Showing papers in "Journal of the royal statistical society series b-methodological in 1981"
909 citations
TL;DR: In this article, a multivariate portmanteau test for checking the adequacy of fitted vector ARMA models is developed, and a simulation study shows that a simple modification of this test improves its accuracy in small samples.
Abstract: The large-sample distribution of the multivariate residual autocorrelations in the vector ARMA model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector ARMA models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.
279 citations
TL;DR: In this paper, the authors present a family of distributions for describing data which are not elliptically symmetric, including the Pareto, Burr and Logistic distributions, and compare the fit to a data set on uranium exploration with that obtained using the usual bivariate normal distribution.
Abstract: SUMMARY The paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation. We present a relatively simple family of distributions for use in describing data which are not elliptically symmetric. Properties of the family are discussed and it is shown that multivariate Pareto, Burr and Logistic distributions are special cases. In addition, simulation methods for applications in Monte Carlo robustness studies are outlined and, finally, the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution.
243 citations
TL;DR: In this paper, the existence of maximum likelihood estimators of the linear regression parameter in binomial response (this includes Logit and Probit) models was examined in an analysis of the relationship of psychiatric "caseness" to scores on a psychiatric screening questionnaire.
Abstract: SUMMARY Necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response (this includes Logit and Probit) models. THE question of existence of maximum likelihood estimators (mle) for Logit models arose in an analysis of the relationship of psychiatric "caseness" to scores on a psychiatric screening questionnaire. Tennant (1977) administered the GHQ (General Health Questionnaire, Goldberg, 1972) to 120 patients attending a General Practitioner's surgery, and also gave each one a standardized psychiatric interview. From the interview, patients were classified as Psychiatric Case/Non-case. In a secondary analysis of Tennant's data, Duncan-Jones and Henderson (1978) fitted a Logit regression of"caseness" on GHQ Score, and obtained a good fit with the model.
223 citations
TL;DR: The theory of bilinear time series models is considered in this article, and the sufficient conditions for asymptotic stationarity of the time-series models are derived, and the expressions for the variance and covariance are obtained.
Abstract: SUMMARY The theory of bilinear time series models is considered in this paper The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained The conditions for the invertibility of the model are also included The estimation of the parameters of the scalar bilinear time series model is considered The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion The forecasting of sunspot numbers is also considered
220 citations
TL;DR: In this article, the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function are established under general conditions under the assumption that all the procedures have the same distribution.
Abstract: SUMMARY The asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions.
206 citations
TL;DR: In this article, the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models, and the portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner.
Abstract: SUMMARY Generalizing Hosking (1980a), the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner and three other tests are obtained for multivariate moving-average models.
93 citations
TL;DR: In this article, the estimation of parameters for a class of regression models using grouped or censored data is considered, and it is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters.
Abstract: SUMMARY The estimation of parameters for a class of regression models using grouped or censored data is considered. It is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters. Apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates, this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data. Two simple examples are given.
93 citations
TL;DR: The residual correlations Rk have been defined in several ways: (a) Rk = DCkD, where D is a diagonal matrix with ith diagonal element (ciiO) as mentioned in this paper.
Abstract: In this context, the residual correlations Rk have been defined in several ways: (a) Rk = DCkD, where D is a diagonal matrix with ith diagonal element (ciiO)(Li and McLeod, 1981)-the standard definition; (b) Rk=CkCO' (Chitturi, 1974)-this gives Ro = I; (c) Rk= LT Ck L, where LLT = Co 1, ie L is a square root of C0(Hosking, 1980, Section 5)this gives Q = n XijkrijkWe write the three forms of Q corresponding to these definitions as Qa, Qb, Qc Theorem P = Qa = Qb = Qc Proof We have in (a) vec Rk = (D 0 D) vec Ck, so
92 citations
87 citations
TL;DR: In this article, an approximation to the sequential updating of the distribution of location parameters of a linear time series model for non-normal observations is developed for a wide range of symmetric, unimodal error distributions and is both more realistic and elegant than the discrete Gaussian Sum approach.
Abstract: SUMMARY An approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non-normal observations. The behaviour of the resulting non-linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non-normal error distributions. Illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned. WE consider here the problem of sequential estimation of the location vector of a linear time series model, termed the Dynamic Linear Model by Harrison and Stevens (1976). The straightforward, exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted, and yet considerations of realism or robustness may strongly suggest such non-normal assumptions. The multi-state model of Harrison and Stevens provides an approximate analysis based on a discrete variance mixture of normal distributions, an approach which has been extensively investigated in the engineering literature under the name of Gaussian Sum approximations; see, for example, Alspach and Sorenson (1971). Our aim in this paper is to provide an approximate, tractible, recursive updating procedure for the location parameters, which is applicable to a wide range of symmetric, unimodal error distributions and is both more realistic and more elegant than the discrete Gaussian Sum approach. In particular, for heavy-tailed distributions our procedures provide approximate Bayesian methods for time series analysis which extend considerably the work of Masreliez and Martin (1977) and have close connections with classical robustness ideas such as M-estimation and influence functions.
