Confidence intervals for finite difference solutions

Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.     

Generalized anticipated backward stochastic differential equations driven by Brownian motion and continuous increasing process*

This article mainly considers a new class of anticipated BSDEs driven by Brownian motion and continuous increasing process, which are called generalized anticipated backward stochastic differential equations(GABSDEs). We first give the form of GABSDEs. Then, existence and uniqueness result for GABSDEs is established as well as a comparison theorem is obtained under the certain assumptions. At last, we give an application about the duality between SDDEs and GABSDEs.     

Quickly variable selection for varying coefficient models with missing response at random

This paper focuses on the variable selections for a varying coefficient models with missing response at random. A procedure is presented by basis function approximations with smooth-threshold estimating equations. Furthermore, the proposed method selects significant variables and estimates coefficients simultaneously avoiding the problem of solving a convex optimization, which reduced the burden of computation. Compared to existing equation based approaches, our procedure is more efficient and quick. With proper choices the regularization parameter, the resulting estimates perform an oracle property. A cross-validation for tuning parameter selection is also proposed, a numerical study confirms the performance of the proposed method.     

Performance of the stein-type two-parameter estimator in multiple linear regression model

In this article, we consider the Stein-type approach to the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The Stein-type two-parameter estimator is proposed when it is suspected that the regression parameter may be restricted to a subspace. The bias and the quadratic risk of the proposed estimator are derived and compared with the two-parameter estimator (TPE), the restricted TPE and the preliminary test TPE. The conditions of superiority of the proposed estimator are obtained. Finally, a real data example is provided to illustrate some of the theoretical results.     

Comparisons of several Pareto distributions based on record values

In order to avoid wrong conclusions in any further analysis, it is of importance to conduct a formal comparison for characteristic quantities of the distributions. These characteristic quantities we are familiar with include mean, quantity and reliability function, and so on. In this paper, we consider two tests aiming at the comparisons for function of parameters in Pareto distribution based on record values. They are generalized p-value-based test and parametric bootstrap-based test, respectively. The resulting procedures are easy to compute and are applicable to small samples. A simulation study is conducted to investigate and compare the performance of the proposed tests. A phenomenon we note is that generalized p-value-based test almost uniformly outperforms the parametric bootstrap-based test.     

Performance of the difference-based Liu-type estimator in partially linear model

This paper discusses the parameter estimation in a partially linear model. We proposed a difference-based Liu-type estimator of the unknown parameters in the partially linear model. The asymptotically properties of the proposed estimator are discussed. We propose a iterative method to choose the biasing parameters. Finally, a simulation study and a numerical example are presented to explain the performance of the estimators.     

Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors

In this paper, the strong laws of large numbers for partial sums and weighted sums of negatively superadditive-dependent (NSD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type strong law of large numbers. Using these strong laws of large numbers, we further investigate the strong consistency and weak consistency of the LS estimators in the EV regression model with NSD errors, which generalize and improve the corresponding ones for negatively associated random variables. Finally, a simulation is carried out to study the numerical performance of the strong consistency result that we established.     

The Development and Initial Validation of a Psychoanalysis Use/Non-Use Scale among a Sample of Hong Kong Helping Professionals.

ABSTRACT

This article reports on the construction and initial validation of the Psychoanalysis Use/Non-Use scale (PUNU) and the complementary Conflicts with Hong Kong Chinese Culture scale (CHKCC), developed for assessing the penetration of psychoanalysis among counseling professionals in Hong Kong. A total of 217 Hong Kong social workers, psychologists, and counselors were surveyed to assess the scales' internal psychometric properties. Factor analysis confirmed a four-factor structure for the PUNU, and a unidimensional structure for the CHKCC, with 17 and 9 items, respectively. Internal reliability of both scales was good and discriminative validity was supported by comparisons with background information. These scales could help to identify factors that affect the understanding of psychoanalysis among professionals and could be useful for educational purposes.