Analysis of rounded data in mixture normal model

Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding errors to the finite normal mixture model with a known number of components, and develop a new estimation method to obtain consistent and asymptotically normal estimates for the unknown parameters based on rounded data drawn from this kind of models.     

Testing for homogeneity in cross-lagged panel studies

Panel studies are statistical studies in which two or more variables are observed for two or more subjects at two or more points In time. Cross- lagged panel studies are those studies in which the variables are continuous and divide naturally into two effects or impacts of each set of variables on the other. If a regression approach is taken5 a regression structure Is formulated for the cross-lagged models This structure may assume that the regression parameters are homogeneous across waves and across subpopulations. Under such assumptions the methods of multivariate regression analysis can be adapted to make inferences about the parameters. These inferences are limited to the degree that homogeneity of the parameters Is 'supported b}T the data. We consider the problem of testing the hypotheses of homogeneity and consider the problem of making statistical inferences about the cross-effects should there be evidence against one of the homogeneity assumptions. We demonstrate the methods developed by applying then to two panel data sets.     

The Performance of Robust Two-Stage Estimator in Nonlinear Regression with Autocorrelated Error

Some statistics practitioners often ignore the underlying assumptions when analyzing a real data and employ the Nonlinear Least Squares (NLLS) method to estimate the parameters of a nonlinear model. In order to make reliable inferences about the parameters of a model, require that the underlying assumptions, especially the assumption that the errors are independent, are satisfied. However, in a real situation, we may encounter dependent error terms which prone to produce autocorrelated errors. A two-stage estimator (CTS) has been developed to remedy this problem. Nevertheless, it is now evident that the presence of outliers have an unduly effect on the least squares estimates. We expect that the CTS is also easily affected by outliers since it is based on the least squares estimator, which is not robust. In this article, we propose a Robust Two-Stage (RTS) procedure for the estimation of the nonlinear regression parameters in the situation where autocorrelated errors come together with the existence of outliers. The numerical example and simulation study signify that the RTS is more efficient than the NLLS and the CTS methods.     

Population constraints on pooled surveys in demographic hazard modeling

In non-experimental research, data on the same population process may be collected simultaneously by more than one instrument. For example, in the present application, two sample surveys and a population birth registration system all collect observations on first births by age and year, while the two surveys additionally collect information on women’s education. To make maximum use of the three data sources, the survey data are pooled and the population data introduced as constraints in a logistic regression equation. Reductions in standard errors about the age and birth-cohort parameters of the regression equation in the order of three-quarters are obtained by introducing the population data as constraints. A halving of the standard errors about the education parameters is achieved by pooling observations from the larger survey dataset with those from the smaller survey. The percentage reduction in the standard errors through imposing population constraints is independent of the total survey sample size.     

Exact conditional inference for two uniform populations

We discuss the nature of ancillary information in the context of the continuous uniform distribution. In the one-sample problem, the existence of sufficient statistics mitigates conditioning on the ancillary configuration. In the two-sample problem, additional ancillary information becomes available when the ratio of scale parameters is known. We give exact results for conditional inferences about the common scale parameter and for the difference in location parameters of two uniform distributions. The ancillary information affects the precision of the latter through a comparison of the sample value of the ratio of scale parameters with the known population value. A limited conditional simulation compares the Type I errors and power of these exact results with approximate results using the robust pooled t-statistic.     

The Siable-Law Model of Stock Returns

This study investigates the tail shapes of empirical distributions of returns on an extensive group of common stocks. The tails of the return distributions are found to be thinner than those of infinite variance stable distributions. Therefore, although homogeneity is evident in general, economic and statistical inferences drawn from stable-law parameters estimated from samples of stock returns may be misleading. This is in spite of the apparent overall similarity (in shape) between empirical and stable distributions.     

Inferences from DNA data: population histories, evolutionary processes and forensic match probabilities

Summary. We develop a flexible class of Metropolis–Hastings algorithms for drawing inferences about population histories and mutation rates from deoxyribonucleic acid (DNA) sequence data. Match probabilities for use in forensic identification are also obtained, which is particularly useful for mitochondrial DNA profiles. Our data augmentation approach, in which the ancestral DNA data are inferred at each node of the genealogical tree, simplifies likelihood calculations and permits a wide class of mutation models to be employed, so that many different types of DNA sequence data can be analysed within our framework. Moreover, simpler likelihood calculations imply greater freedom for generating tree proposals, so that algorithms with good mixing properties can be implemented. We incorporate the effects of demography by means of simple mechanisms for changes in population size and structure, and we estimate the corresponding demographic parameters, but we do not here allow for the effects of either recombination or selection. We illustrate our methods by application to four human DNA data sets, consisting of DNA sequences, short tandem repeat loci, single-nucleotide polymorphism sites and insertion sites. Two of the data sets are drawn from the male-specific Y-chromosome, one from maternally inherited mitochondrial DNA and one from the β -globin locus on chromosome 11.     