TL;DR: In this article, the goodness-of-fit test using the empirical characteristic function proposed by Koutrouvelis (1980) is extended to the case where parameters must be estimated, and the proposed test statistic is shown to have an asymptotic chi-squared distribution with degrees of freedom reduced by the number of parameters estimated.
Abstract: SUMMARY The goodness-of-fit test using the empirical characteristic function proposed by Koutrouvelis (1980) is extended to the case where parameters must be estimated. The proposed test statistic is shown to have an asymptotic chi-squared distribution with degrees of freedom reduced by the number of parameters estimated.
TL;DR: In this article, some properties of models for the outcomes of races are described, these properties being consequences of a stochastic ordering of the permutations which define the outcome of a race.
Abstract: SUMMARY Some properties of models for the outcomes of races are described, these properties being consequences of a stochastic ordering of the permutations which define the outcomes of a race. Order statistics models which lead to stochastic ordering are also discussedparticular cases of these are the first-order model of Plackett (1975) and the normal model of Upton and Brook (1974). An approximation for the normal model is suggested.
TL;DR: In this article, the solution of a system of two-dimensional recurrence equations is discussed, particularly in the context of the auto-correlation structure of a stationary first-order autonormal scheme on the doubly-infinite rectangular lattice.
Abstract: SUMMARY The solution of a system of two-dimensional recurrence equations is discussed, particularly in the context of the auto-correlation structure of a stationary first-order autonormal scheme on the doubly-infinite rectangular lattice. A simple approximation in the region of primary interest is described.
TL;DR: In this article, it was shown that conventional methods, using equal allocations of the treatments under comparison, involve many unnecessary applications of inferior treatments even if the final choice of the "best" treatment relies on a sequential test.
Abstract: SUMMARY Since the idea of sequential allocation was first studied, in a version of what is now called the multi-armed bandit problem, the results of many investigations have shown that, even when an optimal allocation rule can be found, its form depends on the parameters of the model and no single rule has emerged that is widely acceptable in practice. On the other hand, it can be shown that conventional methods, using equal allocations of the treatments under comparison, involve many unnecessary applications of inferior treatments even if the final choice of the "best" treatment relies on a sequential test. The evidence for this claim is based on an investigation of randomized allocation rules, where the choice of the next treatment is randomized in such a way that some preference is given to the "favourite" at any stage, but other treatments are not permanently excluded.
TL;DR: In this paper, the authors examined the small sample power properties of the Cliff-Ord test and found that it is a locally best invariant (LBI) test in the neighbourhood of p = 0, while for a special type of spatial correlation and when the regression has an intercept, it is an Uniformly Most Powerful Invariant test.
Abstract: SUMMARY The Cliff-Ord test for spatial correlation in regression disturbances is found to be a locally CLIFF and ORD (1973) proposed a test for spatial correlation in regression disturbances. They informally argued that for values of the spatial correlation parameter, p, in the neighbourhood of zero, their test coincides with the likelihood ratio test derived assuming the value of p under the alternative hypothesis is known. Recently, Burridge (1980) demonstrated that the Cliff-Ord test is identical to the Lagrange multiplier test and is therefore asymptotically equivalent to the likelihood ratio test. In this note we examine some of the test's small sample power properties. It is found to be a Locally Best Invariant (LBI) test in the neighbourhood of p = 0, while for a special type of spatial correlation and when the regression has an intercept, it is a Uniformly Most Powerful Invariant (UMPI) test. Consider the usual linear regression model,
TL;DR: In this paper, non-parametric estimates of mixing proportions based on kernel-type density estimators are badly suited to several types of data, and their construction involves the crucial choice of the "window size", or smoothing parameter.
Abstract: SUMMARY Non-parametric estimates of mixing proportions based on kernel-type density estimators are badly suited to several types of data. They suffer from aberrations due to rounding or truncation of the measurements, and their construction involves the crucial choice of the "window size", or smoothing parameter. In many circumstances estimators based on the empiric distribution function would be more suitable, and in this paper we investigate their properties. The estimators we introduce lead in a natural way to non-parametric forms of well-known parametric estimators. Their efficiency approaches 100 per cent as the distances between the component distributions increase.
TL;DR: In this paper, the idea of a steady evolution of a time series was extended to multiparameter processes with any observational distribution, such as the multivariate steady process, univariate normal processes and series of multinomial observations with a steady model on the cell probabilities.
