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This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model (due to Baltagi 1995) to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator (WPLSE) and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator (PLSE), and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator (LPE). The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Carroll (2000), ignoring the correlation structure entirely and "pretending" that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups. Some simulation studies are conducted to illustrate the finite sample performances of the proposed procedures. [ABSTRACT FROM AUTHOR]

Insight into the causes and consequences of changes in aquatic biodiversity requires an improved understanding of the nature of the relationships between species richness and ecosystem function over a much longer temporal perspective than we currently possess. We used high-resolution paleoecological records from two prairie lakes to show that diatom species richness (as fossil frustules) was negatively correlated (r² = 0.09-0.24, p < 0.001) with diatom production (as fossil pigments) during the past 2,000 yr. By comparing analyses from intervals of fresh and saline waters, we demonstrate that these significant richness-production relationships arose during freshwater periods (r² = 0.13-0.45, p < 0.001) and could be eliminated (r² < 0.02, p > 0.1) by abiotic disturbances such as droughts. Procrustes analyses of the concordance of species change within freshwater communities and the change in richness--production relationships through time revealed that shifts in diatom community composition could have a large influence in determining the negative relationship between richness and production. Finally, significant correlations (r² = 0.09-0.24, p < 0.0001) between past diatom species richness and ratios of stable isotopes (primarily δ15N) suggested that C and N biogeochemical cycles are also linked to changes in algal biodiversity. Taken together, these analyses suggest that the ongoing disruption of climate and biogeochemical systems by humans may obscure the relationship between aquatic biodiversity and ecosystem function in the future. [ABSTRACT FROM AUTHOR]