Bulletin de la Société des amis de la Bibliothèque de l'Ecole polytechnique, Jun 1, 2015
Eugene Seneta [[Seneta]]-professeur émérite à l'université de Sydney (School of Mathematics and S... more Eugene Seneta [[Seneta]]-professeur émérite à l'université de Sydney (School of Mathematics and Statistics)-est réputé pour ses contributions en probabilités et statistiques dont certaines ont débouché sur des applications aux domaines de la finance. Membre de l'Australian Academy of Sciences depuis 1985, il a aussi beaucoup contribué à l'histoire des probabilités et statistiques; il revient dans cet entretien sur ses collaborations avec François Jongmans ainsi qu'avec Henri Breny, Bernard Bru et Karen Hunger Parshall. Il nous montre ainsi que les articles cosignés avant d'être des traces écrites sont avant tout des histoires de rencontres humaines. When and how do you meet François Jongmans ? The initial contact and further collaboration centered on the figure of the French mathematical the statistician Irenée-Jules Bienaymé (1796-1878), IJB in the sequel. After publication of the book of Heyde and Seneta [1977], I eventually traced a descendant, Alain Bienaymé, a professor of Economics at Paris IX Dauphine, who in a letter of February 2, 1981, mentioned the possibility of existence in the Bienaymé family of some documents of IJB. The next epoch was a paper by Butzer and Jongmans [1989] about P.L. Chebyshev (1821-1894) and his contacts with Western European scientists. IJB had been one such contact.
Our motivation arose out of a multivariate model for asset price moments over time, t ≥ 0. Let X ... more Our motivation arose out of a multivariate model for asset price moments over time, t ≥ 0. Let X (i) t , i = 1, . . . , n, be the marginal log-price increment (“return”) over a unit time period, say X (i) t = logS (i) t − log S (i) t−1. The underlying idea in its univariate form is the comparison of the Variance Gamma (VG) and t models for returns, which both arise from subordinator models alternative to the classical geometric Brownian motion. A subordinator model specifies that the return, i.e. X (i) t , is driven by Brownian motion B(i)(t) evaluated at a random time-change, the so called “activity time” Tt, for t ≥ 0. That is, for returns we assume
Journal of the Royal Statistical Society. Series A (Statistics in Society), 1990
... Lenin's early contact with statistics as a discipline, in the form that it existed at th... more ... Lenin's early contact with statistics as a discipline, in the form that it existed at the time, was through the 1887 book Teoriia Statistiki (Theory of Statistics) by the eminent statistician and economist lulii Eduardovich lanson (or Yanson or Jahnson) (1835-92), on whom more ...
We construct and characterize a stationary scalar-valued random field with domain Rd or Zd, d∈Z+,... more We construct and characterize a stationary scalar-valued random field with domain Rd or Zd, d∈Z+, which is infinitely divisible, can take any (univariate) infinitely divisible distribution with finite variance at any single point of its domain, and has autocorrelation function between any two points in its domain expressed as a product of arbitrary positive and convex functions equal to 1 at the origen. Our method of construction–based on carefully chosen sums of independent and identically distributed random variables–is simple and so lends itself to simulation.
LESSONS FROM PRACTICE disorders who become housebound may be particularly at risk, irrespective o... more LESSONS FROM PRACTICE disorders who become housebound may be particularly at risk, irrespective of their age. The functions of vitamin D in bone metabolism are well known and its deficiency may be reconciled with the failure of spinal fusion, as described in these patients. This report highlights the need for attending surgeons and physicians to be aware of the potential for vitamin D deficiency in their patients, as failure to recognise this easily reversible problem may result in complications of treatment, including failure of spinal fusion surgery, additional morbidity and the substantial costs of further surgery and hospitalisation.
Chebyshev is regarded as the founder of the St. Petersburg School of mathematics, which encompass... more Chebyshev is regarded as the founder of the St. Petersburg School of mathematics, which encompassed path-breaking work in probability theory. The Chebyshev Inequality carries his name; he intitiated rigorous work on a general version of the Central Limit Theorem.
International Statistical Review / Revue Internationale de Statistique, 1987
Summary L. von Bortkiewicz [1868-1931] is remembered partly in connection with his data on deaths... more Summary L. von Bortkiewicz [1868-1931] is remembered partly in connection with his data on deaths from horse kicks. This was one of several data sets used by Bortkiewicz to illustrate his 'Law of Small Numbers'. We discuss this law (which was and is widely misunderstood) in some depth, with special reference to the sensitivity of the divergence coefficient as a test statistic, an aspect which we feel should receive more attention in the analysis of the horse kick data. We dispel some common misconceptions about 'censorship' of this data. The other data sets are mentioned.
