THE CASE FOR PARITY AND BIRTH-ORDER STATISTICS

Parity refers to the number of (live) births that a woman (or man) has had. Birth order refers to whether a birth is the first, second, third or higher‐order birth of the parent. In the context of low and shifting fertility, parity and birth‐order statistics are becoming increasingly important for understanding fertility trends and patterns, for policy, and for carrying out projections of future fertility. In Australia, the main sources of demographic data are birth, death and marriage registers, and the five‐yearly national census. Both the birth registers and the census are ideally placed to collect data required to calculate parity and birth‐order statistics. However not all Australian states and territories collect or code the necessary information in the birth registers, and the parity question ‘For each female, how many babies has she ever had?’ is only asked every second census; that is, once every 10 years. In this paper, we outline the importance and uses of parity and birth‐order statistics. We discuss the Australian data available at present and their gaps and shortcomings. We then describe the ‘gold standard’ of parity and birth‐order statistics and how Australia can achieve this standard through some minor changes to the data collection process.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

ROBUSTNESS PROPERTIES OF LOGNORMAL CONFIDENCE INTERVALS FOR LOGNORMAL AND GAMMA DISTRIBUTED DATA

ABSTRACT

The performances of six confidence intervals for estimating the arithmetic mean of a lognormal distribution are compared using simulated data. The first interval considered is based on an exact method and is recommended in U.S. EPA guidance documents for calculating upper confidence limits for contamination data. Two intervals are based on asymptotic properties due to the Central Limit Theorem, and the other three are based on transformations and maximum likelihood estimation. The effects of departures from lognormality on the performance of these intervals are also investigated. The gamma distribution is considered to represent departures from the lognormal distribution. The average width and coverage of each confidence interval is reported for varying mean, variance, and sample size. In the lognormal case, the exact interval gives good coverage, but for small sample sizes and large variances the confidence intervals are too wide. In these cases, an approximation that incorporates sampling variability of the sample variance tends to perform better. When the underlying distribution is a gamma distribution, the intervals based upon the Central Limit Theorem tend to perform better than those based upon lognormal assumptions.     

Statistical materials: natural increase of population in the USSR

Data are included on the population of the USSR by sex and Union Republic as of January 1, 1981; birth, death, and natural growth rates for 1979 and 1980; distribution of births, deaths, and marriages by month, 1980; distribution of births by birth order; age distribution of birth rates in urban and rural areas and by Union Republic; death rates from cardiovascular disease and cancer, 1979 and 1980; age at first marriage and marriages by age of bride and groom, 1980; and divorces by duration of marriage and age of spouses, 1980.     

A NOTE ON THE DEMOGRAPHIC IMPACT OF CONTRACEPTION IN A MATHEMATICAL MODEL OF HUMAN REPRODUCTION

The application of mathematical models of human reproduction to the study of reproductive behaviour as a function of contraceptive behaviour was pioneered by Perrin and Sheps (1963). More recent work in this area continues to focus on an examination of the birth rate as the principal dependent variable. This note suggests an alternative procedure for studying the demographic impact of contraception through the analysis of birth intervals. A mathematical model is formulated for the waiting time between successive live births, and a procedure is described for incorporating into the model certain contraceptive parameters. A controlled experiment is then performed to determine the effect of these parameters on expected child spacing patterns.     

流动人口女性个体的生育间隔影响因素研究——基于2016年全国流动人口动态监测调查数据

本文采用2016年全国流动人口动态监测调查数据,运用半参数Cox回归对我国流动人口的生育间隔进行分析。结果发现：第一,不仅人口流动会延迟女性的生育时间,而且受教育水平的提高对女性的婚育间隔、第一次生育间隔均有显著的延迟效应。第二,结婚年龄越大,婚后越有可能选择尽早生育,且不同初婚时间对生育间隔的影响差异明显。同时,参加医疗保险对婚育间隔存在显著的缩短效应,而参加生育保险对生育间隔存在显著的延迟效应。越有经济实力以及在工作中担任重要职位的女性越有可能扩大生育间隔;而随着婚育间隔的扩大,第一次生育间隔反而会缩短。第三,初育子女的性别对第一次生育间隔的影响存在显著差异,即若初次生育为女性,则第一次生育间隔会缩短。第四,根据生育政策效果分析发现,放开生育政策虽无法促使女性缩短婚育间隔,但会明显缩短第一次生育间隔。     

