Quantile regression estimation of partially linear additive models

In this paper, we consider the estimation of partially linear additive quantile regression models where the conditional quantile function comprises a linear parametric component and a nonparametric additive component. We propose a two-step estimation approach: in the first step, we approximate the conditional quantile function using a series estimation method. In the second step, the nonparametric additive component is recovered using either a local polynomial estimator or a weighted Nadaraya–Watson estimator. Both consistency and asymptotic normality of the proposed estimators are established. Particularly, we show that the first-stage estimator for the finite-dimensional parameters attains the semiparametric efficiency bound under homoskedasticity, and that the second-stage estimators for the nonparametric additive component have an oracle efficiency property. Monte Carlo experiments are conducted to assess the finite sample performance of the proposed estimators. An application to a real data set is also illustrated.     

Dynamic generalized linear models with application to environmental epidemiology

Summary. We propose modelling short-term pollutant exposure effects on health by using dynamic generalized linear models. The time series of count data are modelled by a Poisson distribution having mean driven by a latent Markov process; estimation is performed by the extended Kalman filter and smoother. This modelling strategy allows us to take into account possible overdispersion and time-varying effects of the covariates. These ideas are illustrated by reanalysing data on the relationship between daily non-accidental deaths and air pollution in the city of Birmingham, Alabama.     

Oil and gas depletion: Diffusion models and forecasting under strategic intervention

Crude oil and natural gas depletion may be modelled by a diffusion process based upon a constrained life-cycle. Here we consider the Generalized Bass Model. The choice is motivated by the realistic assumption that there is a self-evident link between oil and gas extraction and the spreading of the modern technologies in wide areas such as transport, heating, cooling, chemistry and hydrocarbon fuels consumption. Such a model may include deterministic or semi-deterministic regulatory interventions. Statistical analysis is based upon nonlinear methodologies and more flexible autoregressive structure of residuals. The technical aim of this paper is to outline the meaningful hierarchy existing among the components of such diffusion models. Statistical effort in residual component analysis may be read as a significant confirmation of a well-founded diffusion process under rare but strong deterministic shocks. Applications of such ideas are proposed with reference to world oil and gas production data and to particular regions such as mainland U.S.A., U.K., Norway and Alaska. The main results give new evidence in time-peaks location and in residual times to depletion.     

Solution to the hazard function of some two-stage carcinogenesis models when normal cell growth is piecewise linear

A closed form expression is obtained for the hazard function for three stochastic two-stage carcinogenesis models, when the normal cell growth is assumed to be piecewise linear.     

A self-normalizing approach to the specification test of mixed-frequency models

In econometrics and finance, variables are collected at different frequencies. One straightforward regression model is to aggregate the higher frequency variable to match the lower frequency with a fixed weight function. However, aggregation with fixed weight functions may overlook useful information in the higher frequency variable. On the other hand, keeping all higher frequencies may result in overly complicated models. In literature, mixed data sampling (MIDAS) regression models have been proposed to balance between the two. In this article, a new model specification test is proposed that can help decide between the simple aggregation and the MIDAS model.     

Causality and interdependence analysis in linear econometric models with an application to fertility

This paper is an applied analysis of the causal structure of linear multi-equational econometric models. Its aim is to identify the kind of relationships linking the endogenous variables of the model, distinguishing between causal links and feedback loops. The investigation is first carried out within a deterministic framework and then moves on to show how the results may change inside a more realistic stochastic context. The causal analysis is then specifically applied to a linear simultaneous equation model explaining fertility rates. The analysis is carried out by means of a specific RATS programming code designed to show the specific nature of the relationships within the model.     

Parametric relative survival regression using generalized linear models with application to Hodgkin's lymphoma

Changes in survival rates during 1940–1992 for patients with Hodgkin's disease are studied by using population-based data. The aim of the analysis is to identify when the breakthrough in clinical trials of chemotherapy treatments started to increase population survival rates, and to find how long it took for the increase to level off, indicating that the full population effect of the breakthrough had been realized. A Weibull relative survival model is used because the model parameters are easily interpretable when assessing the effect of advances in clinical trials. However, the methods apply to any relative survival model that falls within the generalized linear models framework. The model is fitted by using modifications of existing software (SAS, GLIM) and profile likelihood methods. The results are similar to those from a cause-specific analysis of the data by Feuer and co-workers. Survival started to improve around the time that a major chemotherapy breakthrough (nitrogen mustard, Oncovin, prednisone and procarbazine) was publicized in the mid 1960s but did not level off for 11 years. For the analysis of data where the cause of death is obtained from death certificates, the relative survival approach has the advantage of providing the necessary adjustment for expected mortality from causes other than the disease without requiring information on the causes of death.     