Abstract: SUMMARY This paper generalizes and extends the idea of a steady evolution of a time series to multiparameter processes with any observational distribution. Particular examples of such processes are given. These include the multivariate steady process, univariate normal processes where the observational variance is unknown and series of multinomial observations with a steady model on the cell probabilities.
TL;DR: In this article, a random matrix Y(n x m) is a real matrix in the space En x m of real matrices having location-scale parameters (0, Q) such that O belongs to a linear subspace X# of En m; the distribution Y(Y) exhibits a type of structural symmetry; and a certain transformation T (Y) is translation-invariant with respect to? and is invariant under changes of scale.
Abstract: Let Y(n x m) be a random matrix in the space En x m of real matrices having location-scale parameters (0, Q) such that (i) O belongs to a linear subspace X# of En m; (ii) the distribution Y(Y) exhibits a type of structural symmetry; and (iii) a certain transformation T(Y) is translation-invariant with respect to ? and is invariant under changes of scale. Then the distribution ?{T(Y)} is invariant for all underlying symmetric distributions Y(Y). The types of symmetry are spherical symmetry and symmetry under multiplication on the left by orthogonal and similar matrices; the scale changes are multiplication by a scalar and multiplication on the right by a non-singular matrix. Applications yield the invariance under structural symmetry of distributions usually associated with normal-theory inferences in multivariate regression analysis and in testing equality of dispersion matrices.
TL;DR: In this paper, prediction models are used to study the Horvitz-Thompson estimator in probability-proportional-to-size sampling and six estimators of its variance.
Abstract: SUMMARY Prediction models are used to study the Horvitz-Thompson estimator in probabilityproportional-to-size sampling and six estimators of its variance. The variance estimators include the Horvitz-Thompson, Yates-Grundy, and jackknife statistics, as well as two bias-robust estimators from prediction theory. An empirical study confirms prediction theory's implications about these estimators.
TL;DR: In this article, the authors consider the way in which an individual's previsions are changed by new information, and the expected effect of new data is expressed by a bounded self-adjoint operator on this space.
Abstract: SUMMARY This paper considers the way in which an individual's previsions are changed by new information. Firstly, reasons are discussed for preferring prevision to probability as the fundamental element in the subjective formulation of statistical procedures. Then, following de Finetti, an inner product space is constructed, such that the vectors are random quantities of interest and the inner product corresponds to the previsions of the individual. The expected effect of new data is expressed by a bounded self-adjoint operator on this space. The information expected from the data is represented in terms of the eigenstructure of the operator. If the operator is compact, this representation has particularly simple form. New data impose orthogonal co-ordinate axes on the original inner-product space. The information expected about any random quantity is represented by a specified shrinkage along each axis. To any order of accuracy, all the information may be represented by a finite dimensional subspace. Finally, the geometric representation is related to more conventional, totally specified models.
TL;DR: In this paper, the authors considered the G/G/I queueing system under the assumption of a last-come, first-served queue discipline where each customer begins service immediately upon his arrival.
Abstract: SUMMARY This paper considers the G/G/I queueing system under the assumption of a last-come, first served queue discipline where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It is shown, among other things, that the equilibrium distribution of the number of customers in the system (when the system is considered exclusively at arrival epochs) is geometric.
TL;DR: In this paper, it was shown that an infinite sequence of real random variables, any finite sample from which has a centred spherically symmetric joint distribution, has the property that, conditional on two further random variables (M and V) the variables are independent with the same normal distribution N(M, V).
Abstract: SUMMARY An infinite sequence of real random variables, any finite sample from which has a centred spherically symmetric joint distribution, is shown to have the property that, conditional on two further random variables, M and V, the variables are independent with the same normal distribution N(M, V).
TL;DR: In this article, the authors develop approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorerelations.
Abstract: SUMMARY An important part of the diagnostic checking of space-time autoregressive moving average (STARMA) models is testing the temporal independence of the residuals. In the context of the three-stage modelling procedure,. such a test is based on the sample space-time autocorrelation function. This paper developes approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorrelations.
TL;DR: In this article, a definition of scale parameter φ is given and some suggestions for the estimation of φ and approximations to the marginal posterior distribution of θ, a vector-valued parameter of primary interest, are made.
Abstract: A definition of a scale parameter φ is given which includes the usual definition of a scale parameter in the exponential family. Some suggestions for the estimation of φ and approximations to the marginal posterior distribution of θ, a vector-valued parameter of primary interest, are made. In particular, the possibility of a χ 2 approximation to the posterior distribution of φ, leading to h.p.d. regions for θ based on the F distribution, is explored. Two examples are discussed, where observations are from a normal and gamma distribution.