PPS Sampling Research Articles

How does chronic disease influence subjective life expectancy among middle-aged and older adults? Evidence from the China Health and Retirement Longitudinal Study (CHARLS) 2018 cross-sectional data.

Chronic diseases have become one of the most important factors threatening human health. Subjective life expectancy (SLE) describes an individual's expectation or subjective perception of lifespan. This article aims to explore the relationship between chronic diseases and SLE, as well as the differences among different age groups and different types of chronic diseases in this relationship. China Health and Retirement Longitudinal Study (CHARLS) is a nationwide longitudinal study that evaluates the social, economic, and health conditions of middle-aged and older adult families and individuals aged 45 and above in China. In this study, CHARLS used probability proportional to size sampling (PPS sampling) to ensure the breadth and representativeness of the sample. This study selected cross-sectional data from CHARLS 2018, removed missing values, and obtained a valid sample of 10,658 middle-aged and older individuals, of whom 8564 had chronic diseases. After controlling demographic, health behavior, socioeconomic, psychological, and social security factors, an ordered logistic regression was performed to explore the relationship between chronic disease and SLE in middle-aged and older adults. The results show that chronic diseases negatively correlate with SLE in middle-aged and older adults. Middle-aged and older adults with chronic diseases are 36.2% less likely to have high life expectancy than those without chronic diseases. Many different types of chronic diseases are negatively correlated with SLE. Cancer is most negatively correlated with SLE, far exceeding other chronic diseases. Chronic disease and SLE of middle-aged and older adults have age-heterogeneous differences. For middle-aged people aged 45-59 and young older adults aged 60-79, there is a significant correlation between chronic diseases and SLE. However, there is no correlation between chronic diseases and subjective life expectancy in the older population aged 80 and above. The government and society should pay close attention to the prevention and treatment of chronic diseases among middle-aged and older adults and adjust policies and measures according to the population's age structure. In addition, the government and society should pay attention to the spiritual needs of middle-aged and older adults. The government and society should pay more attention to cancer patients. Finally, the scientific research team should also strengthen research on chronic diseases, research and development of specific drugs and vaccines, improve the cure rate of chronic diseases, promote people's health, and make people no longer afraid of diseases.

Female university students’ fertility intentions and their psychosocial factors

BackgroundRaising the birth rate can effectively increase the resulting labour supply and minimise the adverse impact of an ageing population on high-quality economic development since the demographic dividend is rapidly declining. The Chinese government has a “three-child” policy in place, yet the fertility rate is still falling. This study intends to investigate the present fertility intentions of female university students and assess the extent to which feminism has affected their intentions. It will next investigate the degree to which and the mechanisms by which the psychosocial factors have an impact on those intentions.MethodsA cross-sectional survey of female university students was conducted in Nanjing, China, from February to March 2023. To assure the representativeness of the sample, a technique of stratified proportional sampling, PPS sampling, and convenience sampling was utilized. A total of 1124 valid samples were acquired from female university students in 15 comprehensive universities. The data were mined and analysed by SPSS (version 24.0) and AMOS (version 24.0) software.ResultsOverall female university students’ fertility intentions are low at this stage, with more than half (53.55%) of them having no clear desire to have children. The level of feminist identity significantly negatively affected the Intensity of desire to have children (-0.32) and child-number desires (-0.7). Psychosocial factors had a greater degree of influence on fertility intentions. The direct effect of the level of feminist identity and the perception of fertility hindrances on childbearing desires was -0.63 and -0.50 respectively, and the direct effect of the perception of fertility supports on childbearing intentions was 0.79.ConclusionThe level of feminist identity is significantly and negatively related to childbearing desires. Psychosocial factors have a greater degree of influence on fertility intentions, with the level of feminist identity, the perception of fertility hindrances and the perception of fertility supports all significantly impacting fertility intentions. The findings of this study emphasise the importance of the government providing a full range of social security and employers providing better employee benefits to promote a fertility-friendly society.

Factors associated with dietary and exercise compliance among elderly with chronic conditions of hypertension and type 2 diabetes mellitus residing in rural areas of coastal Karnataka: A community-based cross-sectional study.

