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Erik Schlogl - One of the best experts on this subject based on the ideXlab platform.

  • a square root interest rate model fitting discrete initial term structure data
    Applied Mathematical Finance, 2000
    Co-Authors: Erik Schlogl, Lutz Schlogl
    Abstract:

    This paper presents one-factor and multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type 'square root' diffusions with piece wise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral Chi-Square Distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

  • a square root interest rate model fitting discrete initial term structure data
    Research Paper Series, 1999
    Co-Authors: Erik Schlogl, Lutz Schlogl
    Abstract:

    This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. This model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near-closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral Chi-Square Distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

Lutz Schlogl - One of the best experts on this subject based on the ideXlab platform.

  • a square root interest rate model fitting discrete initial term structure data
    Applied Mathematical Finance, 2000
    Co-Authors: Erik Schlogl, Lutz Schlogl
    Abstract:

    This paper presents one-factor and multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type 'square root' diffusions with piece wise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral Chi-Square Distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

  • a square root interest rate model fitting discrete initial term structure data
    Research Paper Series, 1999
    Co-Authors: Erik Schlogl, Lutz Schlogl
    Abstract:

    This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. This model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near-closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral Chi-Square Distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

Kehai Yuan - One of the best experts on this subject based on the ideXlab platform.

  • empirical correction to the likelihood ratio statistic for structural equation modeling with many variables
    Psychometrika, 2015
    Co-Authors: Kehai Yuan, Yubin Tian, Hirokazu Yanagihara
    Abstract:

    Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is T ML, a slight modification to the likelihood ratio statistic. Under normality assumption, T ML approximately follows a Chi-Square Distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T ML rejects the correct model too often when p is not too small. Various corrections to T ML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T ML so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal Chi-Square Distribution. Results show that empirically corrected statistics follow the nominal Chi-Square Distribution much more closely than previously proposed corrections to T ML, and they control type I errors reasonably well whenever N≥max(50,2p). The formulations of the empirically corrected statistics are further used to predict type I errors of T ML as reported in the literature, and they perform well.

  • on the likelihood ratio test for the number of factors in exploratory factor analysis
    Structural Equation Modeling, 2007
    Co-Authors: Kentaro Hayashi, Peter M Bentler, Kehai Yuan
    Abstract:

    In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the Chi-Square Distribution due to a problem of rank deficiency and nonidentifiability of model parameters. As a result, decisions regarding the number of factors may be incorrect. Several researchers have pointed out this phenomenon, but it is not well known among applied researchers who use exploratory factor analysis. We demonstrate that overfactoring is one cause for the well-known fact that the likelihood ratio test tends to find too many factors.

  • On the asymptotic Distributions of two statistics for two-level covariance structure models within the class of elliptical Distributions
    Psychometrika, 2004
    Co-Authors: Kehai Yuan, Peter M Bentler
    Abstract:

    Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality Distribution assumption, which may not be realistic for practical data. It is of interest to know whether normal theory-based inference can still be valid with violations of the Distribution condition. Various interesting results have been obtained for conventional covariance structure analysis based on the class of elliptical Distributions. This paper shows that similar results still hold for 2-level covariance structure models. Specifically, when both the level-1 (within cluster) and level-2 (between cluster) random components follow the same elliptical Distribution, the rescaled statistic recently developed by Yuan and Bentler asymptotically follows a Chi-Square Distribution. When level-1 and level-2 have different elliptical Distributions, an additional rescaled statistic can be constructed that also asymptotically follows a Chi-Square Distribution. Our results provide a rationale for applying these rescaled statistics to general non-normal Distributions, and also provide insight into issues related to level-1 and level-2 sample sizes.

Feinian Chen - One of the best experts on this subject based on the ideXlab platform.

  • The Noncentral Chi-Square Distribution in Misspecified Structural Equation Models: Finite Sample Results from a Monte Carlo Simulation.
    Multivariate behavioral research, 2002
    Co-Authors: Patrick J. Curran, Kenneth A. Bollen, Pamela Paxton, James B. Kirby, Feinian Chen
    Abstract:

