1467-9884.00206","url":null,"abstract":"Many papers have addressed the problem of fitting a straight line to a set of bivariate data where both the dependent variable Y and the predictor variable X are assumed to be measured subject to error, the problem that has generally become known as errors-in-variables regression. Several statistical models have been suggested to describe the problem, and many papers contain a discussion on the choice of model, generally going on to give a derivation of estimating equations for the parameters of the models. Rather less work has been published on the precision of the estimators derived, and the work published to date applies only in certain special cases. In the present paper the complete asymptotic variance–covariance matrices for all estimators are derived for the linear structural model, when various assumptions are made about the error variances involved. The equations that are obtained can readily be used in practice, though the algebra needed to derive these equations is somewhat lengthy. With the aid of a simulation exercise we show that these asymptotic variance and covariance terms are remarkably accurate even for relatively small data sets. To establish a consistent notation, we give the estimating equations derived from a rigorous and unified framework underpinned by the principle of maximum likelihood. Attention is focused on the special cases of the model for which solutions have been published previously as a useful check on the algebraic integrity of our results.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"138 1","pages":"477-493"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78268983","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}
{"title":"Leverage in Inequality‐constrained Regression Models","authors":"G. Paula","doi":"10.1111/1467-9884.00210","DOIUrl":"https://doi.org/10.1111/1467-9884.00210","url":null,"abstract":"Summary. We derive leverage measures in inequality-constrained linear regression models. When the restricted and unrestricted least squares estimates agree, the usual leverage measure h ii from the unrestricted linear regression is also extended to the restricted case. However, under violation, h ii is decomposed into two new leverage measures which take account of the influence of the observations on their restricted fitted values and on the change in the difference between the restricted and unrestricted fitted values. The last measure may be helpful to assess observations which are discordant with the prior belief for the parameters. We discuss extensions to generalized linear models, and two illustrative examples are given.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"39 1","pages":"529-538"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81728106","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}