Compliance with diet, exercise regimen, and medication is vital to maintain an acceptable range of blood pressure and glycemic level among elderly with hypertension and diabetes mellitus. However, these are considered to be more challenging tasks among elderly. The aim of this study is to identify dietary and exercise compliance among elderly with hypertension and type 2 diabetes mellitus and to find its influencing factors. The community-based survey was done in rural areas of five randomly selected clusters of primary health centers (PHC) using PPS sampling technique. After ethical clearance, a total of 360 consented participants residing in selected clusters were interviewed using pre-designed rating scale and questionnaire on dietary and exercise compliance, respectively. In this study, compliance refers to practicing prescribed diet and exercise regimen regularly by the elderly with HTN and T2DM. The data were analyzed using SPSS version 16.0. Eighty percent (n = 287) of study participants had moderate adherence to diet and only, 37.8% (n = 136) of them practice physical exercise. A Chi-square test report confirmed that there is a significant association (P < 0.05) between dietary compliance and level of education, occupation, family income, procurement of insurance, poor memory, multiple functional impairments, duration of hypertensive, and diabetes illness. Exercise compliance is influenced by factors such as gender, level of education, family income, and procurement of insurance (P < 0.05). Adherence to diet and exercise among elderly with chronic conditions are influenced by various socio-demographic or environmental, poor health or physiological and cognition or psychological factors.

Improved family of estimators for the population mean using supplementary variables under PPS sampling.

In this article, we suggest an enhanced family of estimators for estimation of population mean employing the supplementary variables under probability proportional to size sampling. Up to the first order of approximation, numerical formulations of the bias and mean square error of estimators are obtained. From our suggested improved family of estimators, we give sixteen different members. The recommended family of estimators has specifically been used to derive the characteristics of sixteen estimators based on the known population parameters of the study as well as auxiliary variables. The performances of the suggested estimators have been assessed using three actual data. Furthermore, a simulation investigation is also accompanied to evaluate the effectiveness of estimators. The proposed estimators have a smaller MSE and an advanced PRE when linked to existing estimators, which are based on actual data sets and simulation studies. Theoretically and empirically studies also reveal that the suggested estimators accomplish well than the usual estimators.

Prevalence of tobacco dependence among rural population of Mysuru District

Background: Tobacco is generally a leaf with 1-3% of the alkaloid nicotine Consuming it becomes so dangerous that it is the leading cause of mortality worldwide. Tobacco risks include heart attack, gum disease and pre-cancerous mouth lesions etc. The purpose of the current study is to investigate the prevalence of Tobacco dependence and factors that contribute to tobacco dependence among rural populations. Objectives of current study was to estimate the prevalence of tobacco dependence and to assess the factors influencing Tobacco dependence among rural population. Methods: A community based cross sectional study was carried out in rural areas of Nanjangud taluk for 6months from January 2022 to June 2022. Multistage sampling Technique was adopted to select the study population.one subcentre is selected randomly by lottery method, PPS sampling technique will be applied to select the required number of participants from the villages in the selected subcentre. Sample size is 362 individuals aged above 18years who comes under ICD10 criteria were included in the study. The data were gathered using the pre-tested, semi-structured questionnaire by interview method, and the FRAGESTROM test to assess dependence on nicotine SPSS version 25 was used for analysis. Results: The overall prevalence of Tobacco dependence among rural population of Nanjangud taluk is 62.40%. We found that tobacco dependence was significantly associated with gender, age group, occupation education, and socioeconomic status and there is no significant association between caste and Tobacco dependence. Conclusions: The present study concludes that the prevalence of tobacco dependence is high in a rural population. More tobacco free initiatives to be implemented.

The impact of education level on marital satisfaction: Evidence from China

Marriage is an extremely important part of an individual's life cycle, and marital satisfaction is an important indicator of life happiness. Using the data of China Family Panel Studies (CFPS) in 2018 based on PPS sampling method, this paper studies the impact of education level on marital satisfaction and its mechanism. The baseline regression results show that education level has a significant positive impact on marital satisfaction. The effect remains significant after addressing endogeneity with instrumental variable and CMP method. Mechanism analysis shows that education level can affect marital satisfaction through income mechanism, spiritual abundance mechanism and spousal age gap mechanism. In addition, the effect of education level varies according to gender, age and the places of residence. Improving the development level of educational, breaking the shackles of ideology and economic conditions, and actively serving all families from the community will help improve marital satisfaction and promote social harmony. This paper provides new evidence to identify the causal relationship between education level and marital satisfaction, and can enrich the literature related to the well-being of married people.