We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at leas... more We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at least a 1 and at least a 2, and for the probability that exactly a 1 and a 2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.
We obtain bivariate forms of Gumbel's, Fréchet's and Chung's linear inequalities for ... more We obtain bivariate forms of Gumbel's, Fréchet's and Chung's linear inequalities for P(S> u, T> v) in terms of the bivariate binomial moments {S_i,j}, 1< i< k, 1< j< l of the joint distribution of (S,T). At u=v=1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k,l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.
Arguably the greatest French mathematician of the 17th century, Fermat was instrumental in giving... more Arguably the greatest French mathematician of the 17th century, Fermat was instrumental in giving impetus, together with Pascal, to the theory of probability.
Summary It is difficult, in general, to optain an explicit expression for the limiting-stationary... more Summary It is difficult, in general, to optain an explicit expression for the limiting-stationary distribution, when such a distribution exists, of the process in which teh individuals reproduce as in a Galton-Wastson process, but are also subject to an independent immigration component at each generation. The main result of this paper is a limit theorem which suggests a means of approximating this distribution by a gamma density, when the mean of the offspring distribution is less than, but close to, unity. Following along the same lines, it is easy to show that a similar limit theorem holds for the asymptotic conditional limit distribution of an ordinary subcritical Galton-Watson process, whereby this distribution approaches the exponential as the offspring mean approaches unity.
Publisher Summary Neuroendocrine systems typically communicate via a pulsatile mode of intermitte... more Publisher Summary Neuroendocrine systems typically communicate via a pulsatile mode of intermittent signaling. Cross-correlation analysis typically provides useful insights into the overall coordinate behavior of two series of concurrent measurements, such as serum LH and testosterone concentrations. The level of significance for a cross-correlation coefficient can be approximated by estimating the standard error for the cross-correlation coefficient. More sophisticated statistical analysis of neuroendocrine time series requires the use of autoregressive modeling combined with cross-correlation analysis to determine significant partial cross-correlation coefficients at various lags. Autoregressive modeling is necessary to remove the otherwise artifactual effects of autocorrelation existing within each neurohormone series alone, in which successive hormone values tend to be correlated. Pulse trains can be simulated in a number of ways that may be useful. For example, after identifying individual peaks or pulses in the data, the locations of some specific feature of the peak can be used to quantize or discretize the data.
We describe the life, times and legacy of Andrei Andreevich Markov (1856 -1922), and his writings... more We describe the life, times and legacy of Andrei Andreevich Markov (1856 -1922), and his writings on what became known as Markov chains. One focus is on his first paper [27] of 1906 on this topic, which already contains important contractivity principles embodied in the Markov Dobrushin coefficient of ergodicity, which in fact makes an explicit appearance in that paper. The contractivity principles are shown directly to underpin a number of results of the later theory. The coefficient is especially useful as a condition number in measuring the effect of perturbation of a stochastic matrix on the stationary distribution (sensitivity analysis). Some recent work in this direction is reviewed from the standpoint of the paper [53], presented at the first of the present series of conferences [63].
We first examine the rate of decay to the limit of the lower tail dependence function i.e. the as... more We first examine the rate of decay to the limit of the lower tail dependence function i.e. the asymptotic tail dependence coefficient of a bivariate skew-t distribution. It is important to consider the correction term as the tail dependence function can be much different from its limit. We find that the rate is asymptotically a power-law. The results contain as a special case the usual bivariate symmetric t distribution, and hence the skew t distribution we consider here is an appropriate (skew) extension. We then discuss briefly the rate of convergence for the skew normal distribution under an equal-skewness condition.
An account of the Heyde family is followed by a description of Chris&#39;s childhood, schooli... more An account of the Heyde family is followed by a description of Chris&#39;s childhood, schooling and university training at Sydney and the ANU. Chris spent most of his academic career at the ANU, CSIRO and Columbia University. He made an outstanding contribution to probability theory and its applications. His theoretical work focused mainly on the laws of large numbers, branching processes, martingale theory, estimation theory and, most recently, financial mathematics. He also had a lasting interest in the history of probability and statistics. Chris received considerable recognition, including Fellowship of the Australian Academy of Science and of the Academy of Social Sciences in Australia, as well as Membership of the Order of Australia.
