Hikaru Hasegawa

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 first isolation of unsubstituted porphyrinogen and unsubstituted 21-oxaporphyrinogen by the ‘3+1’ approach from 2,5-bis(hydroxymethyl)pyrrole and tripyrrane derivatives

Abstract The treatment of 2,5-bis(hydroxymethyl)pyrrole or 2,5-bis(hydroxymethyl)furan with pyrrole in the presence of hydrochloric acid gave tripyrrane and 2,5-bis(2-pyrrolylmethyl)furan in 58–61% yield, which afforded the simplest porphyrinogen (hexahydroporphine) and 21-oxaporphyrinogen by the ‘3+1’ approach in 14 and 11% yields, respectively. 21-Oxaporphyrinogen has been shown to adopt a 1,2-alternated conformation in the solid state by X-ray crystallography.

Exclusive 1,4-aryl migration in a stereoselective cyclization of N-benzylalk-4-enylaminyl radicals

Abstract Tandem cyclization of N -benzylalk-4-enylaminyl radicals readily occurs to give 1,4-aryl migration pyrrolidines, trans - N -methyl-2-alkyl-5-(1-phenylalkyl)pyrrolidines, exclusively.

On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

Tandem cyclization of N-allylaminyl radicals: Stereoselective synthesis of 1,2,5-trisubstituted pyrrolizidines

Abstract Radical reaction of N -allylalk-4-enylaminyl radicals, generated from the corresponding N -chloroamines by treatment with Bu 3 SnH-AIBN in refluxing toluene, was carried out. Tandem cyclization of the resulting neutral aminyl radicals readily took place steroselectively to give 1,2,5-trisubstituted pyrrolizidines and a pyrroloindole derivative as a sole product in good yields. The cyclization products contained only two stereoisomers in each reaction, indicating that both of the consecutive cyclizations proceeded in a stereoselective manner.

Organolanthanide Catalyzed Intramolecular 5-endo-dig Hydroamination: An Unusual Anti-Markovnikov Cyclization

Intramolecular 5-endo-dig hydroaminations of homopropargylamine derivatives were efficiently catalyzed by the organolanthanide precatalyst, Cp* 2 YbCH(TMS) 2 (Cp* = C 5 Me 5 ), to give the endocyclic enamine products. The 5-endo-dig hydroamination was also preferred in the presence of another olefin that would afford a 6-exo cyclization.

Stereoselective synthesis of 2-methylenepyrrolizidines by tandem cyclization of N-propargylaminyl radicals

Abstract Tandem cyclization of N-propargylaminyl radicals, generated by N-chlorination of (E)-alk-4-enylamines 2a–d and 2f followed by treatment with tributyltin radical, afforded 2-methylenepyrrolizidines 3a–d and 3f in a highly stereoselective manner. A similar radical cyclization of (Z)-N-propargyl-1-methyl-5-phenylpent-4-enylamine ( 2e ) gave pyrrolizidine 3b having the same stereochemistry as that obtained from the E isomer 2b .

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.

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.

Bayesian Unit Root Test in Nonnormal AR(1) Model

In this paper, we approximate the distribution of disturbances by the Edgeworth series distribution and propose a Bayesian analysis in a nonnormal AR(1) model. We derive the posterior distribution of the autocorrelation and the posterior odds ratio for unit roots hypothesis in the AR(1) model when the first four cumulants of the Edgeworth series distribution are finite and the higher order cumulants are negligible. We also apply the posterior analysis to eight real exchange rates and investigate whether these exchange rates behave like a random walk or not.