The Relationship between Physical Activity and Depressive Symptoms in Middle-Aged and Elderly People Controlling for Demographic and Health Status Variables

Objective: To explore the relationship between physical activity intensity and depressive symptoms in Chinese middle-aged and elderly people, and to provide new evidence for the prevention and treatment of depression by physical activity. Methods: The data came from the 2018 China Health and Retirement Longitudinal Study. Using the PPS sampling method, a baseline survey was conducted among middle-aged and elderly people over the age of 45 across the country to investigate their demographics, health status, economic status, and other information. A total of 6128 people with complete information on depression and physical activity were included in the analysis. The Z-test, analysis of covariance, and logistic regression were performed on the data using SPSS 27.0 software. Results: In terms of depressive symptoms, the proportion of detected depressive symptoms was 33.6% and the proportion of no depressive symptoms was 69.4%, and the prevalence of males was higher than that of females. Participants with high physical activity accounted for 50.9%, participants with low physical activity accounted for 49.1%, and the physical activity of males was significantly higher than that of females. There was a significant relationship between physical activity and depressive symptoms in middle-aged and elderly people (p &lt; 0.05), and after adjusting for demographic variables (location of residence, education level, gender, age, and widowed or not), health status characteristics and living habits (diabetes and disability), self-rated health status, hypertension, stroke, hyperlipidemia, arthritis, and walking 1 km, the association between physical activity and depressive symptoms remained statistically significant (p &lt; 0.05). Conclusion: The proportion of Chinese middle-aged and elderly men suffering from depressive symptoms was slightly higher than that of women, and middle-aged and elderly people with high physical activity had a lower risk of developing depressive symptoms. Attention should be paid to middle-aged and elderly people who are older, have poor self-assessed health status, have disabilities, have high blood pressure, have arthritis, have low physical activity and cannot walk one kilometer, and have low physical activity. Scientific and effective exercise prescriptions should be explored to prevent and improve depressive symptoms in middle-aged and elderly people.

Estimation of population mean under probability proportional to size sampling with and without measurement errors

AbstractThis research paper deals with the problem of estimating population mean of study variable using information of auxiliary variable under varying probability and measurement error. Motivated by Kadilar and Cingi, App Math Lett, 2006, 19, 75 and Zaman, Stat Trans‐New Ser, 2020, 21, 159, generalized ratio and product enhanced regressed exponential (ERE) estimators are proposed to estimate the population mean using different auxiliary parameters under the sampling of probability proportional to size (pps) and extended for the case of measurement error. Further, following the strategies of Naik and Gupta, J Ind Soc Agr Stat, 1996, 48, 151; Jhajj et al., Pak J Stat, 2006, 23, 1; Singh et al., Auxiliary Information and A Priori Values in Construction of Improved Estimators, Renaissance High Press, 2007; and Solanki and Singh, Chil J Stat, 2013, 4, 3, conventional ratio, product, regression, generalized and many other types of estimators have been adopted under pps sampling with and without measurement error. Up to the first order of large sample approximation, the bias and mean square error (MSE) of the suggested ERE and adopted estimators are derived and their properties have been studied. Comparisons have been made theoretically and empirically to comprehend the merits of recommended estimators over the conventional and adopted estimators.

Assessment of iodine deficiency disorder among school going children aged 5-10 years in Sagar district of Madhya Pradesh: an observational cross sectional study

Background: Iodine deficiency (IDD) is the world’s most prevalent cause of brain damage. glaciations, flooding, rivers lead to deficiency of iodine in crops grown on iodine. Diet low in iodine can result in stillbirth and abortions and many more sequelae. Objectives of the research work were to study the prevalence of IDD amongst 6-12 years children by clinical examination and to determine the concentration of iodine in salt sample at consumer level. Also, to determine the urinary iodine excretion amongst 6-12 years age group children.Methods: It was a cross sectional study conducted in the government schools of Sagar district among school children of 6-12 years of age. Total 2700 school children from 30 villages were included using PPS sampling. Students were clinically examined and their urine samples were taken for MUIC estimation.Results: Prevalence of goiter was more in 10 to 11 years of age (14.07%) and less in 8 to 9 years age group (7.59%). Overall prevalence of goiter in district Sagar is 10.51%.Conclusions: Despite NIDDCP, there is still dearth of awareness among general public about the usage and storage of iodized salt which is the root cause of Iodine deficiency.

