Sampling distribution

About: Sampling distribution is a research topic. Over the lifetime, 3994 publications have been published within this topic receiving 210891 citations. The topic is also known as: finite-sample distribution & Sampling distribution.

Bootstrap Methods: Another Look at the Jackknife

Abstract: We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = \(\theta \left( {\hat F} \right) - \theta \left( F \right)\), θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.

Inference and missing data

Abstract: Two results are presented concerning inference when data may be missing. First, ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are “missing at random” and the observed data are “observed at random,” and then such inferences are generally conditional on the observed pattern of missing data. Second, ignoring the process that causes missing data when making Bayesian inferences about θ is generally appropriate if and only if the missing data are missing at random and the parameter of the missing data is “independent” of θ. Examples and discussion indicating the implications of these results are included.

Instrumental variables regression with weak instruments

Abstract: This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).

Introduction to the Theory of Statistics

Abstract: 1 probability 2 Random variables, distribution functions, and expectation 3 Special parametric families of univariate distributions 4 Joint and conditional distributions, stochastic independence, more expectation 5 Distributions of functions of random variables 6 Sampling and sampling distributions 7 Parametric point estimation 8 Parametric interval estimation 9 Tests of hypotheses 10 Linear models 11 Nonparametric method Appendix A Mathematical Addendum Appendix B tabular summary of parametric families of distributions Appendix C References and related reading Appendix D Tables