Bayes sequential estimation for a Poisson process under a LINEX loss function

In this paper, within the framework of a Bayesian model, we consider the problem of sequentially estimating the intensity parameter of a homogeneous Poisson process with a linear exponential (LINEX) loss function and a fixed cost per unit time. An asymptotically pointwise optimal (APO) rule is proposed. It is shown to be asymptotically optimal for the arbitrary priors and asymptotically non-deficient for the conjugate priors in a similar sense of Bickel and Yahav [Asymptotically pointwise optimal procedures in sequential analysis, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, CA, 1967, pp. 401–413; Asymptotically optimal Bayes and minimax procedures in sequential estimation, Ann. Math. Statist. 39 (1968), pp. 442–456] and Woodroofe [A.P.O. rules are asymptotically non-deficient for estimation with squared error loss, Z. Wahrsch. verw. Gebiete 58 (1981), pp. 331–341], respectively. The proposed APO rule is illustrated using a real data set.     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

The rank distribution of the maximin in a random matrix

Let S be a set of tm distinct real numbers and R a random t × m matrix of these tm numbers with rows {r_i} and columns (c_i}. Define b = Max Min x. l≤i≤t x?r_i. Let c be the event Max Min x = Min Max x. l≤i≤t x?r_i l≤i≤m x?c_i. This paper derives the probability distribution of the rank of b in S, as well as the same distribution conditional on c.     

On estimating the dimensionality in discriminant analysis

In discriminant analysis, the dimension of the hyperplane which population mean vectors span is called the dimensionality. The procedures commonly used to estimate this dimension involve testing a sequence of dimensionality hypotheses as well as model fitting approaches based on (consistent) Akaike's method, (modified) Mallows' method and Schwarz's method. The marginal log-likelihood (MLL) method is developed and the asymptotic distribution of the dimensionality estimated by this method for normal populations is derived. Furthermore a modified marginal log-likelihood (MMLL) method is also considered. The MLL method is not consistent for large samples and two modified criteria are proposed which attain asymptotic consistency. Some comments are made with regard to the robustness of this method to departures from normality. The operating characteristics of the various methods proposed are examined and compared.     

Non-parametric estimation of population size from capture–recapture data when the capture probability depends on a covariate

Summary.  In capture–recapture experiments the capture probabilities may depend on individual covariates such as an individual's weight or age. Typically this dependence is modelled through simple parametric functions of the covariates. Here we first demonstrate that misspecification of the model can produce biased estimates and subsequently develop a non-parametric procedure to estimate the functional relationship between the probability of capture and a single covariate. This estimator is then incorporated in a Horvitz–Thompson estimator to estimate the size of the population. The resulting estimators are evaluated in a simulation study and applied to a data set on captures of the Mountain Pygmy Possum.     

Exploring gaps in the online economic inclusion of persons with disabilities in Korea

ABSTRACT

This paper explores the difference in the online economic activities of people with and without disabilities in Korea. We conducted a multiple regression analysis to investigate the impact of socioeconomic characteristics, internet access, and internet skills on online economic activities. Our sample, based on a 2016 dataset that included 1554 people with disabilities and 6004 people without disabilities, was developed using quota sampling based on gender, age, and residence. We determined that individuals with disabilities were more likely to engage in online economic activities if they had higher levels of education, lived in urban areas, were employed, or had greater internet skills. Individuals without disabilities were more likely to engage in online economic activities if they were women, had higher levels of education, were employed, lived in a two-generation or more household, or had greater internet skills. For both people with and without disabilities, the level of education, employment status, and internet skills positively contribute to online economic activites. We also determined that education level, participation in economic activity, living in a two-generation or more household, and internet skills had a statistically significant influence on online economic activity for people both with and without disabilities. These results highlight the importance of education and internet training for people with disabilities, as well as social support systems that help them learn to use the internet in diverse ways through both formal and informal networks. The study also underscores the importance of information and communications technology that adequately addresses people’s needs.     

Values and happiness among Asian adolescents: a cross-national study

Despite policy efforts to increase adolescent happiness, their impact has been unsatisfactory. Their limited impact may be rooted from a discrepancy between values that adolescents pursued and those that the policies were based on. To provide policy implications, our study aims to identify prevailing values for South Korean, Japanese, and Chinese adolescents and to examine the relationship between the values and self-rated happiness (SRH). A cross-sectional study was conducted using survey data collected on approximately 2000 middle and high school students (7th to 12th school grade) from each country in 2008. Firstly, an explanatory factor analysis was conducted to identify salient adolescent values from each country. Subsequently, a multiple logistic regression analysis was conducted for each population group to examine the relationship between the identified values and adolescent SRH after controlling for sociodemographic characteristics. We found that benevolence and altruism were positively associated with adolescent SRH in all three population groups. Patriarchy was associated with SRH positively in Chinese yet inversely in Japanese. Success pursuit was inversely associated with SRH in Korean. Policy efforts based on values of communities or social harmony may benefit adolescents’ SRH in these three countries.     

The Links Between Youth Employment and Educational Attainment Across Racial Groups

Research suggests that the relations between adolescent employment and youth development vary by socioeconomic status (SES) and race/ethnicity. However, it is unclear whether the links between paid work and college outcomes vary by either SES or race/ethnicity, or both. Using data from the Educational Longitudinal Study, we find that low‐intensity work during high school is associated with positive college outcomes for almost all students, whereas the associations between high‐intensity work and negative postsecondary outcomes are mostly limited to White students. Our results suggest that both differential selections into youth employment and differential consequences of youth employment contribute to these varying links between paid work and educational outcomes across different racial groups.     

Estimation of structural mean breaks for long-memory data sets

In long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.