Establishment and development of national community-based collaborative innovation demonstration areas to achieve the control target of hepatitis B in China

BackgroundThe major infectious diseases of hepatitis B has constituted an acute public health challenge in China. An effective and affordable HBV control model is urgently needed. A national project of Community-based Collaborative Innovation HBV (CCI-HBV) demonstration areas has optimized the existing community healthcare resources and obtained initial results in HBV control.MethodsBased on the existing community healthcare network, CCI-HBV project combined the community health management and health contract signing service for long-staying residents in hepatitis B screening. Moreover, HBV field research strategy was popularized in CCI-HBV areas. After screening, patients with seropositive results were enrolled in corresponding cohorts and received treatment at an early stage. And the uninfected people received medical supports including health education through new media, behavior intervention and HBV vaccinations. In this process, a cloud-based National Information Platform (NIP) was established to collect and store residents’ epidemiological data. In addition, a special quality control team was set up for CCI project.ResultsAfter two rounds of screening, HBsAg positive rate dropped from 5.05% (with 5,173,003 people screened) to 4.57% (with 3,819,675 people screened), while the rate of new HBV infections was 0.28 per 100 person-years in the fixed cohorts of 2,584,322 people. The quality control team completed PPS sampling simultaneously and established the serum sample database with 2,800,000 serum samples for unified testing.ConclusionsCCI-HBV project has established a large-scale field research to conduct whole-population screening and intervention. We analyzed the HBsAg prevalence and new infection rate of HBV in the fixed population for the epidemic trend and intervention effect. The purpose of CCI-HBV project is to establish and evaluate a practical model of grid management and field strategy, to realize the new goal to control hepatitis B in China. To provide policymakers with a feasible model, our results are directly applicable.Trial registrationThe project was funded by the Major Projects of Science Research for the 11th and 12th five-year plans of China, entitled “The prevention and control of AIDS, viral hepatitis and other major infectious diseases”, Grant Nos. 2009ZX10004901, 2011ZX10004901, 2013ZX10004904, 2014ZX10004007 and 2014ZX10004008.

Analysis of Chinese citizens' traditional Chinese medicine health culture literacy level and its influence factors in 2017

To analyze the TCM health culture level and influence factors of Chinese citizens in 2017. PPS sampling combined with random sampling was used to select the residents aged between 15-69 years old in 30 provinces as the respondents,and a questionnaire study was conducted to investigate their TCM health culture level. In 2017,there were 87 287 valid questionnaires for Chinese citizens' TCM health culture level,including 48. 25% male and 51. 75% female,with a sex ratio of 1 ∶ 1. 073. In 2017,the overall TCM health culture level was 13. 39%,specifically 18. 77% for the urban areas and 10. 51% for the rural areas. Compared with people who were illiterate or less literate,people with an educational background of elementary school,junior high school,high school/vocational/technical school and junior college/university had a higher TCM health culture level,and the OR values were 1. 584( 95% CI[1. 166,2. 152]),2. 827( 95%CI[1. 839,4. 345]),5. 651( 95%CI[3. 637,8. 781]),9. 785( 95%CI[6. 187,15. 477]) in order. With civil servants as the reference,medical workers had a higher TCM health culture level( OR = 1. 829,95%CI[1. 279,2. 616]),while farmers had the lowest TCM health culture level( OR = 0. 493,95% CI[0. 349,0. 697]). Compared with people with the annual household income per capita of 20 000 yuan and below,people with the annual household income per capita between 20 000-50 000,50 000-80 000,80 000 yuan or above had a higher TCM health culture level,and the OR values were 1. 176( 95% CI[0. 963,1. 437]),1. 458( 95%CI[1. 168,1. 820]) and 1. 930( 95%CI[1. 509,2. 469]). Based on the differences between urban and rural areas,the influence factors of citizens' TCM health culture level include education,occupation and income.

