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Nonparametric estimation procedures that can flexibly account for varying levels of smoothness among different functional parameters, such as penalized likelihoods, have been developed in a variety of settings. However, geometric constraints on power spectra have limited the development of such methods when estimating the power spectrum of a vector-valued time series. This article introduces a penalized likelihood approach to nonparametric multivariate spectral analysis through the minimization of a penalized Whittle negative loglikelihood. This likelihood is derived from the large-sample distribution of the periodogram and includes a penalty function that forms a measure of regularity on multivariate power spectra. The approach allows for varying levels of smoothness among spectral components while accounting for the positive definiteness of spectral matrices and the Hermitian and periodic structures of power spectra as functions of frequency. The consistency of the proposed estimator is derived and its empirical performance is demonstrated in a simulation study and in an analysis of indoor air quality.

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Aging water infrastructure and increased water scarcity have resulted in higher interest in water reuse and decentralization. Rating systems for high-performance buildings implicitly promote the use of building-scale, decentralized water supply and treatment technologies. It is important to recognize the potential benefits and trade-offs of decentralized and centralized water systems in the context of high-performance buildings. For this reason and to fill a gap in the current literature, we completed a life cycle assessment (LCA) of the decentralized water system of a high-performance, net-zero energy, net-zero water building (NZB) that received multiple green building certifications and compared the results with two modeled buildings (conventional and water efficient) using centralized water systems. We investigated the NZB's impacts over varying lifetimes, conducted a break-even analysis, and included Monte Carlo uncertainty analysis. The results show that, although the NZB performs better in most categories than the conventional building, the water efficient building generally outperforms the NZB. The lifetime of the NZB, septic tank aeration, and use of solar energy have been found to be important factors in the NZB's impacts. While these findings are specific to the case study building, location, and treatment technologies, the framework for comparison of water and wastewater impacts of various buildings can be applied during building design to aid decision making. As we design and operate high-performance buildings, the potential trade-offs of advanced decentralized water treatment systems should be considered.

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