Natural mortality at different population densities of a pine shoot moth,Evetria cristata

Summary A field population ofEvetria cristata was studied in 10 plots in 1962 and in 6 plots in 1963. These plots were divided into 2 or 3 groups of different population levels of the shoot moth in respective years. The survival of the insect was then analysed in these different groups of plots. The survival rate ofE. cristata from eggs to adults in the first generation was found always higher in the group with low population density, which indicates the existence of some factors that affect the population more severely when the insect is more abundant.Lissonota evetriae andPediobius sp. seemed to have killed more proportion of the hosts where the shoot moth density was high. However, the total effect of the all natural enemies was not always great in the plots with high density of the moth. The survival of the second generation of the moth in 1963 was observed to be much higher at any population level than in the other generations.     

Simple Computation of Maximum Likelihood Estimates in Latent Class Model with Equality and Constant Constraints

A simple computational method for estimation of parameters via a type of EM algorithm is proposed in restricted latent class analysis, where equality and constant constraints are considered. These constraints create difficulty in estimation. In order to simply and stably estimate parameters in restricted latent class analysis, a simple computational method using only first-order differentials is proposed, where the step-halving method is adopted. A simulation study shows that in almost all cases the new method gives parameter sequences monotonously increasing the Q-function in the EM algorithm. Analysis of real data is provided.     

Nonparametric Estimation Methods of Integrated Multivariate Volatilities

Estimation of integrated multivariate volatilities of an Itô process is an interesting and important issue in finance, for example, in order to evaluate portfolios. New non-parametric estimators have been recently proposed by Malliavin and Mancino (2002 Malliavin , P. , Mancino , M. ( 2002 ). Fourier series method for measurement of multivariate volatilities . Finance and Stochastics 6 : 49 – 61 .[Crossref], [Web of Science ®] , [Google Scholar]) and Hayashi and Yoshida (2005a Hayashi , T. , Yoshida , N. (2005a). On covariance estimation of nonsynchronously observed diffusion processes. Bernoulli 11(2):359–379.[Crossref], [Web of Science ®] , [Google Scholar]) as alternative methods to classical realized quadratic covariation. The purpose of this article is to compare these alternative estimators both theoretically and empirically, when high frequency data is available. We found that the Hayashi–Yoshida estimator performs the best among the alternatives in view of the bias and the MSE. The other estimators are shown to have possibly heavy bias mostly toward the origin. We also applied these estimators to Japanese Government Bond futures to obtain the results consistent with our simulation.     

Asymptotic Inference with Incomplete Data

This article discusses asymptotic theory for the maximum likelihood estimator based on incomplete data. Although much literature has implicitly assumed the basic properties of the estimator, such as consistency and asymptotic normality, it is hard to find their precise and comprehensive proofs. In this article, we first show that under MAR an estimator based on the likelihood function ignoring the missing-data mechanism is strongly consistent. The estimator is then shown to be asymptotically normal. When the data are NMAR and when the data are MAR without parameter distinctness, the consistency and the asymptotic normality are shown. Several examples are provided.     

Incomplete-data Fisher scoring method with steplength adjustment

An incomplete-data Fisher scoring method is proposed for parameter estimation in models where data are missing and in latent-variable models that can be formulated as a missing data problem. The convergence properties of the proposed method and an accelerated variant of this method are provided. The main features of this method are its ability to accelerate the rate of convergence by adjusting the steplength, to provide a second derivative of the observed-data log-likelihood function using only the functions used in the proposed method, and the ability to avoid having to explicitly solve the first derivative of the object function. Four examples are presented to demonstrate how the proposed method converges compared with the EM algorithm and its variants. The computing time is also compared.     

On the use of the selection matrix in the maximum likelihood estimation of normal distribution models with missing data

In this article, by using the constant and random selection matrices, several properties of the maximum likelihood (ML) estimates and the ML estimator of a normal distribution with missing data are derived. The constant selection matrix allows us to obtain an explicit form of the ML estimates and the exact relationship between the EM algorithm and the score function. The random selection matrix allows us to clarify how the missing-data mechanism works in the proof of the consistency of the ML estimator, to derive the asymptotic properties of the sequence by the EM algorithm, and to derive the information matrix.     

Finite-sample analysis of impacts of unlabeled data and their labeling mechanisms in linear discriminant analysis

It is widely believed that unlabeled data are promising for improving prediction accuracy in classification problems. Although theoretical studies about when/how unlabeled data are beneficial exist, an actual prediction improvement has not been sufficiently investigated for a finite sample in a systematic manner. We investigate the impact of unlabeled data in linear discriminant analysis and compare the error rates of the classifiers estimated with/without unlabeled data. Our focus is a labeling mechanism that characterizes the probabilistic structure of occurrence of labeled cases. Results imply that an extremely small proportion of unlabeled data has a large effect on the analysis results.