Composite conditional likelihood for sparse clustered data

Summary.  Sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference. First, it is difficult to model and interpret the full joint probability of dependent discrete data, which limits the utility of full likelihood methods. Second, standard methods for clustered data, such as pairwise likelihood and the generalized estimating function approach, are unsuitable when the data are sparse owing to the presence of many nuisance parameters. We present a composite conditional likelihood for use with sparse clustered data that provides valid inferences about covariate effects on both the marginal response probabilities and the intracluster pairwise association. Our primary focus is on sparse clustered binary data, in which case the method proposed utilizes doubly discordant quadruplets drawn from each stratum to conduct inference about the intracluster pairwise odds ratios.     

Statistical studies of infectious disease incidence

Methods for the analysis of data on the incidence of an infectious disease are reviewed, with an emphasis on important objectives that such analyses should address and identifying areas where further work is required. Recent statistical work has adapted methods for constructing estimating functions from martingale theory, methods of data augmentation and methods developed for studying the human immunodeficiency virus–acquired immune deficiency syndrome epidemic. Infectious disease data seem particularly suited to analysis by Markov chain Monte Carlo methods. Epidemic modellers have recently made substantial progress in allowing for community structure and heterogeneity among individuals when studying the requirements for preventing major epidemics. This has stimulated interest in making statistical inferences about crucial parameters from infectious disease data for such community settings.     

Bayesian quantile regression for hierarchical linear models

The paper proposes a Bayesian quantile regression method for hierarchical linear models. Existing approaches of hierarchical linear quantile regression models are scarce and most of them were not from the perspective of Bayesian thoughts, which is important for hierarchical models. In this paper, based on Bayesian theories and Markov Chain Monte Carlo methods, we introduce Asymmetric Laplace distributed errors to simulate joint posterior distributions of population parameters and across-unit parameters and then derive their posterior quantile inferences. We run a simulation as the proposed method to examine the effects on parameters induced by units and quantile levels; the method is also applied to study the relationship between Chinese rural residents' family annual income and their cultivated areas. Both the simulation and real data analysis indicate that the method is effective and accurate.     

Bootstrapping: as easy as 1-2-3

The bootstrap is a powerful non-parametric statistical technique for making probability-based inferences about a population parameter. Through a Monte-Carlo resampling simulation, bootstrapping empirically generates a statistic's entire distribution. From this simulated distribution, inferences can be made about a population parameter. Assumptions about normality are not required. In general, despite its power, bootstrapping has been used relatively infrequently in social science research, and this is particularly true for business research. This under-utilization is likely due to a combination of a general lack of understanding of the bootstrap technique and the difficulty with which it has traditionally been implemented. Researchers in the various fields of business should be familiar with this powerful statistical technique. The purpose of this paper is to explain how this technique works using Lotus 1-2-3, a software package with which business people are very familiar.     

Nonparametric predictive inference for stock returns

In finance, inferences about future asset returns are typically quantified with the use of parametric distributions and single-valued probabilities. It is attractive to use less restrictive inferential methods, including nonparametric methods which do not require distributional assumptions about variables, and imprecise probability methods which generalize the classical concept of probability to set-valued quantities. Main attractions include the flexibility of the inferences to adapt to the available data and that the level of imprecision in inferences can reflect the amount of data on which these are based. This paper introduces nonparametric predictive inference (NPI) for stock returns. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. NPI is presented for inference about future stock returns, as a measure for risk and uncertainty, and for pairwise comparison of two stocks based on their future aggregate returns. The proposed NPI methods are illustrated using historical stock market data.     

Semiparametric likelihood-based inference for biased and truncated data when the total sample size is known

Biased and truncated data arise in many practical areas. Many efficient statistical methods have been studied in the literature. This paper discusses likelihood-based inferences for the two types of data in the presence of auxiliary information of known total sample size. It is shown that this information improves inference about the underlying distribution and its parameters in which we are interested. A semiparametric likelihood ratio confidence interval technique is employed. Also some simulation results are reported.     

Bayesian inference of multiple structural change models with asymmetric GARCH errors

Structural change in any time series is practically unavoidable, and thus correctly detecting breakpoints plays a pivotal role in statistical modelling. This research considers segmented autoregressive models with exogenous variables and asymmetric GARCH errors, GJR-GARCH and exponential-GARCH specifications, which utilize the leverage phenomenon to demonstrate asymmetry in response to positive and negative shocks. The proposed models incorporate skew Student-t distribution and prove the advantages of the fat-tailed skew Student-t distribution versus other distributions when structural changes appear in financial time series. We employ Bayesian Markov Chain Monte Carlo methods in order to make inferences about the locations of structural change points and model parameters and utilize deviance information criterion to determine the optimal number of breakpoints via a sequential approach. Our models can accurately detect the number and locations of structural change points in simulation studies. For real data analysis, we examine the impacts of daily gold returns and VIX on S&P 500 returns during 2007–2019. The proposed methods are able to integrate structural changes through the model parameters and to capture the variability of a financial market more efficiently.

