Variable Selection for Naive Bayes Semisupervised Learning

This article deals with a semisupervised learning based on naive Bayes assumption. A univariate Gaussian mixture density is used for continuous input variables whereas a histogram type density is adopted for discrete input variables. The EM algorithm is used for the computation of maximum likelihood estimators of parameters in the model when we fix the number of mixing components for each continuous input variable. We carry out a model selection for choosing a parsimonious model among various fitted models based on an information criterion. A common density method is proposed for the selection of significant input variables. Simulated and real datasets are used to illustrate the performance of the proposed method.     

Structured kernel quantile regression

Quantile regression can provide more useful information on the conditional distribution of a response variable given covariates while classical regression provides informations on the conditional mean alone. In this paper, we propose a structured quantile estimation methodology in a nonparametric function estimation setup. Through the functional analysis of variance decomposition, the optimization of the proposed method can be solved using a series of quadratic and linear programmings. Our method automatically selects relevant covariates by adopting a lasso-type penalty. The performance of the proposed methodology is illustrated through numerical examples on both simulated and real data.     

Minimum variance unbiased estimation in natural exponential families generated by stable distributions

The class of nature exponential families generated by stable distributions has been introduced in different contexts by several authors. Tweedie (1984) and Jorgensen (1987) studied this class in the context of generalized liner models and exponential dispersion models. Bar-Lev and Enis (1986) introduced this class in the context of the property of reproducibility in natural exponential families and Hougaard (1986) found the distributions in this class to be natural candidates for applications as survival distributions in life tables for heterogeneous populations. In this note, we consider such a class in the context of minimum variance unbiased estimation. For each family in this class, we obtain an explicit expression for the uniformly minimum variance unbiased estimator for the r-th cumlant, the density function, and the reliability function.     

Effects of Parent Effectiveness Training Program on Family Communication and Flexibility of Korean Parents

This study examines the effects of an 8‐week Parent Effective Training (PET) program on family communication and flexibility. Forty‐two pairs of Korean parents were randomly assigned to either an experimental group that provided the PET program or a control group that did not offer the program. The two groups were compared on pre‐, post‐, and follow‐up measures of PAC(Parent‐Adolescent Communication), ENRICH(Enriching and Nurturing Relationship Issues, Communication and Happiness), and FACES(Family Adaptability Cohesion Evaluation Scale), while controlling for the effects of socio‐demographic variables. Compared with the control group, the experimental group showed significant improvements in family communication between parents and children and between the husband and the wife but no such improvements in family flexibility. These findings suggest that the PET program is a useful short‐term tool for Korean parents wishing to enhance family communication.     

Teachers' Theory‐of‐mind Coaching and Children's Executive Function Predict the Training Effect of Sociodramatic Play on Children's Theory of Mind

Theory of mind (ToM), the ability to interpret one's own and others' mental states, is essential for social interaction; thus, it is important to promote the early development of ToM. The current study investigated (1) whether sociodramatic play (SDP) promotes the development of ToM in kindergarten children; (2) whether teachers' ToM coaching, as well as children's individual differences in language and executive function (EF), may influence how children benefit from SDP; and (3) whether SDP improves children's development in language and EF. Seventy‐one kindergarteners (M age = 60.2 months, SD = 5.7) divided into 12 groups were randomly assigned to three conditions: free play, SDP, or SDP + ToM coaching. Each condition included four weekly sessions, 45 min per session. Before and after the training, children's ToM, language and EF were measured. The results showed that after children's individual differences in ToM were considered, (1) SDP positively predicted children's post‐test ToM; (2) teachers' ToM‐related guidance during SDP and children's pretest EF positively predicted the training effect of SDP on children's ToM; (3) teachers' ToM‐related guidance during SDP, but not SDP alone, predicted children's post‐test language; and (4) neither SDP nor teachers' ToM‐related guidance during SDP predicted children's post‐test EF.     

A balanced multi-level rotation sampling design and its efficient composite estimators

We present a multi-level rotation sampling design which includes most of the existing rotation designs as special cases. When an estimator is defined under this sampling design, its variance and bias remain the same over survey months, but it is not so under other existing rotation designs. Using the properties of this multi-level rotation design, we derive the mean squared error (MSE) of the generalized composite estimator (GCE), incorporating the two types of correlations arising from rotating sample units. We show that the MSEs of other existing composite estimators currently used can be expressed as special cases of the GCE. Furthermore, since the coefficients of the GCE are unknown and difficult to determine, we present the minimum risk window estimator (MRWE) as an alternative estimator. This MRWE has the smallest MSE under this rotation design and yet, it is easy to calculate. The MRWE is unbiased for monthly and yearly changes and preserves the internal consistency in total. Our numerical study shows that the MRWE is as efficient as GCE and more efficient than the existing composite estimators and does not suffer from the drift problem [Fuller W.A., Rao J.N.K., 2001. A regression composite estimator with application to the Canadian Labour Force Survey. Surv. Methodol. 27 (2001) 45–51] unlike the regression composite estimators.     

Simple Transformation Techniques for Improved Non-parametric Regression

We propose and investigate two new methods for achieving less bias in non- parametric regression. We show that the new methods have bias of order h ⁴, where h is a smoothing parameter, in contrast to the basic kernel estimator's order h ². The methods are conceptually very simple. At the first stage, perform an ordinary non-parametric regression on { x_i , Y_i } to obtain m^ ( x_i ) (we use local linear fitting). In the first method, at the second stage, repeat the non-parametric regression but on the transformed dataset { m^ ( x_i , Y_i )}, taking the estimator at x to be this second stage estimator at m^ ( x ). In the second, and more appealing, method, again perform non-parametric regression on { m^ ( x_i , Y_i )}, but this time make the kernel weights depend on the original x scale rather than using the m^ ( x ) scale. We concentrate more of our effort in this paper on the latter because of its advantages over the former. Our emphasis is largely theoretical, but we also show that the latter method has practical potential through some simulated examples.     

Relative error prediction via kernel regression smoothers

In this article, we introduce and study local constant and local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of the ratio of conditional expectations of two functions of the response variable. We also provide a good bandwidth selection method for the estimators. Examples of application, limited simulation results and discussion of related problems and approaches are also given.     

A Bayesian approach for improved pavement performance prediction

We present a method for predicting future pavement distresses such as longitudinal cracking. These predicted distress values are used to plan road repairs. Large inherent variability in measured cracking and an extremely small number of observations are the nature of the pavement cracking data, which calls for a parametric Bayesian approach. We model theoretical pavement distress with a sigmoidal equation with coefficients based on prior engineering knowledge. We show that a Bayesian formulation akin to Kalman filtering gives sensible predictions and provides defendable uncertainty statements for predictions. The method is demonstrated on data collected by the Texas Transportation Institute at several sites in Texas. The predictions behave in a reasonable and statistically valid manner.     

Goodness-of-fit test for uniform stochastic ordering among several distributions

The likelihood-ratio test (LRT) is considered as a goodness-of-fit test for the null hypothesis that several distribution functions are uniformly stochastically ordered. Under the null hypothesis, H₁ : F₁ ? F₂ ?···? F_N, the asymptotic distribution of the LRT statistic is a convolution of several chi-bar-square distributions each of which depends upon the location parameter. The least-favourable parameter configuration for the LRT is not unique. It can be two different types and depends on the number of distributions, the number of intervals and the significance level α. This testing method is illustrated with a data set of survival times of five groups of male fruit flies.