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  • 5999n337h?file=thumbnail
    Creator: Uhlig, Harald, 1961-
    Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.)
    Number: 342
    Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X---- a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers (*) Xdl = U. In this paper we propose to interpret (*) as a Pettis integral. Using the corresponding Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vector-valued version of the law of large numbers for economies.
    Keyword: Random variable, Large numbers, L2 law of large numbers, Khinchines law of large numbers, Pettis integral, and Riemann integral
    Subject: C10 - Econometric and statistical methods : General - General
  • Vd66vz90d?file=thumbnail
    Creator: Uhlig, Harald, 1961-
    Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.)
    Number: 342
    Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X---- a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers (*) Xdl = U. In this paper we propose to interpret (*) as a Pettis integral. Using the corresponding Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vector-valued version of the law of large numbers for economies.
    Keyword: Random variable, Large numbers, L2 law of large numbers, Khinchines law of large numbers, Pettis integral, and Riemann integral
    Subject: C10 - Econometric and statistical methods : General - General