Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb{N }=\{1, 2, 3, \ldots \}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="double-struck">N</mi> <mo>=</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo stretchy="false">}</mo> </mrow> </math> </EquationSource> </InlineEquation>. Let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\{X, X_{n}; n \in \mathbb N \}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">{</mo> <mi>X</mi> <mo>,</mo> <msub> <mi>X</mi> <mi>n</mi> </msub> <mo>;</mo> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> <mo stretchy="false">}</mo> </mrow> </math> </EquationSource> </InlineEquation> be a sequence of i.i.d. random variables, and let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$S_{n}=\sum _{i=1}^{n}X_{i}, n \in \mathbb N $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>S</mi> <mi>n</mi> </msub> <mo>=</mo> <msubsup> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math> </EquationSource> </InlineEquation>....</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting...

Nabil Al-Najjar (2008) showed how games with countably infinite player sets can be used to approximate games with large finite player sets. Unfortunately, we have found an error in the proof of Al-Najjarʼs Theorem 5. In this correction we discuss the error and offer two slightly weaker versions...

The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the...

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of...

We prove a law of large numbers for a class of Zd-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called conditional cone-mixing and that the random walk tends to stay inside wide enough space–time...

Nicolas Bernoulli suggested the St Petersburg game, nearly 300 years ago, which is widely believed to produce a paradox in decision theory. This belief stems from a long standing mathematical error in the original calculation of the expected value of the game. This article argues that, in...

Consider an i.i.d. random field {Xk:k∈Z+d}, together with a sequence of unboundedly increasing nested sets Sj=⋃k=1jHk,j≥1, where the sets Hj are disjoint. The canonical example consists of the hyperbolas Hj={k∈Z+d:|k|=j}. We are interested in the number of “hyperbolas” Hj that...

Let X1,…,Xn be i.i.d. copies of random variable X where 0E|X|∞ and let X̄=1n∑i=1nXi. One can show that X1−X̄,…,Xn−X̄ are exchangeable, and as a result identically distributed, but not independent. We use this result to prove that for n≥3, X is symmetric about a point if and only...