On efficient estimators of the proportion of true null hypotheses in a multiple testing setup

We consider the problem of estimating the proportion $\theta$ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval $[0,1]$ with prior probability $\theta$ and a nonparametric density $f$. We discuss asymptotic efficiency results and establish that two different cases occur whether $f$ vanishes on a set with non null Lebesgue measure or not. In the first case, we exhibit estimators converging at parametric rate, compute the optimal asymptotic variance and conjecture that no estimator is asymptotically efficient (i.e. attains the optimal asymptotic variance). In the second case, we prove that the quadratic risk of any estimator does not converge at parametric rate. We illustrate those results on simulated data

Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation

In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of $p$-values under the null hypothesis and the other component $f$ is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component $f$ in the mixture, relying on a preliminary estimator of the unknown proportion $\theta$ of true null hypotheses. We propose and study the asymptotic properties of two different estimators for this unknown component. The first estimator is a randomly weighted kernel estimator. We establish an upper bound for its pointwise quadratic risk, exhibiting the classical nonparametric rate of convergence over a class of H\"older densities. To our knowledge, this is the first result establishing convergence as well as corresponding rate for the estimation of the unknown component in this nonparametric mixture. The second estimator is a maximum smoothed likelihood estimator. It is computed through an iterative algorithm, for which we establish a descent property. In addition, these estimators are used in a multiple testing procedure in order to estimate the local false discovery rate. Their respective performances are then compared on synthetic data

RAGLAI ETHNIC GROUP’S LIFESTYLE IN KHANH HOA PROVINCE, VIETNAM

Lifestyle is seen as a human product; however, it plays a huge role in helping human define their goals, create motivations, form personality and establish ethical behavior patterns in harmony with ethics, customs and trends of the times, all of which are to ensure a stable and developing community. Raglai ethnic group is one of 54 ethnic groups in Vietnam, which has been distributed mainly in several provinces, mostly in Khanh Hoa province. The goal of the article is to clarify some issues such as views on lifestyle; a profile of the Raglai ethnic group in Khanh Hoa province, and a study about the Raglai people's lifestyles. In order to accomplish our goals, we use several research methods namely analysis, synthesis; logic and history, field trip and interview. Article visualizations

THE IMPACT OF INTEGRATION PROCESS ON NATIONAL CULTURAL IDENTITY

The integration process has brought certain advantages in all fields in general as well as in cultural field in particular. Besides, the influence of foreign culture tends to push back traditional cultural values. To overcome those challenges, it is essential to preserve and promote the traditional cultural values of Vietnam in the integration process. Thus, those issues that have been posed for upholding the traditional values of Vietnam can be solved by some solutions such as: Promoting the role of Vietnamese people in preserving the traditional cultural values in Vietnam today; Further enhancing the management role of authorities at all levels in perpetuating and stimulating the traditional cultural values in the integration process; Ensuring infrastructure for preserving traditional cultural values; Further strengthening the role of the law in administration of traditional culture to adapt to the new situation. Article visualizations

Policy for developing the cultural tourism industry in Vietnam

Cultural tourism not only attracts international tourists to explore and experience Vietnam's unique culture but also contributes to creating an important source of income for the national economy. Vietnam has a diverse history and culture, expressed through architecture, art, culinary culture, and many unique traditions. Destinations such as Hue, Hoi An, Sapa, Hanoi, and Saigon are not only places where visitors can learn about Vietnam's history and culture but also experience the unique traditions and cultural beauty in each region. In particular, combining cultural tourism with cultural heritage conservation and sustainable development is an important trend. This includes building aesthetically pleasing tourist areas that do not harm the environment and local culture. The emphasis on preserving and honoring classical cultural values is also an important part of cultural tourism. Thus, cultural tourism is not only a source of cultural value and helps promote the country's image but also positively contributes to the economic development and preservation of Vietnam's cultural heritage. Cultural tourism will continue to play an important role in promoting the sustainable development and sublimation of Vietnamese culture in the future