An analysis pipeline for estimating true intake from repeated measurements with random errors

The accurate estimation of an individual's usual dietary intake is an important topic in nutritional epidemiology. This paper considers the best linear unbiased predictor (BLUP) computed from repeatedly measured dietary data and derives several nonparametric prediction intervals for true intake. However, the performance of the BLUP and the validity of prediction intervals depends on whether required model assumptions for the true intake estimation problem hold. To address this issue, the paper examines how the BLUP and prediction intervals behave in the case of a violation of model assumptions, and then proposes an analysis pipeline for checking them with data.     

Estimating kurtosis and confidence intervals for the variance under nonnormality

Exact confidence intervals for variances rely on normal distribution assumptions. Alternatively, large-sample confidence intervals for the variance can be attained if one estimates the kurtosis of the underlying distribution. The method used to estimate the kurtosis has a direct impact on the performance of the interval and thus the quality of statistical inferences. In this paper the author considers a number of kurtosis estimators combined with large-sample theory to construct approximate confidence intervals for the variance. In addition, a nonparametric bootstrap resampling procedure is used to build bootstrap confidence intervals for the variance. Simulated coverage probabilities using different confidence interval methods are computed for a variety of sample sizes and distributions. A modification to a conventional estimator of the kurtosis, in conjunction with adjustments to the mean and variance of the asymptotic distribution of a function of the sample variance, improves the resulting coverage values for leptokurtically distributed populations.     

Statistical materials: natural increase of population in the USSR

Data on the population of the USSR by sex and Union republic as of January 1, 1982, are presented. Data are included on population by sex; birth, death, and natural growth rates, 1980 and 1981; distribution of births, deaths, and marriages by month, 1981; distribution of births by birth order, 1981; age-specific birth rates for rural and urban areas, 1980 and 1981; mortality from cardiovascular disease and cancer, 1980 and 1981; marriages by age of bride and groom, 1981; and divorces by duration of marriage and age of husband and wife, 1981.     

Statistical materials,Part 1: natural increase of population in the USSR

Data are presented on the population of the USSR by sex and Union Republic as of January 1, 1983. Data are included on birth rate, death rate, and natural growth rate, 1981 and 1982; distribution of births, deaths, and marriages by month, 1982; distribution of births by birth order, 1982; age-specific birth rates by rural or urban area and Union Republic, 1981 and 1982; mortality from cardiovascular disease and cancer, 1981 and 1982; marriages by age of bride and groom, 1982; and number of divorces by duration of marriage and age of husband and wife, 1982.     

On simultaneous confidence intervals based on rank-estimates with application to analysis of gene expression data

Abstract

Inferential methods based on ranks present robust and powerful alternative methodology for testing and estimation. In this article, two objectives are followed. First, develop a general method of simultaneous confidence intervals based on the rank estimates of the parameters of a general linear model and derive the asymptotic distribution of the pivotal quantity. Second, extend the method to high dimensional data such as gene expression data for which the usual large sample approximation does not apply. It is common in practice to use the asymptotic distribution to make inference for small samples. The empirical investigation in this article shows that for methods based on the rank-estimates, this approach does not produce a viable inference and should be avoided. A method based on the bootstrap is outlined and it is shown to provide a reliable and accurate method of constructing simultaneous confidence intervals based on rank estimates. In particular it is shown that commonly applied methods of normal or t-approximation are not satisfactory, particularly for large-scale inferences. Methods based on ranks are uniquely suitable for analysis of microarray gene expression data since they often involve large scale inferences based on small samples containing a large number of outliers and violate the assumption of normality. A real microarray data is analyzed using the rank-estimate simultaneous confidence intervals. Viability of the proposed method is assessed through a Monte Carlo simulation study under varied assumptions.     

The population of the USSR

Official population data for the USSR for 1986 and 1987 are presented. Tables are included on age and sex distribution; rural and urban population; birth, death, and natural increase rates, 1970-1986; fertility and mortality by sex, 1970-1986; birth order; age-specific birth rates by rural and urban area and Union republic; age-specific death rates, 1970-1986; infant mortality, 1970-1986; life expectancy, 1926-1986; life tables; marriage and age at marriage; and divorce.     

