Hideo Kozumi

Estimation of Lorenz curves: a Bayesian nonparametric approach

Abstract In this article, we estimate Lorenz curves using the recent development of the Bayesian nonparametric method with Dirichlet process prior. We also consider contaminated observations of income and propose a method for removing these contaminated observations. Further, we present examples using both simulated data and real data to illustrate our approach.

The VAR-VARCH model: A Bayesian approach

In this paper, we develop a combined Bayesian vector autoregressive and conditional heteroskedasticity (VAR-VARCH) models. A Gibbs sampling approach is suggested for the univariate and multivariate VAR-VARCH model. Using a random coefficient formulation it is shown that full conditional distributions are derived in closed analytical forms. The method is applied to monthly exchange rate series, the Swiss Franc, and the Deutsch Mark to the U.S. Dollar.

Bayesian Analysis on Engel Curves Estimation With Measurement Errors and an Instrumental Variable

In this article, we consider the Bayesian estimation of Engel curves specified as the Working–Leser form with the measurement errors on both the left and the right sides. It is noteworthy that in the Bayesian approach no additional variation data (i.e., instrumental variables) are required in contrast with the non-Bayesian approach. We present the Bayesian estimation procedure in both models without an instrumental variable and with an instrumental variable. We also compare our results with the generalized method of moments estimates proposed by Lewbel.

The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators

Abstract In this paper, we derive the general formulae for the moments of a linear functional of the Stein-rule and positive-part Stein-rule estimators (i.e., h′bSR and h′bPSR) in a different way from Phillips (1984). The MSE dominance of h′bPSR over h′bSR and a sufficient condition for h′bSR to dominate a linear functional of the OLS estimator (h′b) are shown. Using the formulae for the moments, we evaluate numerically the first four moments of bSR and bPSR, and examine the bias, variance, MSE, skewness, and kurtosis.

The general expressions for the moments of lawless and wang's ordinary ridge regression estimator

In this paper, we derive the exact general expressions for the moments of an ordinary ridge regression (ORR) estimator for individual regression coefficients in a different way from Firinguetti (1987). Using the derived expressions, we evaluate numerically the first four moments of the ORR estimator, and examine its bias, mean square error, skewness and kurtosis. Further, Monte Carlo experiments are carried out in order to examine the shape of the density function of the ORR estimator.

Posterior analysis of latent competing risk models by parallel tempering

Latent competing risk models are examined from a Bayesian point of view. The parallel tempering algorithm is applied for posterior inference and compared with different Markov chain algorithms such as the Gibbs sampler in terms of mixing. A simple remedy is suggested for reducing the computational cost of the parallel tempering, and posterior estimates are obtained from the relabeling algorithm. The methodology is illustrated by both simulated and real data.

A Bayesian Analysis of Structural Changes with an Application to the Displacement Effect

In this paper we propose a new approach to the problem of structural change from a Bayesian point of view. Our approach is based on a hierarchical model with a Dirichlet process prior. A notable feature of the Dirichlet process is its discreteness which is useful for detecting structural changes. The approach developed in the paper is illustrated using simulated and real data sets. For the real data set, we examine possible structural changes in government expenditure in Japan using the annual data from 1957 to 1995. It is shown that two structural breaks occurred, before and after the first oil crisis.

A Bayesian Semiparametric Analysis of ARCH Models

This paper provides a Bayesian analysis of a semiparametric autoregressive conditional heteroscedasticity (ARCH) model. We propose a semiparametric ARCH model using a Dirichlet process prior and show a Markov chain Monte Carlo method for the posterior inference. The model is estimated with a data set of monthly exchange rate for the Deutsche Mark to the U. S. Dollar.

Irregularly Spaced AR (ISAR) Models

High frequency data in finance are time series which are often measured at unequally or irregularly spaced time intervals. This paper suggests a modeling approach by so-called AR response surfaces where the AR coefficients are declining functions in continuous lag time. The irregularly spaced ISAR models contain the usual AR models as a special case if the time series is equally spaced. We illustrate our methodology with two examples.

Bayes’sche Modelle zur Prognose des langfristigen Zinssatzes in Deutschland

In dieser Arbeit werden einige einfache Bayes’sche Modelle, die mit Hilfe des Gibbs- Samplers geschatzt werden konnen, vorgestellt und auf die Prognosefahigkeit hin uberpruft. Da nur zwei multivariate Methoden zur Schatzung zur Verfugung standen, kann diese Arbeit nur als ein erster Beitrag und nicht als eine abschliessende Diskussion des Bayes’sehen Zugangs in der Okonometrie angesehen werden.