Showing papers in "Statistica in 1996"
TL;DR: In this article, the authors consider a parametric approach which establishes the dissimilarity between dynamic structures by means of the comparison of the corresponding linear models and derive the asymptotic distribution of that criterion in the case of stationary and independent time series and show how it can be adequately approximated.
Abstract: In a number of practical problems we need to group time series into homogeneous classes or clusters. In this paper we consider a parametric approach which establishes the dissimilarity between dynamic structures by means of the comparison of the corresponding linear models. In particular, we refer to the metric introduced by Piccolo (1984) on the class of ARIMA invertible models as the Euclidean distance between the weights of their Autoregressive expansions. We derive the asymptotic distribution of that criterion in the case of stationary and independent time series and show how it can be adequately approximated. A simulation study concludes the paper.
11 citations
TL;DR: In this article, two generalized ridge estimators of the linear regression model are compared with respect to the matrix mean square error criterion, using a result concerning the difference of nonnegative definite matrices modified by two matrices of rank one, the investigations by Kawai and Okamoto (1979) and D. Trenkler (1986) are extended to the most general situation of competing estimators.
Abstract: Two given generalized ridge estimators of the linear regression model are compared with respect to the matrix mean square error criterion. Using a result concerning the difference of nonnegative definite matrices modified by two matrices of rank one, the investigations by Kawai and Okamoto (1979) and D. Trenkler (1986) are extended to the most general situation of competing estimators.
11 citations
TL;DR: In this paper, a longitudinal analysis of the poverty phenomenon is performed by latent class Markov models, which interpret poverty as a latent variable and Markov chains are used to correct measurement error in panel data.
Abstract: The aim of this work is the longitudinal analysis of the poverty phenomenon. In particular the attention is pointed out to the distinction between transitory and permanent poverty situations, which cannot be distinguished in a traditional cross-section analysis. The empirical analysis is performed by latent class Markov models: this approach interprets poverty as a latent variable and Markov chains are used to correct measurement error in panel data. These models are used in a specific territorial context and show a good performance in fitting observed data, due to the different possible definition of restrictions as characteristics of the process under examination.
5 citations
TL;DR: The celebrated papers giving rise to statistical mechanics that L. Boltzmann wrote between 1868 and 1877, are based on two fundamental presuppositions: first, statistical mechanics is a probabilistic theory; second, each probability distribution must be characterised in finitary terms, especially probability densities as mentioned in this paper.
Abstract: The celebrated papers giving rise to statistical mechanics that L. Boltzmann wrote between 1868 and 1877, are based on two fundamental presuppositions: first, statistical mechanics is a probabilistic theory; second, each probability distribution must be characterised in finitary terms, especially probability densities. Moreover an accurate analysis of these papers shows that Boltzmann used distributions which were unknown to contemporary statisticians, for example Beta and Gamma distributions, and that he was well aware of convergences in distribution binding them.
5 citations
TL;DR: The applicability and the efficiency of an extremely simple rule which entails only the ability to count a number of days, and always the same way is evaluated.
Abstract: Suppose that in each menstrual cycle a group of couples abstains for k days from intercourse, otherwise allowed in any other phase of the cycle. In a given cycle, the conception probability will depend on k, on the location within the cycle of the period of abstinence and on the pattern of intercourse episodes. An elaboration of this as-sumption on groups of cycles for which the relevant documentation is available gives idea of its consequences. For each group, under various conditions, an average concep-tion probability in a cycle is estimated. For that purpose, several hypotheses are made: about the size of k; about the location of the period of abstinence within the cycle; about frequency of intercourse outside that phase and the pattern of fecundability on different days of the menstrual cycle. Two fecundability models have been chosen from the literature and the calculations have been made on groups of cycles conveniently selected from a large data base of empirical observations. The results of the exercise give information of some relevance for fertility regulation through the use of calendar methods.
4 citations
TL;DR: In this paper, the different measures of non normality, proposed in the statistical literature on projection pursuit as projection indices, are critically reviewed and the affine invariant version of each of the presented indices is reported, and the results, obtained on real and simulated data, are compared highlighting the confirmations and denials towards the ones reported in the literature for sphere data.
