Monotonicity of certain functionals under rearrangement

Adriano Garsia; Eugène Rodemich

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Some estimates of the integral $\int_{0}^{2 π} Log | P (e^{i θ}) | {(2 π)}^{- 1} d θ$ .

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Financial returns are often modelled as autoregressive time series with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studied in financial and econometric literature as risk models of many financial time series. Analyzing two data sets of stock prices we try to fit AR(1) processes with GARCH or EGARCH errors to the log returns. Moreover, hyperbolic or generalized error distributions occur to...

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According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case...

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Simple large sample estimators of scale and location parameters based on blocks of order statistics.

Peter Kubat (1982)

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In this paper quite efficient large sample estimation procedures are derived for jointly estimating the parameters of the location-scale family of distributions. These estimators are linear combinations of the means of suitably chosen blocks of order statistics. For specific distributions, such as the extreme-value, normal, and logistic, little is to be gained by using more than three blocks. For these distributions we can obtain joint relative asymptotic efficiencies of 97-98% using...

Plurisubharmonic functions with logarithmic singularities

E. Bedford, B. A. Taylor (1988)

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To a plurisubharmonic function $u$ on $C^{n}$ with logarithmic growth at infinity, we may associate the Robin function $ρ_{u} (z) = \underset{λ \to \infty}{lim sup} u (λ z) - log (λ z)$ defined on $P^{n - 1}$ , the hyperplane at infinity. We study the classes $L_{+}$ , and (respectively) $L_{p}$ of plurisubharmonic functions which have the form $u = log (1 + | z |) + O (1)$ and (respectively) for which the function $ρ_{u}$ is not identically $- \infty$ . We obtain an integral formula which connects the Monge-Ampère measure on the space $C^{n}$ with the Robin function on $P^{n - 1}$ . As an application we obtain a criterion...