IDEAS home Printed from
   My bibliography  Save this paper

Sampling Errors and Confidence Intervals for Order Statistics: Implementing the Family Support Act


  • William C. Horrace
  • Peter Schmidt
  • Ann Dryden Witte


The Family Support Act allows states to reimburse child care costs up to the 75th percentile of local market price for child care. States must carry out surveys to estimate these 75th percentiles. This estimation problem raises two major statistical issues: (1) picking a sample design that will allow one to estimate the percentiles cheaply, efficiently and equitably; and (2) assessing the sampling variability of the estimates obtained. For Massa- chusetts, we developed a sampling design that equalized the standard errors of the estimated percentiles across 65 distinct local markets. This design was chosen because state administrators felt public day care providers and child advocates would find it equitable, thus limiting costly appeals. Estimation of standard errors for the sample 75th percentiles requires estimation of the density of the population at the 75th percentile. We implement and compare a number of parametric and nonparametric methods of density estimation. A kernel estimator provides the most reasonable estimates. On the basis of the mean integrated squared error criterion we selected the Epanechnikov kernel and the Sheather-Jones automatic bandwidth selection procedure. Because some of our sample sizes were too small to rely on asymptotics, we also constructed nonparametric confidence intervals using the hypergeometric distrition. For most of our samples, these confidence intervals were similar to those based on the asymptotic standard errors. Substantively we find wide variation in the price of child care, depending on the child's age, type of care and geographic location. For full-time care, the 75th percentiles ranged from $242 per week for infants in child care centers in Boston to $85 per week for family day care in western Massachusetts.

Suggested Citation

  • William C. Horrace & Peter Schmidt & Ann Dryden Witte, 1995. "Sampling Errors and Confidence Intervals for Order Statistics: Implementing the Family Support Act," NBER Working Papers 5387, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:5387
    Note: LS PE

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    JEL classification:

    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
    • H52 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Education


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:5387. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: () or (Joanne Lustig). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.