    The noncentral Chi-Square Distribution plays a key role in structural equation modeling (SEM). The likelihood ratio test statistic that accompanies virtually all SEMs asymptotically follows a noncentral Chi-Square under certain assumptions relating to misspecification and multivariate Distribution. Many scholars use the noncentral Chi-Square Distribution in the construction of fit indices, such as Steiger and Lind's (1980) Root Mean Square Error of Approximation (RMSEA) or the family of baseline fit indices (e.g., RNI, CFI), and for the computation of statistical power for model hypothesis testing. Despite this wide use, surprisingly little is known about the extent to which the test statistic follows a noncentral Chi-Square in applied research. Our study examines several hypotheses about the suitability of the noncentral Chi-Square Distribution for the usual SEM test statistic under conditions commonly encountered in practice. We designed Monte Carlo computer simulation experiments to empirically test these research hypotheses. Our experimental conditions included seven sample sizes ranging from 50 to 1000, and three distinct model types, each with five specifications ranging from a correct model to the severely misspecified uncorrelated baseline model. In general, we found that for models with small to moderate misspecification, the noncentral Chi-Square Distribution is well approximated when the sample size is large (e.g., greater than 200), but there was evidence of bias in both mean and variance in smaller samples. A key finding was that the test statistics for the uncorrelated variable baseline model did not follow the noncentral Chi-Square Distribution for any model type across any sample size. We discuss the implications of our findings for the SEM fit indices and power estimation procedures that are based on the noncentral Chi-Square Distribution as well as potential directions for future research.

Patrick A. Tibbits - One of the best experts on this subject based on the ideXlab platform.

  • Percentiles of von Mises Stress from Combined Random Vibration and Static Loading by Approximate Noncentral Chi Square Distribution
    Journal of Vibration and Acoustics, 2012
    Co-Authors: Patrick A. Tibbits
    Abstract:

    Firstly, a calculation for percentiles of von Mises stress in linear structures subjected to Gaussian random loads is extended to the case of Gaussian random loads having nonzero mean values, i.e.,the inclusion of static loads. The development is restricted to the case of plane stress. The method includes calculation of a given percentile of von Mises stress to any desired accuracy, a rapid estimate of the percentile, and upper and lower bounds on the von Mises stress. The calculation expands the cumulative Distribution function of the von Mises stress as a series of noncentral Chi-Square Distributions. Summation of a sufficient number of terms of the series calculates the percentile to the desired accuracy. The rapid estimate of the percentile interpolates the Distribution of the von Mises stress in a small number of inverse noncentral Chi-Square2 Distribution functions. The upper and lower bounds on the percentiles take advantage of the noncentral Chi-Square Distribution of summations of normally distributed stress components. Second and third calculation methods arise from approximations of the Distribution of quadratic forms of noncentral normal variables, or equivalently, linear combinations of noncentral Chi-Square variables. These methods provide rapid estimates of percentiles of von Mises stress in linear structures under random loads having nonzero mean values. The accuracy and computational efficiency of the methods are reviewed and compared. The methods are expected to have wide application in design of and prognostics for components subjected to constant structural loads coupled with random loading arising from vibrations caused by wind, waves, seismic events, engines, turbulence, acoustic noise, etc.

  • Percentiles of von Mises Stress From Combined Random Vibration and Static Loading by Approximate Noncentral Chi Square Distribution
    Volume 8: Mechanics of Solids Structures and Fluids; Vibration Acoustics and Wave Propagation, 2011
    Co-Authors: Patrick A. Tibbits
    Abstract:

    Firstly, a calculation for percentiles of von Mises stress in linear structures subjected to Gaussian random loads is extended to the case of Gaussian random loads having nonzero mean values, i.e., the inclusion of static loads. The development is restricted to the case of plane stress. The method includes calculation of a given percentile of von Mises stress to any desired accuracy, a rapid estimate of the percentile, and upper and lower bounds on the von Mises stress. The calculation expands the cumulative Distribution function of the von Mises stress as a series of noncentral chi square Distributions. Summation of a sufficient number of terms of the series calculates the percentile to the desired accuracy. The rapid estimate of the percentile interpolates the Distribution of the von Mises stress in a small number of inverse noncentral Chi-Square Distribution functions. The upper and lower bounds on the percentiles take advantage of the noncentral Chi-Square Distribution of summations of normally distributed stress components. Second and third calculation methods arise from approximations of the Distribution of quadratic forms of noncentral normal variables, or equivalently, linear combinations of noncentral chi square variables. These methods provide rapid estimates of percentiles of von Mises stress in linear structures under random loads having nonzero mean values. The accuracy and computational efficiency of the methods are reviewed and compared. The methods are expected to have wide application in design of and prognostics for components subjected to constant structural loads coupled with random loading arising from vibrations caused by wind, waves, seismic events, engines, turbulence, acoustic noise, etc.© 2011 ASME