Analysis of knowledge acquisition behavior of traditional Chinese medicine based on internet

The study aims at understanding the situation of Chinese residents' access to Chinese medicine health culture knowledge through the Internet and analyze its influencing factors. A multi-stage PPS sampling method was used to collect 90 720 people for questionnaire survey. The survey found thatthe probability of Chinese residents accessing Chinese medicine health culture knowledge through the Internet was 54.7%. The females(with the males as reference, OR=1.076, 95% CI 1.018-1.137) and central population(with the east as reference, OR=1.235, 95% CI 1.048-1.456), people with Chinese medicine health culture literacy(with the people who do not have Chinese medicine health culture literacy as reference, OR=2.363, 95% CI 1.976-2.827) had a higher probability of acquiring Chinese medicine health culture knowledge through the Internet. Referring to people who were illiterate or less literate,the OR values of people who went to elementary school, junior school, high school/vocational/technical school and junior college/university was 2.396(95% CI 2.062-2.784),4.481(95% CI 3.751-5.352), 6.687(95% CI 5.541-8.07),and 9.109(95% CI 7.385-11.235). The higher the age, the lower the probability of acquiring Chinese medicine health culture knowledge through the Internet. Taking civil servants as a reference, teachers, students, farmers, and workers had a low probability of acquiring Chinese medicine health culture knowledge through the Internet. The OR values was 0.736(95% CI 0.548-0.988),0.609(95% CI 0.449-0.826), 0.424(95% CI 0.325-0.554),and 0.707(95% CI 0.539-0.927). Regions, gender, age, education level, occupation, and possession of Chinese medicine health culture literacy are factors influencing whether residents obtain Chinese medicine health culture knowledge through the Internet.

Homogeneous Imputation under Two Phase Probability Proportional to Size Sampling

In this paper, we consider the problem of missing complete at random (MCAR) values in two-phase probability proportional to size ( pps) sampling for the estimation of population mean. For comprehensive examination of missing values, we discuss four possible situations for the occurrence of non-response. A class of estimators is considered by using an unknown constant with the traditional estimators for imputing the missing values. Theoretically, bias and mean squared errors of the proposed estimators are obtained up to the first order approximation. Two numerical studies are carried out for the relative comparison of the proposed estimators with mean estimator under two-phase ppssampling for each of the predefined situation.

3단계 무관질문모형에 의한 드문 민감한 속성의 확률비례 추정

최근 Land et al.(2011)은 무관질문모형을 활용하여 드문 민감한 속성(rare sensitive attributes)을 가지고 있는 사람들의 수 평균을 추정하는 방법으로 포아송분포를 이용하는 방안을 제안하였다. 그들은 드문 민감한 속성과 드문 무관한 속성을 이용하여 드문 민감한 속성에 대한 정보를 얻어내고 있다. 본 연구에서는 조사하고자 하는 내용이 매우 민감하고 모집단이 크기가 서로 차이가 있는 집락으로 구성되어 있을 때, 집락의 크기를 고려하여 추출확률을 부여하는 확률비례추출법을 Land et al.(2011)이 사용한 무관질문모형 대신에 3단계 무관질문모형에 적용하여 드문 민감한 속성을 효율적으로 추정하는 방법을 제안하였다. 드문 무관한 속성의 모비율을 알 때, 확률비례 추출 및 등확률 2단계 추출법을 적용하여 드문 민감한 속성에 대한 추정량과 그 분산 및 분산추정량을 구하였다. 그리고 확률비례 복원추출법과 확률비례 비복원추출법에 의해 얻어진 드문 민감한 속성의 추정량과 등확률 2단계 추출법에 의해 얻어진 드문 민감한 속성의 추정량간의 효율성을 비교하였다. 그 결과 집락의 크기가 서로 차이가 있을 때는 확률비례복원추출에 의한 추정이 등확률 복원 2단계 추출에 의한 추정보다 효율이 높아짐을 확인할 수 있었다.Land et al. (2011) have suggested a method to estimate the mean number of persons possessing a rare sensitive attribute by utilizing the Poisson distribution in survey sampling. They obtain information about a rare sensitive attribute through unrelated question randomized response model which is made of a rare sensitive and unrelated attribute. In this paper, we suggest an efficient method of estimating a rare sensitive attribute by using three-stage unrelated randomized response model instead of the Land et al.’s model (2011) when the population consists of some different sized clusters and clusters are selected by probability proportional to size (pps) sampling. Under the assumption that the parameter of a rare unrelated attribute is known, we estimate the parameter of a rare sensitive attribute and it’s variance and variance estimator. We compare the efficiency of our suggested pps estimation method with equal probability two-stage sampling method and ascertain that the estimation by pps with replacement is more efficiency than equal probability two-stage sampling with replacement.