Abstract: In this paper the different measures of non normality, proposed in the statistical literature on projection pursuit as projection indices, are critically reviewed. In order to guarantee an affine invariant final solution, evidence is given for the preferability of affine invariant indices, rather than sphere data. Starting from these considerations, the affine invariant version of each of the presented indices is reported, and the results, obtained on real and simulated data, are compared highlighting the confirmations and the denials towards the ones reported in the literature for sphere data.
3 citations
TL;DR: In this paper, an elegant simple derivation of Pearson's c2 goodness-of-fit statistic is given without making use of chisquaredness of quadratic forms or other such results.
Abstract: One of the most popular test statistics is Pearson's c2 goodness-of-fit statistic which is known to have an approximate chi-square distribution for large sample size. All the proofs so far seem to make use of the chisquaredness of quadratic forms in normal variables, manipulations of quadratic forms and singular covariance matrix. An elegant simple derivation of this result is given here without making use of chisquaredness of quadratic forms or other such results. Two numerical examples are also given to caution about the use of this statistic.
3 citations
TL;DR: In this paper, a lattice path combinatorial technique for computing transient probabilities concerning M/M/1 bulk arrival queuing model is presented, which is free from generating functions and transforms.
Abstract: This paper demonstrates simple and elegant lattice path combinatorial technique for computing transient probabilities concerning M/M/1 bulk arrival queuing model. The results computed are free from generating functions and transforms. As a special case the results for ordinary M/M/1 queues are checked.
3 citations
TL;DR: In this article, the authors proposed the stylized spectrum estimate, whose estimate reflects the main features of the power distribution of the latent series components over the frequency axis, thus enabling us to detect the power contribution of the frequency ranges corresponding to the components of interest.
Abstract: This article aims to give a methodological contribution - with considerable operational implications - to economic time series analysis resting on a frequency-domain approach, which finds its roots into Granger's seminal paper (1966). The novelty of the proposal is the introduction of the notion of stylized spectrum, whose estimate reflects the main features of the power distribution of the latent series components over the frequency axis. The stylized spectrum arises transforming the observed series by a battery of filters which cause a sufficiently]v fine partition of the frequency axis; thus enabling us to detect the power contribution of the frequency ranges corresponding to the components of interest, i.e trend, cyclical and seasonal - possibly evolutive - components. The stylized spectrum estimate is an efficient tool to solve some crucial problems of time series analysis, such as: - setting clear criteria to evaluate the contribution of the latent component to the series dynamics; - comparing the actual performances of alternative procedures of components estimation; - evaluating the definition degree corresponding to different filtering methods, and the relevant accuracy of procedures outcomes.
2 citations
TL;DR: In this paper, the authors show that a confidence coefficient must inevitably be interpreted as a subjective probability, at least when there is a large uncertainty in the assignment of a prior distribution.
Abstract: It is well known that one of the conflicts between Bayesian and frequentist approach to inference lies in the determination and interpretation of "interval estimates". In particular, Bayesians deny any probabilistic meaning to realised confidence intervals. On the contrary, the author shows that a confidence coefficient must inevitably be interpreted as a subjective probability, at least when there is a large uncertainty in the assignment of a prior distribution. Besides, this viewpoint is operationally sustained by some formal relationships between confidence and Bayesian intervals: exact equality between the respective coverage probabilities in some special cases (Lindley, amongst others), exact equality again between mean values of posterior probabilities and mean values of confidence coefficients in all cases (Pratt), and approximate equality between coverage probabilities in most cases, especially if the interval is calculated on a sample with a not too small size (Welch and Peers and others).
1 citations
TL;DR: In this article, a new systematic sampling which uses both label and auxiliary information has been introduced, which is shown to yield positive first order inclusion probabilities for all units and positive second order inclusion probability for all pairs of units.
Abstract: In this paper, a new systematic sampling which uses both label and auxiliary information has been introduced. The suggested scheme is shown to yield positive first order inclusion probabilities for all units and positive second order inclusion probabilities for all pairs of units.