Modeling household fertility decisions: a nonlinear simultaneous probit model

"This article proposes new methods for modeling household fertility decisions....Specifically, we model the trivariate distribution of wife's stated desire for additional children, husband's stated desire for additional children, and subsequent fertility. In the model, the stated desire of the husband (wife) is viewed as an indicator of the husband's (wife's) latent disposition toward subsequent fertility. The husband's (wife's) disposition is allowed to depend on the wife's (husband's) disposition. The two dispositions are then combined to generate the couple's propensity for subsequent fertility. We show how such models can be estimated and tested and how the parameters can be used to assess the relative influence of each partner on the propensity." The model is tested using U.S. data from the Princeton Fertility Study for the 1950s and 1960s. The results indicate that "both husband's disposition score and wife's disposition score affect the propensity score, and, under some additional assumptions, that husbands and wives have equal relative influence on the propensity."     

Model fusion and multiple testing in the likelihood paradigm: shrinkage and evidence supporting a point null hypothesis

ABSTRACT

According to the general law of likelihood, the strength of statistical evidence for a hypothesis as opposed to its alternative is the ratio of their likelihoods, each maximized over the parameter of interest. Consider the problem of assessing the weight of evidence for each of several hypotheses. Under a realistic model with a free parameter for each alternative hypothesis, this leads to weighing evidence without any shrinkage toward a presumption of the truth of each null hypothesis. That lack of shrinkage can lead to many false positives in settings with large numbers of hypotheses. A related problem is that point hypotheses cannot have more support than their alternatives. Both problems may be solved by fusing the realistic model with a model of a more restricted parameter space for use with the general law of likelihood. Applying the proposed framework of model fusion to data sets from genomics and education yields intuitively reasonable weights of evidence.     

Restricted most powerful Bayesian tests for linear models

Uniformly most powerful Bayesian tests (UMPBTs) are a new class of Bayesian tests in which null hypotheses are rejected if their Bayes factor exceeds a specified threshold. The alternative hypotheses in UMPBTs are defined to maximize the probability that the null hypothesis is rejected. Here, we generalize the notion of UMPBTs by restricting the class of alternative hypotheses over which this maximization is performed, resulting in restricted most powerful Bayesian tests (RMPBTs). We then derive RMPBTs for linear models by restricting alternative hypotheses to g priors. For linear models, the rejection regions of RMPBTs coincide with those of usual frequentist F‐tests, provided that the evidence thresholds for the RMPBTs are appropriately matched to the size of the classical tests. This correspondence supplies default Bayes factors for many common tests of linear hypotheses. We illustrate the use of RMPBTs for ANOVA tests and t‐tests and compare their performance in numerical studies.     

Optimally weighted,fixed sequence and gatekeeper multiple testing procedures

We consider a class of closed multiple test procedures indexed by a fixed weight vector. The class includes the Holm weighted step-down procedure, the closed method using the weighted Fisher combination test, and the closed method using the weighted version of Simes’ test. We show how to choose weights to maximize average power, where “average power” is itself weighted by importance assigned to the various hypotheses.Numerical computations suggest that the optimal weights for the multiple test procedures tend to certain asymptotic configurations. These configurations offer numerical justification for intuitive multiple comparisons methods, such as downweighting variables found insignificant in preliminary studies, giving primary variables more emphasis, gatekeeping test strategies, pre-determined multiple testing sequences, and pre-determined sequences of families of tests. We establish that such methods fall within the envelope of weighted closed testing procedures, thus providing a unified view of fixed sequences, fixed sequences of families, and gatekeepers within the closed testing paradigm. We also establish that the limiting cases control the familywise error rate (or FWE), using well-known results about closed tests, along with the dominated convergence theorem.     

