In this paper we study the ideal variable bandwidth kernel density estimator introduced by McKay [9,10] and Jones et al. [7] and the plug-in practical version of the variable bandwidth kernel estimator with two sequences of bandwidths as in Giné and Sang [4]. Based on the bias and variance analysis of the ideal and true variable bandwidth kernel density estimators, we study the central limit theorems for each of them.MSC 2010 subject classification: 62G07, 62E20, 62H12, 60F05 Key words and phrases: central limit theorem, variable bandwidth kernel density estimation.
Background Intimate partner violence (IPV) is physical, sexual, or psychological harm perpetrated by a spouse or an intimate partner. Its detrimental effects on women’s physical, mental, sexual, and reproductive health are well-documented. However, its impact on nutritional status is not well-studied, and previous studies have led to contradictory findings. This study aimed to explore the association between intimate partner violence and the nutritional status of married Nepalese women. Methods The study used the 2016 Nepal Demographic Health Survey data, which employed a modified version of the Conflict Tactics Scale to determine women’s exposure to IPV. Anemia and low body mass index (BMI) were used as proxies of nutritional status. Multinomial regression was used to analyze the relationship between BMI and IPV; multivariable logistic regression was used to analyze the association between anemia and IPV. Results The prevalence of underweight, overweight/obesity, and anemia were respectively 13.9%, 25.1%, and 38.7%. The prevalence of physical, sexual, and emotional IPVs experienced in the preceding year were respectively 9.8%, 4.6%, and 7.6%. Likewise, the prevalence of lifetime physical, sexual, emotional, and controlling behavior IPVs were respectively 21.8%, 7.4%, 12.3%, and 32.1%. The low intensity of emotional IPV (AOR 1.62; CI: 1.02–2.56) and moderate intensity of physical IPV (AOR 3.70; CI: 1.64–8.35) experienced in the preceding year, and low intensity of lifetime emotional IPV (AOR 1.69; CI: 1.11–2.58) were associated with an increased risk of overweight/obesity. Moderate intensity of sexual IPV (AOR 2.59; CI: 1.099–6.108) experienced in the preceding year was associated with an increased risk of underweight BMI. The low intensity of lifetime controlling behavior (AOR1.25; CI: 1.03–1.53) was associated with an increased risk of anemia. Conclusions Emotional and Physical IPVs are significantly associated with an increased risk of overweight/obesity. Sexual IPV is significantly associated with an increased risk of underweight BMI, and controlling behavior is significantly associated with an increased risk of anemia. Seeking help could offset the detrimental effects of IPV; therefore, IPV screening should be a part of regular healthcare assessment for married women, and appropriate rehabilitation should be offered to IPV survivors.
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