1,662 research outputs found
On the decomposition into Discrete, type II and type III -algebras
We obtained a "decomposition scheme" of C*-algebras. We show that the classes
of discrete C*-algebras (as defined by Peligard and Zsido), type II C*-algebras
and type III C*-algebras (both defined by Cuntz and Pedersen) form a good
framework to "classify" C*-algebras. In particular, we found that these classes
are closed under strong Morita equivalence, hereditary C*-subalgebras as well
as taking "essential extension" and "normal quotient". Furthermore, there exist
the largest discrete finite ideal , the largest discrete essentially
infinite ideal , the largest type II finite ideal , the
largest type II essentially infinite ideal , and the largest
type III ideal of any C*-algebra such that is an essential ideal of
. This "decomposition" extends the corresponding one for -algebras.
We also give a closer look at C*-algebras with Hausdorff primitive spectrum,
AW*-algebras as well as local multiplier algebras of C*-algebras. We find that
these algebras can be decomposed into continuous fields of prime C*-algebras
over a locally compact Hausdorff space, with each fiber being non-zero and of
one of the five types mentioned above.Comment: 41 pages; we added a lot of details and some new result
Robust Estimation of Multiple Regression Model with asymmetric innovations and Its Applicability on Asset Pricing Model
In this paper, we first develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the parameters in the Capital Asset Pricing Model by comparing its performance with that of least squares estimators (LSE) on the monthly returns of US portfolios. Our empirical study reveals that the MML estimators are more efficient than the LSE in terms of relative efficiency of one-step-ahead forecast mean square error for small samples.Maximum likelihood estimators, Modified maximum likelihood estimators, Student’s t family, Capital Asset Pricing Model, Robustness
Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution
In this paper, we develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the parameters in the Capital Asset Pricing Model by comparing its performance with that of least squares estimators (LSE) on the monthly returns of US portfolios. Our empirical study reveals that the MML estimators are more efficient than the LSE in terms of relative efficiency of one-step-ahead forecast mean square error for small samples.Maximum likelihood estimators, Modified maximum likelihood estimators, Student's t family, Capital Asset Pricing Model, Robustness.
Preferences over Meyer’s Location-Scale Family
This paper extends Meyer’s (1987) location-scale family with general n random seed sources. Firstly, we clarify and generalize existing results to this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Secondly, we introduce and study some general non-expected utility functions defined over the location-scale (LS) family. Special care is made in characterizing the shape of the indifference curves induced by the LS expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first-, second- order stochastic dominance, the mean -variance rule, and a newly defined location-scale dominance.
Estimating Parameters in Autoregressive Models with Asymmetric Innovations
Tiku et al (1999) considered the estimation in a regression model with autocorrelated error in which the underlying distribution be a shift-scaled Student’s t distribution, developed the modified maximum likelihood (MML) estimators of the parameters and showed that the proposed estimators had closed forms and were remarkably efficient and robust. In this paper, we extend the results to the case, where the underlying distribution is a generalized logistic distribution. The generalized logistic distribution family represents very wide skew distributions ranging from highly right skewed to highly left skewed. Analogously, we develop the MML estimators since the ML (maximum likelihood) estimators are intractable for the generalized logistic data. We then study the asymptotic properties of the proposed estimators and conduct simulation to the study.
Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot
In this paper we investigate the asymptotic behavior of the colored Jones
polynomials and the Turaev-Viro invariants for the figure eight knot. More
precisely, we consider the -th colored Jones polynomials evaluated at
-th root of unity with a fixed limiting ratio, , of and
. We find out the asymptotic expansion formula (AEF) of the colored
Jones polynomials of the figure eight knot with close to . Nonetheless,
we show that the exponential growth rate of the colored Jones polynomials of
the figure eight knot with close to is strictly less than those with
close to . It is known that the Turaev Viro invariant of the figure
eight knot can be expressed in terms of a sum of its colored Jones polynomials.
Our results show that this sum is asymptotically equal to the sum of the terms
with close to 1. As an application of the asymptotic behavior of the
colored Jones polynomials, we obtain the asymptotic expansion formula for the
Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible
generalization of our approach so as to relate the AEF for the colored Jones
polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic
knots.Comment: 40 pages, 0 figure
Two-moment decision model for location-scale family with background asset
This paper studies the impact of background risk on the indifference curve. We first study the shape of the indifference curves for the investment with background risk for risk averters, risk seekers, and risk-neutral investors. Thereafter, we study the comparative statics of
the change in the shapes of the indifference curves when the means and the standard deviations of the returns of the financial asset and/or the background asset change. In addition, we draw inference on risk vulnerability and investment decisions in financial crises and bull and bear markets
New Variance Ratio Tests to Identify Random Walk from the General Mean Reversion Model
We develop some properties on the autocorrelation of the k-period returns for the general mean reversion (GMR) process in which the stationary component is not restricted to the AR(l) process but take the form of a general ARMA process. We then derive some properties of the GMR process and three new non-parametric tests comparing the relative variability of returns over different horizons to validate the GMR process as an alternative to random walk. We further examine the asymptotic properties of these tests which can then be applied to identify random walk models from the GMR processes.mean reversion, variance ratio test, random walk, stock price, stock return
On the Estimation of Cost of Capital and its Reliability
Gordon and Shapiro (1956) first equated the price of a share with the present value of future dividends and derived the well-known relationship. Since then, there have been many improvements on the theory. For example, Thompson (1985, 1987) combined the "dividend yield plus growth" method with Box-Jenkins time series analysis of past dividend experience to estimate the cost of capital and its "reliability" for individual firms. Thompson and Wong (1991, 1996) proved the existence and uniqueness of the cost of capital and provided formula to estimate both the cost of capital and its reliability. However, their approaches cannot be used if the "reliability" does not exist or if there are multiple solutions for the "reliability". In this paper, we extend their theory by proving the existence and uniqueness of this reliability. In addition, we propose the estimators for the reliability and prove that the estimators converge to a true parameter. The estimation approach is further simplified, hence rendering computation easier. In addition, the properties of the cost of capital and its reliability will be analyzed with illustrations of several commonly used Box-Jenkins models.
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