Bulletin de la Société des amis de la Bibliothèque de l'Ecole polytechnique, Jun 1, 2015
Eugene Seneta [[Seneta]]-professeur émérite à l'université de Sydney (School of Mathematics and S... more Eugene Seneta [[Seneta]]-professeur émérite à l'université de Sydney (School of Mathematics and Statistics)-est réputé pour ses contributions en probabilités et statistiques dont certaines ont débouché sur des applications aux domaines de la finance. Membre de l'Australian Academy of Sciences depuis 1985, il a aussi beaucoup contribué à l'histoire des probabilités et statistiques; il revient dans cet entretien sur ses collaborations avec François Jongmans ainsi qu'avec Henri Breny, Bernard Bru et Karen Hunger Parshall. Il nous montre ainsi que les articles cosignés avant d'être des traces écrites sont avant tout des histoires de rencontres humaines. When and how do you meet François Jongmans ? The initial contact and further collaboration centered on the figure of the French mathematical the statistician Irenée-Jules Bienaymé (1796-1878), IJB in the sequel. After publication of the book of Heyde and Seneta [1977], I eventually traced a descendant, Alain Bienaymé, a professor of Economics at Paris IX Dauphine, who in a letter of February 2, 1981, mentioned the possibility of existence in the Bienaymé family of some documents of IJB. The next epoch was a paper by Butzer and Jongmans [1989] about P.L. Chebyshev (1821-1894) and his contacts with Western European scientists. IJB had been one such contact.
Our motivation arose out of a multivariate model for asset price moments over time, t ≥ 0. Let X ... more Our motivation arose out of a multivariate model for asset price moments over time, t ≥ 0. Let X (i) t , i = 1, . . . , n, be the marginal log-price increment (“return”) over a unit time period, say X (i) t = logS (i) t − log S (i) t−1. The underlying idea in its univariate form is the comparison of the Variance Gamma (VG) and t models for returns, which both arise from subordinator models alternative to the classical geometric Brownian motion. A subordinator model specifies that the return, i.e. X (i) t , is driven by Brownian motion B(i)(t) evaluated at a random time-change, the so called “activity time” Tt, for t ≥ 0. That is, for returns we assume
Journal of the Royal Statistical Society. Series A (Statistics in Society), 1990
... Lenin's early contact with statistics as a discipline, in the form that it existed at th... more ... Lenin's early contact with statistics as a discipline, in the form that it existed at the time, was through the 1887 book Teoriia Statistiki (Theory of Statistics) by the eminent statistician and economist lulii Eduardovich lanson (or Yanson or Jahnson) (1835-92), on whom more ...
We construct and characterize a stationary scalar-valued random field with domain Rd or Zd, d∈Z+,... more We construct and characterize a stationary scalar-valued random field with domain Rd or Zd, d∈Z+, which is infinitely divisible, can take any (univariate) infinitely divisible distribution with finite variance at any single point of its domain, and has autocorrelation function between any two points in its domain expressed as a product of arbitrary positive and convex functions equal to 1 at the origen. Our method of construction–based on carefully chosen sums of independent and identically distributed random variables–is simple and so lends itself to simulation.
LESSONS FROM PRACTICE disorders who become housebound may be particularly at risk, irrespective o... more LESSONS FROM PRACTICE disorders who become housebound may be particularly at risk, irrespective of their age. The functions of vitamin D in bone metabolism are well known and its deficiency may be reconciled with the failure of spinal fusion, as described in these patients. This report highlights the need for attending surgeons and physicians to be aware of the potential for vitamin D deficiency in their patients, as failure to recognise this easily reversible problem may result in complications of treatment, including failure of spinal fusion surgery, additional morbidity and the substantial costs of further surgery and hospitalisation.
Chebyshev is regarded as the founder of the St. Petersburg School of mathematics, which encompass... more Chebyshev is regarded as the founder of the St. Petersburg School of mathematics, which encompassed path-breaking work in probability theory. The Chebyshev Inequality carries his name; he intitiated rigorous work on a general version of the Central Limit Theorem.
International Statistical Review / Revue Internationale de Statistique, 1987
Summary L. von Bortkiewicz [1868-1931] is remembered partly in connection with his data on deaths... more Summary L. von Bortkiewicz [1868-1931] is remembered partly in connection with his data on deaths from horse kicks. This was one of several data sets used by Bortkiewicz to illustrate his 'Law of Small Numbers'. We discuss this law (which was and is widely misunderstood) in some depth, with special reference to the sensitivity of the divergence coefficient as a test statistic, an aspect which we feel should receive more attention in the analysis of the horse kick data. We dispel some common misconceptions about 'censorship' of this data. The other data sets are mentioned.
