Semiparametric regression analysis with missing response at random

We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases: a semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal. The three special estimators have the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoskedastic Gaussian case. We show that the Jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, that severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed estimators and the related estimators.

An introduction to simulation of risk processes

A typical model for insurance risk, the so-called collective risk model, has two main components: one characterizing the frequency (or incidence) of events and another describing the severity (or size or amount) of gain or loss resulting from the occurrence of an event. Here we focus on simulating the point process N(t) of the incidence of events. We discuss five prominent examples of N(t), namely the classical (homogeneous) Poisson process, the non-homogeneous Poisson process, the mixed Poisson process, the Cox process (also called the doubly stochastic Poisson process) and the renewal process.Collective risk model; Poisson process; Non-homogeneous Poisson process; Mixed Poisson process; Cox process; Renewal process;

Transactions That Did Not Happen and Their Influence on Prices

This paper studies data from the wholesale fruit and vegetables market in Marseille. We have details of counteroffers to the prices that were proposed by the seller even when no transaction took place. With a simple heoretical model we analyse the evolution of prices during the day and in particular the relation between the final price struck and the proposals of the two parties. Periods with no buyer refusals, of offers or bargaining with no transaction will lead to a revision of the sellerÕs first price. More importantly the sharing of the surplus moves in the buyerÕs favour during the day. These presumptions are then shown to be confirmed by our data set.bargaining, markets

Forecasting in Blockchain-Based Local Energy Markets

Increasingly volatile and distributed energy production challenges traditional mechanisms to manage grid loads and price energy. Local energy markets (LEMs) may be a response to those challenges as they can balance energy production and consumption locally and may lower energy costs for consumers. Blockchain-based LEMs provide a decentralized market to local energy consumer and prosumers. They implement a market mechanism in the form of a smart contract without the need for a central authority coordinating the market. Recently proposed blockchain-based LEMs use auction designs to match future demand and supply. Thus, such blockchain-based LEMs rely on accurate short-term forecasts of individual households’ energy consumption and production. Often, such accurate forecasts are simply assumed to be given. The present research tested this assumption by first evaluating the forecast accuracy achievable with state-of-the-art energy forecasting techniques for individual households and then, assessing the effect of prediction errors on market outcomes in three different supply scenarios. The evaluation showed that, although a LASSO regression model is capable of achieving reasonably low forecasting errors, the costly settlement of prediction errors can offset and even surpass the savings brought to consumers by a blockchain-based LEM. This shows that, due to prediction errors, participation in LEMs may be uneconomical for consumers, and thus, has to be taken into consideration for pricing mechanisms in blockchain-based LEMs.Peer Reviewe

Applied Nonparametric Methods

We review different approaches to nonparametric density and regression estimation. Kernel estimators are motivated from local averaging and solving ill-posed problems. Kernel estimators are compared to k-NN estimators, orthogonal series and splines. Pointwise and uniform confidence bands are described, and the choice of smoothing parameter is discussed. Finally, the method is applied to nonparametric prediction of time series and to semiparametric estimation.

Derivative estimation and testing in generalized additive models

Estimation and testing procedures for generalized additive (interaction) model are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets

Structural tests in additive regression

We consider the component analysis problem for a regression model with an additive structure. The problem is to test if some of the additive components is of polynomial structure, e.g. linear, without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The presented method is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the design and smoothness of the regression function. The results demonstrate that each component of the model can be tested with the rate corresponding to the case if all the remaining components were known. The proposed procedure is also computationally straightforward. Simulation results and a real data example about female labor supply demonstrate the good performance of the test