Improved estimator of population total in PPS sampling

ABSTRACTIn this paper, we have considered an estimation of the population total Y of the study variable y, making use of information on an auxiliary variable x. A class of estimators for the population total Y using transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usual PPS estimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given.

Estimation of the proportion of a sensitive attribute based on a two-stage randomized response model with stratified unequal probability sampling

To estimate the proportion of a sensitive attribute of the population that is composed of the number of different sized clusters, we suggest a two-stage randomized response model with unequal probability sampling by using Abdelfatah et al.’s procedure [Braz. J. Probab. Stat. 27 (2013) 608–617]. We compute the estimate of the sensitive parameter, its variance, and the variance estimator for both pps sampling and two-stage equal probability sampling. We extend our model to the case of stratified unequal probability sampling and compute them. Finally, we compare the efficiency of the two estimators, one obtained by unequal probability sampling and the other by stratified unequal probability sampling.

The Micronutrient Status of Children Aged 24–60 Months Living in Rural Disaster Areas One Year after the Wenchuan Earthquake

ObjectiveIn order to evaluate micronutrient status of children aged 24–60 months living in rural disaster areas after one year of the earthquake in Wenchuan.DesignAfter one year of Wenchuan Earthquake, using PPS sampling methods, a total of 270 children from six-randomized townships near seismic center, in each township sample size consisted of 30 to 50 children, were sampled for evaluating Z-score of children's growth status, anemia prevalence, vitamin A, vitamin D, vitamin B12, folic acid status. Final sample consisted of 152 boys and 118 girls, and blood samples were drawn from 206 children.ResultsThe stunting (HAZ<2SD) and wasting (WHZ<2SD) were respectively 14.7% and 0.7%. Prevalence of anemia was 17.3% and percentage of iron deficiency was 45.7%. The prevalence of vitamin A deficiency and marginal deficiency was 15.4% and 30.3%, respectively. The sum of vitamin D deficiency and marginal deficiency was near 90%. Percentages of Zinc deficiency including marginal and deficiency were 65.5%. Percentages of vitamin B12 marginal and deficiency were 8.6% and 10.6% and the prevalence of marginal deficiency was significantly higher in boys than in girls. Folic acid deficiency was not found in surveyed children using serum folic acid level <16.9 ng/ml.ConclusionIn areas affected by Earthquake, preschool children had higher stunting prevalence and a relatively higher prevalence suffered from micronutrient deficiencies, including iron-deficiency anemia, and deficiencies of iron, zinc, vitamin A and vitamin B12.

An efficient non-rejective implementation of the πps sampling designs

Poisson sampling is a method for unequal probabilities sampling with random sample size. There exist several implementations of the Poisson sampling design, with fixed sample size, which almost all are rejective methods, that is, the sample is not always accepted. Thus, the existing methods can be time-consuming or even infeasible in some situations. In this paper, a fast and non-rejective method, which is efficient even for large populations, is proposed and studied. The method is a new design for selecting a sample of fixed size with unequal inclusion probabilities. For the population of large size, the proposed design is very close to the strict πps sampling which is similar to the conditional Poisson (CP) sampling design, but the implementation of the design is much more efficient than the CP sampling. And the inclusion probabilities can be calculated recursively.

Negative Dependence in Sampling

Abstract. The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that and are two families of 0‐1 random variables that satisfy the strong Rayleigh property and let . We show that {Zi} conditioned on is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea &amp; Brändén (Invent. Math., 177, 2009, 521–569). This entails that a number of important πps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.

Algorithms to find exact inclusion probabilities for 2Pπps sampling designs

The statistical literature contains several proposals for methods generating fixed-size without-replacement πps sampling designs. πps designs with fixed size have rarely been used due to difficulties with implementation. Recently, a new method was proposed viz. the 2Pπps design using a two-phase approach. It was shown that the first-order inclusion probabilities of the 2Pπps design are asymptotically equal to the target inclusion probabilities of a πps design.