Intergenerational fertility changes

Intergenerational changes in fertility in Poland are analyzed using data from a 1977 sample survey of 38,600 women. The author notes that total fertility declined from 4.4 to 2.5 within the space of two generations. An analysis of fertility is presented by various characteristics of females, including age group, education, duration of marriage, and economic status.     

Construction of Confidence Intervals for the IVIean of a Population Containing Many Zero Values

The likelihood ratio method is used to construct a confidence interval for a population mean when sampling from a population with certain characteristics found in many applications, such as auditing. Specifically, a sample taken from this type of population usually consists of a very large number of zero values, plus a small number of nonzero values that follow some continuous distribution. In this situation, the traditional confidence interval constructed for the population mean is known to be unreliable. This article derives confidence intervals based on the likelihood-ratio-test approach by assuming (1) a normal distribution (normal algorithm) and (2) an exponential distribution (exponential algorithm). Because the error population distribution is usually unknown, it is important to study the robustness of the proposed procedures. We perform an extensive simulation study to compare the percentage of confidence intervals containing the true population mean using the two proposed algorithms with the percentage obtained from the traditional method based on the central limit theorem. It is shown that the normal algorithm is the most robust procedure against many different distributional error assumptions.     

Estimating DEA confidence intervals with statistical panel data analysis

This paper describes a statistical method for estimating data envelopment analysis (DEA) score confidence intervals for individual organizations or other entities. This method applies statistical panel data analysis, which provides proven and powerful methodologies for diagnostic testing and for estimation of confidence intervals. DEA scores are tested for violations of the standard statistical assumptions including contemporaneous correlation, serial correlation, heteroskedasticity and the absence of a normal distribution. Generalized least squares statistical models are used to adjust for violations that are present and to estimate valid confidence intervals within which the true efficiency of each individual decision-making unit occurs. This method is illustrated with two sets of panel data, one from large US urban transit systems and the other from a group of US hospital pharmacies.     

Statistical materials. Part 4: natural increase of population in the USSR

Data are presented on the natural increase of the population in the USSR. Data for 1982-1983 are included on birth, death, and natural increase rates; births, deaths, and marriages by month; age-specific birth rates by urban or rural area and by Union Republic; deaths due to circulatory disease or cancer; marriage by age; and divorces by marriage duration and age of husband and wife.     

Shrinkage confidence intervals for the normal mean: Using a guess for greater efficiency

If the unknown mean of a univariate population is sufficiently close to the value of an initial guess then an appropriate shrinkage estimator has smaller average squared error than the sample mean. This principle has been known for some time, but it does not appear to have found extension to problems of interval estimation. The author presents valid two‐sided 95% and 99% “shrinkage” confidence intervals for the mean of a normal distribution. These intervals are narrower than the usual interval based on the Student distribution when the population mean lies in such an “effective interval.” A reduction of 20% in the mean width of the interval is possible when the population mean is sufficiently close to the value of the guess. The author also describes a modification to existing shrinkage point estimators of the general univariate mean that enables the effective interval to be enlarged.     

Exact bootstrap confidence intervals for regression coefficients in small samples

ABSTRACT

Regression analysis is one of the important tools in statistics to investigate the relationships among variables. When the sample size is small, however, the assumptions for regression analysis can be violated. This research focuses on using the exact bootstrap to construct confidence intervals for regression parameters in small samples. The comparison of the exact bootstrap method with the basic bootstrap method was carried out by a simulation study. It was found that on a very small sample (n ≈ 5) under Laplace distribution with the independent variable treated as random, the exact bootstrap was more effective than the standard bootstrap confidence interval.     

A generalised stochastic model for the most recent inter-arrival time

The analysis of intervals between successive arrivals is an important component in any study of point processes. In this context, the most recent inter-arrival time (MRIAT), that is, the interval between last and second-last arrivals has a prominent place in the characterization of such a process if the study is made only for a limited period of time. In this paper, a general probability model for MRIAT is derived under some realistic assumptions. Some particular cases of the model have also been obtained which might be applicable in real data sets.     

Women in the USSR

This is a selection of statistical data on women from the 1989 Soviet census. The data include total female population by republic; rural and urban female population; women's age distribution, income, labor force participation, educational status, and life expectancy; marriage and divorce; birth weight of children born to unmarried women; induced abortion; maternal mortality; and infant mortality.