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- Fridén, Håkan, et al.
(författare)
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Multivariate process monitoring and forcasting by projection methods
- 1994
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Ingår i: Proceedings of the Third IEEE Conference on Control Applications Glasgow, 24-26 aug 1994. - Piscataway : IEEE Control Systems Society. ; , s. 1345-1346
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Konferensbidrag (refereegranskat)abstract
- Immense amounts of data are collected into today's modern process monitoring systems. There are, however, few methods that have the capability to grasp the essentials in these, usually heavily correlated, data. The multivariate statistical techniques, principal components (PC) modelling and modelling by projection to latent structures (PLS) are two methods that have a great potential for process monitoring and forecasting in these situations
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- Jansson, Ingegärd
(författare)
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On Statistical Modeling of Social Networks
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A social network is formed by a collection of individuals and the contacts or relations between them. The focus is here on relations defined by sociometric choices, implying that the individuals in the network have been required to choose among the other individuals in the group according to some criteria.Some statistical models of the sociometric choice structure in a social network are presented. A recurrent assumption in the models is the assumption that there exists latent or underlying structures in a network, structures that can not be directly observed. The models also have in common the assumption of independence or conditional independence between entities of the network, assumptions not uncommon in statistical network models. These assumptions are often crucial for the possibility to find simple ways of estimating models. Here an attempt is made to find probabilistic models where independence is an ingredient but which also allow for structure.The models are illustrated and evaluated by application to data where the sociometric choices are based on friendship or cooperation. The large number of networks available makes it possible to find and evaluate empirical distributions of the test statistics.The simplest model presented assumes dyad independence. Possible simplifications by choice or edge independence are also discussed. It appears that dyad independence can not be ruled out, but that choice independence is inappropriate.In order to model the transitive structure of a network, a model is introduced that is based on a random choice structure and an unknown underlying clique structure. Two different approaches for estimating the clique structure are discussed, the maximum likelihood approach and the Bayesian approach. The empirical results show no large deviation between model and observations.A model of popularity structure is introduced where popularity is viewed as a latent attribute of the individuals in the network. The group of individuals is assumed to have a latent popularity structure, composed of individuals from three popularity groups. It is shown how the popularity structure can be estimated and how latent popularity can be considered in combination with manifest individual attributes.A model is also presented for the situation when two sociometric relations are measured on one set of individuals. The model assumes that there exists a latent network structure which can not be observed directly. When the relations are measured on the network, deviations from the underlying structure might occur with some probability. Approximate estimates of model parameters are given. Empirical findings suggest that the birelational latent model is sufficiently accurate for the data, but that there appear to be convergence problems, possibly due to the relatively large number of parameters in the model.
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- Karlberg, Martin, 1970-
(författare)
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Triad count estimation and transitivity testing in graphs and digraphs
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Triads and transitivity are two concepts within the field of social network analysis that are closely related to each other. We study some estimation and testing problems related to those concepts, using the tools of graph theory; the results obtained could be applied to graphs representing other kinds of data than social relations. Throughout this thesis, we focus on the role of local networks. A local network for an individual in a friendship network may be regarded as the network between the friends of this person. Two local network attributes that we pay special attention to are the size and the density. The local size of a vertex is defined so that it counts the number of transitive relationships in which that vertex is involved; this definition is not undisputable in the digraph situation, since not all edges in the local network are counted using that definition. We define the local density of a vertex in such a way, that its expected value is equal to the expected overall density of the network under some commonly used simple random graph and random digraph models. When dealing with triad count estimation, we consider the situation when we have observed information about a probability sample of vertices in a graph or digraph; we let the amount of information observed for each vertex range from the vertex degree to the entire local network of that vertex. Horvitz-Thompson estimators (and variance estimators for those estimators) for the triad counts are given. A main result is that when local networks without information on the identities of the vertices in that network are observed, the triad counts may be expressed as sums of vertex attributes; this greatly facilitates the estimation based on vertex sampling designs more complex than simple random sampling. Transitivity testing is considered for graphs and digraphs that are observed in their entirety. We study two different kinds of transitivity tests; tests based on the counts of transitive and intransitive triads and triples, and tests based on the mean local density over all vertices. The null hypothesis used is that the graphs and digraphs observed have been generated according to some conditional uniform random graph model that does not imply a high degree of transitivity. The powers of the tests against random graph distributions that generate highly transitive graphs are examined in simulation studies. In other simulation studies, the tests are applied to a large set of school class sociograms. When (undirected) graphs are considered, the test based on the proportion of transitive triads out of the non-vacuously transitive ones is found to be best at detecting transitivity; for digraphs, the test based on the difference between the mean local density and the overall network density is the best transitivity detector.
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- Lyhagen, Johan
(författare)
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Essays on univariate long memory models
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of five papers dealing with univariate long memory modelsin time series analysis.The first paper examines the performance of information criteria when usedto determine the lag order of a long memory process. The results indicate thatinformation criteria cannot be used successfully for small sample sizes. For largersample sizes the probability of successfully identifying the lag order is substantially higher.The covariance matrix of ARMA errors is the subject of the second paper.We generalise the matrix expression of the covariance matrix for ARIMA errorsto involve ARFIMA errors. In practise, it is necessary to truncate the orders ofthe matrices. The truncation only has a mild effect for small and medium valuesof the long memory parameter, but for large values, very large matrices must beused.A matrix representation of the moving average representation is given in thethird paper. The first two coefficients of the moving average representation of anARFIMA (1, d, 1) are presented as an example.The fourth paper examines the consequences of using forecasts from an ARIMA model when the process is an ARFIMA. Ignoring long memory increases the meansquared error of prediction substantially for long memory processes with high longmemory. Using information criteria to choose lag lengths does not improve theperformance of the forecasts. Further, the parameters of the misspecified modelare evaluated by maximising the expected likelihood.The existence of long memory in the Swedish OMX index and in the Swedish stock market is investigited in the fifth paper. We find no long memory, but do identify short memory and conditional heteroscedasticity.
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- Oke, Thimothy
(författare)
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Pre-testing and specification search in an autoregressive moving average process with extension to unit root cases
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Several methods are applied in well defined contexts in the search for an appropriatestatistical model to fit a data set. Preliminary tests of significance for this end aretermed pre-testing. The aim of this study was to investigate some of the consequencesof such pre-testing in a few specific time series processes. The principal results aresimulation-based to allow the accuracy of the analytical derivations to be checked.In simple AutoRegressive Moving Average (ARMA) settings, we illustrate thatthe pre-test estimator is not always dominated by one or other of its components, interms of its bias and mean square error. Further, we found that the degree of sizedistortion, of the test statistic for pre-testing, is generally associated with modelmisspecification. The accuracy of forecasting, after pre-testing, is often seen to followthe behaviour of the underlying "true" process. Moreover we demonstrated that thisprediction accuracy might well depend on some combinations of parameter values,rather than the sole correctness of the estimated model and the forecast horizon. Theseresults are discussed in detail in the first two papers.The study is extended to the Augmented Dickey-Fuller (ADF) regression in thethird and the fourth papers. Here we concentrate on pre-testing for unit root, where weillustrate limitations of an analytical derivation in studying some properties of the pre-test estimator. We also show how the bootstrapping technique can be used to forecastthe Swedish GDP while pre-testing. Through extensive simulations, our analysesreveal that the presence and/or absence of a drift and a time trend in a data generatingprocess has remarkable effects on the behaviour of the subsequent tests for unit root.In the fifth paper, results of an appropriate specification are used to test for theshort memory of a series. A proxy for total OECD demand and Swedish exports areused to demonstrate how the short term forecastability of a series can be extended.
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