novel empirical likelihood test approach is proposed, and under the null hypothesis it is shown to follow asymptotically a

chi-square distribution. Finally, simulation studies and a real data example are conducted to illustrate the performance of

the proposed method.]]>

P_new^a(u_a)=∫_0^∞ ∫_0^∞ ψ^ab(u_a;v_a,v_b) P_old^a(v_a) P_old^b(v_b) dv_a dv_b, a,b = 1 or 2

The mechanical proof of the Maxwell-Boltzmann speed distribution presented in this paper reveals the unsolved mechanical mystery of the Maxwell-Boltzmann speed distribution since it was proposed by Maxwell in 1860. Also, since the validation is carried out in an analytical approach, it proves that there is no theoretical limitation of mass ratio to the Maxwell-Boltzmann speed distribution. This provides a foundation and methodology for analyzing the interaction between particles with an extreme mass ratio, such as gases and neutrinos.

]]>A total of 14,495 and 33,419 records were extracted for men and women respectively from the 2016-2017 Multiple Indicator Cluster Survey (MICS) in Nigeria. The outcome variable was ATDV. The study framework described the role of education on ATDV in the light of demographic characteristics, socioeconomic profile, and lifestyle. Selection bias was checked among the levels of education using the multinomial logit regression. Propensity scores (PS) and PS weights were generated for the treatment variable and average treatment effects (ATE) of ATDV were estimated using logistic regression that combined regression adjustment and inverse-probability weight. Descriptive statistics, odds ratios and 95%CI were presented.

The mean age of men and women were 30.8±10.2 years and 29±9.4 years respectively. About 22% men and 35% women justified domestic violence (DV) respectively. Selection bias was found between the covariates and level of education (p<0.05). PSM effectively corrected the selection bias (SD diff ≈ 0, Variance ratio ≈ 1). Men (AOR = 0.84, 95% CI: 0.78, 0.92) and women (AOR=0.94, 95%CI: 0.80, 2.22) who have attained tertiary level of education were less likely to justify DV in comparison to their uneducated counterparts.

Tertiary education was protective for ATDV among men and women. The use of PSM effectively controlled for selection bias in estimating the effect of education on ATDV. PSM will enable researchers make causal inference from non-experimental/cross-sectional studies in situations where randomized control trials are not feasible.

]]>