Improvement over bayes prediction in small samples in the presence of model uncertainty

In an online prediction context, the authors introduce a new class of mongrel criteria that allow for the weighing of candidate models and the combination of their predictions based both on model‐based and empirical measures of their performance. They present simulation results which show that model averaging using the mongrel‐derived weights leads, in small samples, to predictions that are more accurate than that obtained by Bayesian weight updating, provided that none of the candidate models is too distant from the data generator.     

OECD's ‘Better Life Index’: can any country be well ranked?

We critically review the Better Life Index (BLI) recently introduced by the Organization for Economic Co-operation and Development (OECD). We discuss methodological issues in the definition of the criteria used to rank the countries, as well as in their aggregation method. Moreover, we explore the unique option offered by the BLI to apply one's own weight set to 11 criteria. Although 16 countries can be ranked first by choosing ad hoc weightings, only Canada, Australia and Sweden do so over a substantial fraction of the parameter space defined by all possible weight sets. Furthermore, most pairwise comparisons between countries are insensitive to the choice of the weights. Therefore, the BLI establishes a hierarchy among the evaluated countries, independent of the chosen set of weights.     

Fertility in Poland during the 1980s: analysis of a maternity questionnaire

Recent fertility trends in Poland are analyzed using data from a mail survey conducted in 1984. The demographic, social, and economic characteristics of women who gave birth in 1984, their husbands, and their parents are examined. The results show an increase in fertility in the early 1980s, particularly in urban areas.     

Multiple Hypotheses Testing with Weights

In this paper we offer a multiplicity of approaches and procedures for multiple testing problems with weights. Some rationale for incorporating weights in multiple hypotheses testing are discussed. Various type-I error-rates and different possible formulations are considered, for both the intersection hypothesis testing and the multiple hypotheses testing problems. An optimal per family weighted error-rate controlling procedure a la Spjotvoll (1972) is obtained. This model serves as a vehicle for demonstrating the different implications of the approaches to weighting. Alternative approach es to that of Holm (1979) for family-wise error-rate control with weights are discussed, one involving an alternative procedure for family-wise error-rate control, and the other involving the control of a weighted family-wise error-rate. Extensions and modifications of the procedures based on Simes (1986) are given. These include a test of the overall intersec tion hypothesis with general weights, and weighted sequentially rejective procedures for testing the individual hypotheses. The false discovery rate controlling approach and procedure of Benjamini & Hochberg (1995) are extended to allow for different weights.     

Weighing the Evidence for Hypotheses with Small Samples of Right-censored Exponential Data

The p-value evidence for an alternative to a null hypothesis regarding the mean lifetime can be unreliable if based on asymptotic approximations when there is only a small sample of right-censored exponential data. However, a guarded weight of evidence for the alternative can always be obtained without approximation, no matter how small the sample, and has some other advantages over p-values. Weights of evidence are defined as estimators of 0 when the null hypothesis is true and 1 when the alternative is true, and they are judged on the basis of the ensuing risks, where risk is mean squared error of estimation. The evidence is guarded in that a preassigned bound is placed on the risk under the hypothesis. Practical suggestions are given for choosing the bound and for interpreting the magnitude of the weight of evidence. Acceptability profiles are obtained by inversion of a family of guarded weights of evidence for two-sided alternatives to point hypotheses, just as confidence intervals are obtained from tests; these profiles are arguably more informative than confidence intervals, and are easily determined for any level and any sample size, however small. They can help understand the effects of different amounts of censoring. They are found for several small size data sets, including a sample of size 12 for post-operative cancer patients. Both singly Type I and Type II censored examples are included. An examination of the risk functions of these guarded weights of evidence suggests that if the censoring time is of the same magnitude as the mean lifetime, or larger, then the risks in using a guarded weight of evidence based on a likelihood ratio are not much larger than they would be if the parameter were known.     

