<Emphasis Type="Italic">Z</Emphasis>-process method for change point problems with applications to discretely observed diffusion processes

The aim of this paper is to develop a general, unified approach, based on some partial estimation functions which we call “Z-process”, to some change point problems in mathematical statistics. The method proposed can be applied not only to ergodic models but also to some models where the Fisher information matrix is random. Applications to some concrete models, including a parametric model for volatilities of diffusion processes are presented. Simulations for randomly time-transformed Brownian bridge process appearing as the limit of the proposed test statistics are performed with computer intensive use.     

Laplace approximations and Bayesian information criteria in possibly misspecified models

We provide general conditions to ensure the valid Laplace approximations to the marginal likelihoods under model misspecification, and derive the Bayesian information criteria including all terms of order O_p(1). Under conditions in theorem 1 of Lv and Liu [J. R. Statist. Soc. B, 76, (2014), 141–167] and a continuity condition for prior densities, asymptotic expansions with error terms of order o_p(1) are derived for the log-marginal likelihoods of possibly misspecified generalized linear models. We present some numerical examples to illustrate the finite sample performance of the proposed information criteria in misspecified models.     

Cultural constraints on rising income inequality: A U.S.–Japan comparison

Prior research has identified fundamental cultural and normative concepts—including wa, enryo, giri, and amae—that are typically argued to be integral to Japanese society. We advance this line of research by discussing how these traditional cultural concepts may influence labor market relations and thereby constrain the degree of income inequality in Japan relative to the U.S. Collectivist cultural attitudes are embedded in Japanese work organization, and are naturally inherited social constraints when compared to more unbridled labor market relations of the “New Economy” in the U.S. While studies of rising inequality in the U.S. and Europe consider how governmental policies impinge upon market forces in order to moderate labor market outcomes, our analysis suggests how culture may sometimes directly constrain income inequality without imposing legal regulations or instituting official programs.     

Investigation of the properties of the “switching decision rule” described in the Japanese guideline for human bioequivalence studies

In a human bioequivalence (BE) study, the conclusion of BE is usually based on the ratio of geometric means of pharmacokinetic parameters between a test and a reference products. The “Guideline for Bioequivalence Studies of Generic Products” (2012) issued by the Japanese health authority and other similar guidelines across the world require a 90% confidence interval (CI) of the ratio to fall entirely within the range of 0.8 to 1.25 for the conclusion of BE. If prerequisite conditions are satisfied, the Japanese guideline provides for a secondary BE criterion that requires the point estimate of the ratio to fall within the range of 0.9 to 1.11. We investigated the statistical properties of the “switching decision rule” wherein the secondary criterion is applied only when the CI criterion fails. The behavior of the switching decision rule differed from either of its component criteria and displayed an apparent type I error rate inflation when the prerequisite conditions were not considered. The degree of inflation became greater as the true variability increased in comparison to the assumed variability used in the sample size calculation. To our knowledge, this is the first report in which the overall behavior of the combination of the two component criteria was investigated. The implications of the in vitro tests on human BE and the accuracy of the intra‐subject variability have impacts on appropriate planning and interpretation of BE studies utilizing the switching decision rule.     

On Z-estimation by rounded data

It is often assumed in statistics that the random variables under consideration come from a continuous distribution. However, real data is always given in a rounded (discretized) form. The rounding errors become serious when the sample size is large. In this paper, we consider the situation where the mesh of discretization tends to zero as the sample size tends to infinity, and give some sets of sufficient conditions under which the rounding errors can be asymptotically ignored, in the context of Z-estimation. It is theoretically proved that the mid-point discretization is preferable.     

A host shift from wild blue cohosh to cultivated potato by the phytophagous ladybird beetle, Epilachna yasutomii (Coleoptera, Coccinellidae)

Life history traits of the phytophagous ladybird beetle Epilachna yasutomii were compared between a nonpest population feeding on wild blue cohosh and a pest population feeding on cultivated solanaceous crops, mainly potato. Newly emerged adults of the nonpest population entered diapause early in midsummer when blue cohosh withered, while adults of the pest population were found in tomato and eggplant fields until late autumn. The pest population had larger females, a higher population growth rate, a shorter larval developmental period, and reduced longevity of overwintered females, compared with the nonpest population. ANOVA indicated that all these life history traits were influenced by the food plant, and that the number of eggs laid per female and the longevity of overwintered females were also affected by the population type. These findings suggest that the life history pattern of E. yasutomii changed to high fecundity with a short life span from low fecundity with a long life span as a result of the host shift from wild blue cohosh to cultivated solanaceous crops. Received: May 22, 1998 / Accepted: January 13, 1999     

Testing for the Null Hypothesis of Cointegration with a Structural Break

In this paper we propose residual-based tests for the null hypothesis of cointegration with a structural break against the alternative of no cointegration. The Lagrange Multiplier (LM) test is proposed and its limiting distribution is obtained for the case in which the timing of a structural break is known. Then the test statistic is extended to deal with a structural break of unknown timing. The test statistic, a plug-in version of the test statistic for known timing, replaces the true break point by the estimated one. We show the limiting properties of the test statistic under the null as well as the alternative. Critical values are calculated for the tests by simulation methods. Finite-sample simulations show that the empirical size of the test is close to the nominal one unless the regression error is very persistent and that the test rejects the null when no cointegrating relationship with a structural break is present. We provide empirical examples based on the present-value model, the term structure model, and the money-output relationship model.     

Laplace approximations to means and variances with asymptotic modes

The moment-generating function method, which is proposed by Tierney et al. [1989a. Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Amer. Statist. Assoc. 84, 710–716], is an asymptotic technique of approximating a posterior mean of a general function by approximating the moment-generating function (MGF), and then differentiating it. In this article, we give approximations to the posterior means and variances by combining the MGF method and the Laplace approximations with asymptotic modes. We prove that asymptotic errors of the approximate means and variances are of order n^-2$n^{-2}$ and of order n^-3$n^{-3}$, respectively. Our approximation is closely related to a standard-form approximation, and is given without evaluating the exact posterior mode and third derivatives of the log-likelihood function. The MGF method also improves numerical instability of the fully exponential Laplace approximation for a predictive mean in logistic regression.     

Longevity, flight ability and reproductive performance of the diamondback moth,Plutella xylostella (L.) (Lepidoptera: Yponomeutidae), related to adult body size

Plutella xylostella in the temperate zone shows a clear seasonal change in adult body size. In the laboratory, large and small moths were produced during immature stages at 15°C and 25°C, respectively. These moths were then used to evaluate longevity, age-specific flight ability, flight ability of mated and unmated females, and the influence of flight experience on the subsequent reproductive success. The large moths lived longer and displayed a greater flight ability over 3 weeks. Irrespective of body size, unmated females flew for a longer time than mated females, and flight experience affected their subsequent reproductive success. Females of both sizes mated and laid eggs soon after emergence, without any obvious pre-reproductive period. More flight experience did not delay oviposition, but did reduce egg production. It is likely that large moths with a longer adult life span and greater flight ability are better fitted for long-distance flight and more fecund than small ones. These experimental results may explain why long-distance migration ofP. xylostella is mostly seen during cool seasons, when relatively large moths with long forewing appear in the field.     

Probabilistic assignment of indivisible goods with single-peaked preferences

We consider the problem of assigning indivisible goods among a group of agents with lotteries when the preference profile is single-peaked. Unfortunately, even on this restricted domain of preferences, equal treatment of equals, stochastic dominance efficiency, and stochastic dominance strategy-proofness are incompatible.