A NOTE ON HOUSING WEALTH AND PRIVATE CONSUMPTION

This paper analyses the relationship between house prices and private consumption of the US economy. Based on Granger's causality test, we ask whether this relationship is driven by causality or whether it is merely an ambiguous connection. Based on latest quartely data, our results show that there is indeed a causal relationship with changes in house prices affeting private consumption, fundamentally supporting economic theory. Considering existing research, it is therefore suggested that the US economy is at the outset of a severe economic downturn, confirming pessimist's expectations.Wealth effect; House prices; Consumption; Granger causality

State Discrimination with Post-Measurement Information

We introduce a new state discrimination problem in which we are given additional information about the state after the measurement, or more generally, after a quantum memory bound applies. In particular, the following special case plays an important role in quantum cryptographic protocols in the bounded storage model: Given a string x encoded in an unknown basis chosen from a set of mutually unbiased bases, you may perform any measurement, but then store at most q qubits of quantum information. Later on, you learn which basis was used. How well can you compute a function f(x) of x, given the initial measurement outcome, the q qubits and the additional basis information? We first show a lower bound on the success probability for any balanced function, and any number of mutually unbiased bases, beating the naive strategy of simply guessing the basis. We then show that for two bases, any Boolean function f(x) can be computed perfectly if you are allowed to store just a single qubit, independent of the number of possible input strings x. However, we show how to construct three bases, such that you need to store all qubits in order to compute f(x) perfectly. We then investigate how much advantage the additional basis information can give for a Boolean function. To this end, we prove optimal bounds for the success probability for the AND and the XOR function for up to three mutually unbiased bases. Our result shows that the gap in success probability can be maximal: without the basis information, you can never do better than guessing the basis, but with this information, you can compute f(x) perfectly. We also exhibit an example where the extra information does not give any advantage at all.Comment: twentynine pages, no figures, equations galore. v2 thirtyone pages, one new result w.r.t. v

Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation

In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.Comment: 15 pages, 16 figure

Measuring Concentration in Data with an Exogenous Order

Concentration measures order the statistical units under observation according to their market share. However, there are situations where an order according to an exogenous variable is more appropriate or even required. The present article introduces a generalized definition of market concentration and defines a corresponding concentration measure. It is shown that this generalized concept of market concentration satisfies the common axioms of (classical) concentration measures. In an application example, the proposed approach is compared with classical concentration measures; the data are transfer spendings of German Bundesliga soccer teams, the ``obvious'' exogenous order of the teams is the league ranking