Simple random sampling. Sampling for proportions. Estimation of sample size. Sampling with varying probabilities. Sampling: stratified, systematic, cluster, double, sequential, incomplete. Also listed as SURV 440.


STAT 401 or STAT 420


Basic concepts

Populations, samples, sampling frames.
Sampling design, statistics, bias.
Sampling and nonsampling errors.
(0.5 week)

Simple Random Sampling

Estimates of population mean, total, proportion and variance and their sampling properties.
Confidence limits, use of normal approximation.
Auxiliary information, ratio and regression estimators.
(4.5 weeks)

Stratified Samples

Definitions, weighting and estimators.
Optimal allocation, poststratification.
(2 weeks)

Unbiased Estimation for Cluster and Two-Stage Sampling

Single-stage, two-stage, and multi-stage cluster sampling.
Fixed and random clusters.
With-replacement and without-replacement sampling of PSU's.
Approximate variance estimators.
(4 weeks)

Advanced Topics

Variance estimation, categorical data analysis, regression in complex surveys.

  • Anomalous diffusion for some kinetic equations

    Speaker: Marjolaine Puel (University of Nice Sophia-Antipolis) -

    When: Thu, November 19, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Kinetic equations involve a large number of variables, time, space and velocity and one important part of the study of those equation consists in giving an approximation of their solution for large time and large observation length. For example, when we model collisions via the linear Boltzmann equation, it is well known that when the equilibria are given by Gaussian distributions, we can approximate the solution by the product of an equilibrium that gives the dependence with respect to velocity multiplied by a density depending on time and position that satisfies a diffusion equation. But different models like inelastic collisions lead to heavy tails equilibria for which depending on the power of the tail, we get different situations. When the diffusion coefficient is no more defined, in the case of linear Boltzmann, the density satisfies a fractional diffusion equation. The same kind of problem arises when the interaction between particles are modeled via the Fokker Planck operator with an additional difficulty. I will present a probabilistic method to study the critical case where we obtain still a diffusion but with an anomalous scaling and present the problems arising for the subcritical exponents.

  • Energy scaling laws for compressed thin elastic sheets

    Speaker: Ian Tobasco (Courant Institute) -

    When: Thu, November 5, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: A long-standing open problem in elasticity is to identify the minimum energy scaling law of a crumpled sheet of paper as thickness tends to zero. Though much is known about scaling laws for thin sheets in tensile settings, the compressive regime is mostly unexplored. I will discuss the analysis of two examples: an axially compressed thin elastic cylinder, and an indented cone. My focus in this talk will be the dependence of the minimum energy on the thickness and loading in the Foppl-von Karman model. I will prove upper and lower bounds for these scalings. The material for this talk is drawn from two papers in preparation; the work on indented cones is in collaboration with H. Olbermann and S. Conti.
  • Spectral representation of generalized Laguerre semigroups and hypocoercitivity

    Speaker: Pierre Patie (Cornell University) -

    When: Thu, October 1, 2015 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: The first aim of this to talk is to present an original methodology for developing the spectral representation of a class of non-self-adjoint (NSA) invariant semigroups. This class is defined in terms of self-similar semigroups on the positive real line and we name it the class of generalized Laguerre semigroups. Our approach is based on an in-depth analysis of an intertwinning relationship that we establish between this class and the classical Laguerre semigroup which is self-adjoint. We proceed by discussing substantial difficulties that one may face when studying the spectral representation of NSA operators.
    Finally, we also show that our approach enables us to get precise information regarding the speed of convergence towards stationarity. In particular, we observe in some cases the hypocoercivity phenomena which, in our context, can be interpreted in terms of the spectral norms.

  • Transonic problems on multidimensional conservation laws

    Speaker: Eun Heui Kim (California State University Long Beach) -

    When: Thu, September 24, 2015 - 3:30pm
    Where: Math 3206
  • Fractional thin film equations and hydraulic fractures

    Speaker: Antoine Mellet (UMD) -

    When: Thu, September 17, 2015 - 3:30pm
    Where: Math 3206
  • Nonlinear Schrödinger equations: The interplay of modeling, numerics and physics

    Speaker: Norbert Mauser (Wolfang Pauli Institute and Univ. of Vienna) -

    When: Fri, August 14, 2015 - 11:00am
    Where: Math 1311