The perinatal period is a vulnerable time for the development of psychopathology, particularly mood and anxiety disorders. In the study of maternal anxiety, important questions remain regarding the association between maternal anxiety symptoms and subsequent child outcomes. This study examined the association between depressive and anxiety symptoms, namely social anxiety, panic, and agoraphobia disorder symptoms during the perinatal period and maternal perception of child behavior, specifically different facets of development and temperament. Participants (N = 104) were recruited during pregnancy from a community sample. Participants completed clinician-administered and self-report measures of depressive and anxiety symptoms during the third trimester of pregnancy and at 16 months postpartum; child behavior and temperament outcomes were assessed at 16 months postpartum. Child development areas included gross and fine motor skills, language and problem-solving abilities, and personal/social skills. Child temperament domains included surgency, negative affectivity, and effortful control. Hierarchical multiple regression analyses demonstrated that elevated prenatal social anxiety symptoms significantly predicted more negative maternal report of child behavior across most measured domains. Elevated prenatal social anxiety and panic symptoms predicted more negative maternal report of child effortful control. Depressive and agoraphobia symptoms were not significant predictors of child outcomes. Elevated anxiety symptoms appear to have a distinct association with maternal report of child development and temperament. Considering the relative influence of anxiety symptoms, particularly social anxiety, on maternal report of child behavior and temperament can help to identify potential difficulties early on in mother–child interactions as well as inform interventions for women and their families.

Ever since Immanuel Kant suggested that ‘the problem of setting up a state can be solved even by a nation of devils’ so long as citizens’ selfish tendencies worked to counterbalance one another (Immanuel Kant, ‘Perpetual Peace,’ Hans Reiss, ed., Kant's Political Writing [New York: Cambridge University Press 1970], 112), critics have complained that liberalism is indifferent to individual character and, worse still, is predicated on the notion that citizens ought to be concerned primarily with their private interests and little, if at all, with the public weal. Lately, this line of criticism has been pressed with renewed force by theorists who argue that liberal states can flourish only if citizens develop the distinctive virtues that, ‘taken together … constitute a disposition to foster, support, and participate in liberal political institutions,’ but that liberal states committed to neutrality with respect to the good cannot realistically expect their citizens to develop these virtues.

This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example) or some strict subset of the natural numbers (such as for a Binomial or Uniform distribution). The theory for these two cases is studied separately.

For the case where the arrivals have support on the natural numbers, a new asymptotically efficient semiparametric test, the effective score (Neyman-Rao) test, is derived. The semiparametric Likelihood-Ratio, Wald and score tests are shown to be asymptotically equivalent to the effective score test, and hence also asymptotically efficient. Asymptotic relative efficiency calculations demonstrate that the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation coefficient, which is most commonly applied in practice.

For the case where the arrivals have support that is a strict subset of the natural numbers, the theory is considerably altered because the support of the observations becomes different under the null and alternative hypotheses. The semiparametric Likelihood-Ratio, Wald and score tests become asymptotically degenerate in this case, while the effective score test remains valid. Remarkably, in this case the effective score test is also found to have power against local alternatives that shrink to the null at the rate T−1. In rare cases where the arrival support is partly or totally known, additional tests exploiting this information are considered.

Finite sample properties of the tests in these various cases demonstrate the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation test implied by a parametric Poisson specification. The simulations also reveal situations in which the first order autocorrelation is preferable in finite samples, so a hybrid of the effective score and autocorrelation tests is proposed to capture most of the benefits of each test.