We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at leas... more We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at least a 1 and at least a 2, and for the probability that exactly a 1 and a 2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.
We obtain bivariate forms of Gumbel's, Fréchet's and Chung's linear inequalities for ... more We obtain bivariate forms of Gumbel's, Fréchet's and Chung's linear inequalities for P(S> u, T> v) in terms of the bivariate binomial moments {S_i,j}, 1< i< k, 1< j< l of the joint distribution of (S,T). At u=v=1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k,l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.
Arguably the greatest French mathematician of the 17th century, Fermat was instrumental in giving... more Arguably the greatest French mathematician of the 17th century, Fermat was instrumental in giving impetus, together with Pascal, to the theory of probability.
Summary It is difficult, in general, to optain an explicit expression for the limiting-stationary... more Summary It is difficult, in general, to optain an explicit expression for the limiting-stationary distribution, when such a distribution exists, of the process in which teh individuals reproduce as in a Galton-Wastson process, but are also subject to an independent immigration component at each generation. The main result of this paper is a limit theorem which suggests a means of approximating this distribution by a gamma density, when the mean of the offspring distribution is less than, but close to, unity. Following along the same lines, it is easy to show that a similar limit theorem holds for the asymptotic conditional limit distribution of an ordinary subcritical Galton-Watson process, whereby this distribution approaches the exponential as the offspring mean approaches unity.
Publisher Summary Neuroendocrine systems typically communicate via a pulsatile mode of intermitte... more Publisher Summary Neuroendocrine systems typically communicate via a pulsatile mode of intermittent signaling. Cross-correlation analysis typically provides useful insights into the overall coordinate behavior of two series of concurrent measurements, such as serum LH and testosterone concentrations. The level of significance for a cross-correlation coefficient can be approximated by estimating the standard error for the cross-correlation coefficient. More sophisticated statistical analysis of neuroendocrine time series requires the use of autoregressive modeling combined with cross-correlation analysis to determine significant partial cross-correlation coefficients at various lags. Autoregressive modeling is necessary to remove the otherwise artifactual effects of autocorrelation existing within each neurohormone series alone, in which successive hormone values tend to be correlated. Pulse trains can be simulated in a number of ways that may be useful. For example, after identifying individual peaks or pulses in the data, the locations of some specific feature of the peak can be used to quantize or discretize the data.
We describe the life, times and legacy of Andrei Andreevich Markov (1856 -1922), and his writings... more We describe the life, times and legacy of Andrei Andreevich Markov (1856 -1922), and his writings on what became known as Markov chains. One focus is on his first paper [27] of 1906 on this topic, which already contains important contractivity principles embodied in the Markov Dobrushin coefficient of ergodicity, which in fact makes an explicit appearance in that paper. The contractivity principles are shown directly to underpin a number of results of the later theory. The coefficient is especially useful as a condition number in measuring the effect of perturbation of a stochastic matrix on the stationary distribution (sensitivity analysis). Some recent work in this direction is reviewed from the standpoint of the paper [53], presented at the first of the present series of conferences [63].
We first examine the rate of decay to the limit of the lower tail dependence function i.e. the as... more We first examine the rate of decay to the limit of the lower tail dependence function i.e. the asymptotic tail dependence coefficient of a bivariate skew-t distribution. It is important to consider the correction term as the tail dependence function can be much different from its limit. We find that the rate is asymptotically a power-law. The results contain as a special case the usual bivariate symmetric t distribution, and hence the skew t distribution we consider here is an appropriate (skew) extension. We then discuss briefly the rate of convergence for the skew normal distribution under an equal-skewness condition.
An account of the Heyde family is followed by a description of Chris&#39;s childhood, schooli... more An account of the Heyde family is followed by a description of Chris&#39;s childhood, schooling and university training at Sydney and the ANU. Chris spent most of his academic career at the ANU, CSIRO and Columbia University. He made an outstanding contribution to probability theory and its applications. His theoretical work focused mainly on the laws of large numbers, branching processes, martingale theory, estimation theory and, most recently, financial mathematics. He also had a lasting interest in the history of probability and statistics. Chris received considerable recognition, including Fellowship of the Australian Academy of Science and of the Academy of Social Sciences in Australia, as well as Membership of the Order of Australia.
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