Robust minimum distance inference based on combined distances

The minimum disparity estimators proposed by Lindsay (1994) for discrete models form an attractive subclass of minimum distance estimators which achieve their robustness without sacrificing first order efficiency at the model. Similarly, disparity test statistics are useful robust alternatives to the likelihood ratio test for testing of hypotheses in parametric models; they are asymptotically equivalent to the likelihood ratio test statistics under the null hypothesis and contiguous alternatives. Despite their asymptotic optimality properties, the small sample performance of many of the minimum disparity estimators and disparity tests can be considerably worse compared to the maximum likelihood estimator and the likelihood ratio test respectively. In this paper we focus on the class of blended weight Hellinger distances, a general subfamily of disparities, and study the effects of combining two different distances within this class to generate the family of “combined” blended weight Hellinger distances, and identify the members of this family which generally perform well. More generally, we investigate the class of "combined and penal-ized" blended weight Hellinger distances; the penalty is based on reweighting the empty cells, following Harris and Basu (1994). It is shown that some members of the combined and penalized family have rather attractive properties     

Inference for Multi‐dimensional High‐frequency Data with an Application to Conditional Independence Testing

We find the asymptotic distribution of the multi‐dimensional multi‐scale and kernel estimators for high‐frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that the classes of multi‐scale and kernel estimators for smoothing noise perturbation are asymptotically equivalent in the sense of having the same asymptotic distribution for corresponding kernel and weight functions. The theory leads to multi‐dimensional stable central limit theorems and feasible versions. Hence, they allow to draw statistical inference for a broad class of multivariate models, which paves the way to tests and confidence intervals in risk measurement for arbitrary portfolios composed of high‐frequently observed assets. As an application, we enhance the approach to construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.     

新汇改以来人民币汇率参考一篮子货币权重的估计及经验验证

本文首先构建人民币对美元汇率指数和篮子货币汇率指数,根据人民币对美元汇率指数和篮子货币相关性指数最大化可以确定篮子货币的权重和数量,并对新汇改后篮子货币的权重和数量进行测度。我们的研究发现：在参考一篮子货币中,美元的权重最高,英镑的权重最小,但是其他货币权重都占有一定比例,我们的货币篮子和央行的货币篮子线性相关性较高。根据每一种货币的权重大小,我们可以计算出篮子中每一种货币的数量。根据最优货币权重,我们研究发现人民币对美元汇率和篮子货币之间存在长期协整关系,误差修正模型显示人民币汇率参考篮子货币调整的短期弹性和长期弹性比较接近,说明人民币汇率参考篮子货币调整相对比较稳定。本文检验了模型的预测效果,模型拟合度较高,说明我们选取的货币篮子具有较好的代表性。     

Weighted Wilcoxon Estimates for Autoregression

This paper explores the class of weighted Wilcoxon (WW) estimates in the context of autoregressive parameter estimation, giving special attention to three sub-classes of so-called WW-estimates. When the weights are constant, the estimate is equivalent to using Jaeckel's estimate with Wilcoxon scores. The paper presents asymptotic linearity properties for the three sub-classes of WW-estimates. These properties imply that the estimates are asymptotically normal at rate n ^½. Tests of hypotheses as well as standard errors for confidence interval procedures can be based on such results. Furthermore, the estimates can be computed with an L ₁ regression routine once the weights have been calculated. Examples and a Monte Carlo study over innovation and additive outlier models suggest that WW-estimates can be both robust and highly efficient.     

Disambiguating Author Names

For the first installment of the new column, “Problem Solved!,” coedited by Kelly Smith and Scott Vieira, Vieira provides the first of two columns that will look into the nature of the problem surrounding author identity and how ORCID, a registry for author identifiers, may help resolve this challenge for researchers, publishers, and other institutions. Author identity remains a challenging problem for systems tasked with managing and analyzing bibliographical resources. Additionally, researchers and research institutions need more effective tools to manage their own scholarly production.     

