Abstract. We consider kernel density estimation in the multivariate case, focusing on the use of some elements of parametric estimation. We present a two-step method, based on a modification of the EM algorithm and the generalized kernel density estimator, and compare this method with a couple of well known multivariate kernel density estimation methods.

This paper addresses the problem of learning in greenhouse gas (GHG) emission inventories understood as reductions in uncertainty, i.e., inaccuracy and/or imprecision, over time. We analyze the National Inventory Reports (NIRs) submitted annually to the United Nations Framework Convention on Climate Change. Each NIR contains data on the GHG emissions in a given country for a given year as well as revisions of past years' estimates. We arrange the revisions, i.e., estimates of historical emissions published in consecutive NIRs into a table, so that each column contains revised estimates of emissions for the same year, reflecting different realizations of uncertainty. We propose two variants of a two-step procedure to investigate the changes of uncertainty over time. In step 1, we assess changes in inaccuracy, which we consider constant within each revision, by either detrending the revisions using the smoothing spline fitted to the most recent revision (method 1) or by taking differences between the most recent revision and the previous ones (method 2). Step 2 estimates the imprecision by analyzing the columns of the data table. We assess learning by detecting and modeling a decreasing trend in inaccuracy and/or imprecision. We analyze carbon dioxide (CO 2) emission inventories for the European Union (EU-15) as a whole and its individual member countries. Our findings indicate that although there is still room for improvement, continued efforts to improve accounting methodology lead to a reduction of uncertainty of emission estimates reported in NIRs, which is of key importance for monitoring the realization of countries' emission reduction commitments.

Abstract-The paper addresses the problem of uncertainty in the greenhouse gas emission inventories, by proposing an alternative method for assessing uncertainty and its evolution over time. To estimate the inventory accuracy, the revisions published in consecutive years are used. These revisions are considered nonstationary time series. We describe evolution by time-dependent models, used to analyze data from the National Inventory Reports published annually up to 2015, for selected EU countries. We present a parametric model and a procedure for estimating parameters, along with the results obtained.

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