     

Autocorrelation in real-time continuous monitoring of microenvironments

Interpretation of continuous measurements in microenvironmental studies and exposure assessments can be complicated by autocorrelation, the implications of which are often not fully addressed. We discuss some statistical issues that arose in the analysis of microenvironmental particulate matter concentration data collected in 1998 by the Harvard School of Public Health. We present a simulation study that suggests that Generalized Estimating Equations, a technique often used to adjust for autocorrelation, may produce inflated Type I errors when applied to microenvironmental studies of small or moderate sample size, and that Linear Mixed Effects models may be more appropriate in small-sample settings. Environmental scientists often appeal to longer averaging times to reduce autocorrelation. We explore the functional relationship between averaging time, autocorrelation, and standard errors of both mean and variance, showing that longer averaging times impair statistical inferences about main effects. We conclude that, given widely available techniques that adjust for autocorrelation, longer averaging times may be inappropriate in microenvironmental studies.     

Bayesian inference for partially observed stochastic epidemics

The analysis of infectious disease data is usually complicated by the fact that real life epidemics are only partially observed. In particular, data concerning the process of infection are seldom available. Consequently, standard statistical techniques can become too complicated to implement effectively. In this paper Markov chain Monte Carlo methods are used to make inferences about the missing data as well as the unknown parameters of interest in a Bayesian framework. The methods are applied to real life data from disease outbreaks.     

Estimating percentile-specific treatment effects in counterfactual models: a case-study of micronutrient supplementation, birth weight and infant mortality

Summary.  Clinical trials of micronutrient supplementation are aimed at reducing the risk of infant mortality by increasing birth weight. Because infant mortality is greatest among the low birth weight (LBW) infants (2500 g or under), an effective intervention increases the birth weight among the smallest babies. The paper defines population and counterfactual parameters for estimating the treatment effects on birth weight and on survival as functions of the percentiles of the birth weight distribution. We use a Bayesian approach with data augmentation to approximate the posterior distributions of the parameters, taking into account uncertainty that is associated with the imputation of the counterfactuals. This approach is particularly suitable for exploring the sensitivity of the results to unverifiable modelling assumptions and other prior beliefs. We estimate that the average causal effect of the treatment on birth weight is 72 g (95% posterior regions 33–110 g) and that this causal effect is largest among the LBW infants. Posterior inferences about average causal effects of the treatment on birth weight are robust to modelling assumptions. However, inferences about causal effects for babies at the tails of the birth weight distribution can be highly sensitive to the unverifiable assumption about the correl-ation between the observed and the counterfactuals birth weights. Among the LBW infants who have a large causal effect of the treatment on birth weight, we estimate that a baby receiving the treatment has 5% less chance of death than if the same baby had received the control. Among the LBW infants, we found weak evidence supporting an additional beneficial effect of the treatment on mortality independent of birth weight.     

Effect on Bayesian inference of the degree of precision of recorded data

In a previous study, the effect of rounding on classical statistical techniques was considered. Here, we consider how rounded data may affect the posterior distribution and, thus, any Bayesian inferences made. The results in this paper indicate that Bayesian inferences can be sensitive to the roundingprocess.     

Causal inferences from many experiments

The underlying statistical concept that animates empirical strategies for extracting causal inferences from observational data is that observational data may be adjusted to resemble data that might have originated from a randomized experiment. This idea has driven the literature on matching methods. We explore an un-mined idea for making causal inferences with observational data – that any given observational study may contain a large number of indistinguishably balanced matched designs. We demonstrate how the absence of a unique best solution presents an opportunity for greater information retrieval in causal inference analysis based on the principle that many solutions teach us more about a given scientific hypothesis than a single study and improves our discernment with observational studies. The implementation can be achieved by integrating the statistical theories and models within a computational optimization framework that embodies the statistical foundations and reasoning.     

On randomized response surveys for estimating a proportion

In studies about sensitive characteristics, randomized response (RR) methods are useful for generating reliable data, protecting respondents’ privacy. It is shown that all RR surveys for estimating a proportion can be encompassed in a common model and some general results for statistical inferences can be used for any given survey. The concepts of design and scheme are introduced for characterizing RR surveys. Some consequences of comparing RR designs based on statistical measures of efficiency and respondent’ protection are discussed. In particular, such comparisons lead to the designs that may not be suitable in practice. It is suggested that one should consider other criteria and the scheme parameters for planning a RR survey.