Evaluation of Conditional Weight Approximations for Two-Level Models

This article evaluates two methods of approximating cluster-level and conditional sampling weights when only unconditional sampling weights are available. For estimation of a multilevel analysis that does not include all facets of a sampling design, conditional sampling weights at each stage of the model should be used, but typically only the unconditional sampling weight of the ultimate sampling unit is provided on federal publicly-released datasets. Methods of approximating these conditional weights have been suggested but there has been no study of their adequacy. This demonstration and simulation study examines the feasibility of using these weight approximations.     

Guarded Weights of Evidence and Acceptability Profiles Based on Signs: II. Asymptotic Results

The concepts of guarded weights of evidence and acceptability profiles have been extended to the distribution-free setting in Dollinger, Kulinskaya & Staudte (1999). In that first of two parts the advantages of these concepts relative to traditional ones such as p -values and confidence intervals derived from hypothesis tests are emphasized for small samples. Here in Part II asymptotic expressions are found for guarded weights of evidence for hypothesesregarding the median of a symmetric distribution and related acceptability profiles for the median. It is also seen that for local alternatives the efficacy and Pitman asymptotic relative efficiency of the sign statistic for testing hypotheses carries over to the more general setting of guarded weights of evidence.     

A note on a family of criteria for evaluating test statistics

ABSTRACT

In noting that the usual criteria for choosing an optimal test, Uniform Power and Local Power are at opposite ends of a spectrum of dominance criteria, a complete “Power Dominance” family of criteria for classifying and choosing optimal tests on the basis of their power characteristics is identified, wherein successive orders of dominance attach increasing weight to power close to the null hypothesis. Indices of the extent to which a preferred test has superior power characteristics over other members in its class, and an index of the proximity of a test to the envelope function of alternative tests are also provided. The ideas are exemplified using various optimal test statistics for Normal and Laplace population distributions.     

Comparison of genomic sequences using the Hamming distance

The paper considers the problem of homogeneity among groups by comparison of genomic sequences. Some alternative procedures that attach less emphasis on the likelihood approach, and more on alternative measures that deal with similar homogeneity problems are considered here. On this approach, a one-sided hypothesis test is considered and the classical ANOVA decomposition can be directly adapted to sample measures based on the Hamming distance, without necessarily going through their second moments. Some results of U-statistics theory will be useful for the decomposition of the test statistic and to find its asymptotic distribution. An application of this test with real data is shown and the p-value of the test statistic is found via bootstrap resampling.     

Inverse Probability Weighting with Missing Predictors of Treatment Assignment or Missingness

Inverse probability weighting (IPW) can deal with confounding in non randomized studies. The inverse weights are probabilities of treatment assignment (propensity scores), estimated by regressing assignment on predictors. Problems arise if predictors can be missing. Solutions previously proposed include assuming assignment depends only on observed predictors and multiple imputation (MI) of missing predictors. For the MI approach, it was recommended that missingness indicators be used with the other predictors. We determine when the two MI approaches, (with/without missingness indicators) yield consistent estimators and compare their efficiencies.We find that, although including indicators can reduce bias when predictors are missing not at random, it can induce bias when they are missing at random. We propose a consistent variance estimator and investigate performance of the simpler Rubin’s Rules variance estimator. In simulations we find both estimators perform well. IPW is also used to correct bias when an analysis model is fitted to incomplete data by restricting to complete cases. Here, weights are inverse probabilities of being a complete case. We explain how the same MI methods can be used in this situation to deal with missing predictors in the weight model, and illustrate this approach using data from the National Child Development Survey.     

Further studies on the scale estimation in the censored two sample accelerated life model

Yang (1998) proposes a new class of scale estimators for the censored two sample accelerated life model. Unlike most previous results, Yang's estimators have the property that their asymptotic variance can be easily and reliably estimated, and the inferences on the scale parameter can be easily obtained. In this article, we further study the estimation function of Yang. Several new classes of weights and a new slope estimate are considered. Throughout extensive numerical studies, it was found that a new weight together with the use of the new slope results in an estimating function that improved the choices recommended by Yang.