Econometric approaches to the specification of life-cycle labour supply and commodity demand behaviour

Many of the recently developed alternative ecocometric approaches to the construction and estimation of life-cycle consistent models using individual data can be viewed as alternative choices for conditioning variables that summarise past decisions and future anticipations. By ingenious choice of this conditioning variable and by exploitation of the duality relationships between the alternative specifications, many currently available micro-data sets can be used for the estimation of life-cycle consistent models. In reviewing the alternative approaches their stochastic properties and implicit preference restrictions are highlighted. Indeed, empirical specifications that are parameterised in a form of direct theoretical interest often can be shown to be unnecessarily restrictive while dual representations may provide more flexible econometric models. These results indicate the particular advantages of different types of data in retrieving life-cycle consistent preference parameters and the appropriate, most flexible, econometric approach for each type of data. A methodology for relaxing the intertemporal separability assumption is developed and the advantages and disadvantages of alternative approaches in this framework are considered.     

On the estimation of variance parameters in non-standard generalised linear mixed models: application to penalised smoothing

Statistics and Computing - We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (J Am Stat Assoc...     

On additive and multiplicative damage models and the characterizations of linear and logarithmic exponential families

Rao (1963) has formulated a damage model which we call an additive damage model. A suitable damage model, which we call a multiplicative damage model, has been considered by Krishnaji (1970) for income-related problems. In these models, an original observation is subjected to damage, e.g., death or under-reporting, according to a specified probability law. Within the framework of an additive damage model, with a special form of damage, characterizations of the linear and logarithmic exponential families are formulated using regression properties of the damaged part on the undamaged part. The characterizations of the gamma and Pareto distributions that have been found of some use in the theory of income distributions, are obtained as special cases. Similar results are investigated within the framework of the multiplicative damage model.     

Least absolute value regression: a special case of piecewise linear minimization

The Barrodale and Roberts algorithm for least absolute value (LAV) regression and the algorithm proposed by Bartels and Conn both have the advantage that they are often able to skip across points at which the conventional simplex-method algorithms for LAV regression would be required to carry out an (expensive) pivot operation.

We indicate here that this advantage holds in the Bartels-Conn approach for a wider class of problems: the minimization of piecewise linear functions. We show how LAV regression, restricted LAV regression, general linear programming and least maximum absolute value regression can all be easily expressed as piecewise linear minimization problems.     

Statistical models for disaggregation and reaggregation of natural gas consumption data

In this paper, we present a unified framework for natural gas consumption modeling and forecasting. This consists of models of GAM class and their nonlinear extension, tailored for easy estimation, aggregation and treatment of the delayed relationship between temperature and consumption. Since the consumption data for households and small commercial customers are routinely available in many countries only as long-term sum meter readings, their disaggregation and possibly reaggregation to different time intervals is necessary for a variety of purposes. We show some examples of specific models based on the presented framework and then we demonstrate their use in practice, especially for the disaggregation and reaggregation tasks.     

A restricted Liu estimator for binary regression models and its application to an applied demand system

In this article, we propose a restricted Liu regression estimator (RLRE) for estimating the parameter vector, β, in the presence of multicollinearity, when the dependent variable is binary and it is suspected that β may belong to a linear subspace defined by Rβ?=?r. First, we investigate the mean squared error (MSE) properties of the new estimator and compare them with those of the restricted maximum likelihood estimator (RMLE). Then we suggest some estimators of the shrinkage parameter, and a simulation study is conducted to compare the performance of the different estimators. Finally, we show the benefit of using RLRE instead of RMLE when estimating how changes in price affect consumer demand for a specific product.     

Econometric approaches to the specification of life cycle labour supply and commodity demand behaviour

Many of the recently developed alternative econometric approaches to the construction and estimation of life-cycle consistent models using individual data can be viewed as alternative choices for conditioning variables that summarise past decisions and future anticipations. By ingenious choice of this conditioning variable and by exploitation of the duality relationships between the alternative specifications, many currently available micro-data sets can be used for the estimation of life-cycle consistent models. In reviewing the alternative approaches their stochastic properties and implict preference restrictions are highlighted. Indeed, empirical specifications that are parameterised in a form of direct theoretical interest often can be shown to be unnecessarily restrictive while dual representations may provide more flexible econometric models. These results indicate the particular advantages of different types of data in retrieving life-cycle consistent preference parameters and the appropriate, most flexible, econometric approach for each type of data. A methodology for relaxing the intertemporal separability assumption is developed and the advantages and disadvantages of alternative approaches in this framework are considered.     

Missing data and forecasting in multivariate time series: An application of the common components dynamic linear model

Summary The paper deals with missing data and forecasting problems in multivariate time series making use of the Common Components Dynamic Linear Model (DLMCC), presented in Quintana (1985), and West and Harrison (1989). Some results are presented and discussed: exploiting the correlation between series, estimated by the DLMCC, the paper shows as it is possible to update state vector posterior distributions for the unobserved series. This is realized on the base of the updating of the observed series state vectors, for which the usual Kalman filter equations can be applied. An application concerning some Italian private consumption series provides an example of the model capabilities.     

Application of generalized additive models to butterfly transect count data

We investigate the use of generalized additive models for describing patterns in butterfly transect counts during the flight period. Models were applied to sets of simulated data and to transect counts from the British Butterfly Monitoring Scheme (BMS) recorded at a large number of sites in the UK. The models successfully described patterns in counts in a range of species with different life cycles and the approach can be used to estimate an index of butterfly abundance allowing for missing counts. The method could be extended to include other factors such as temperature, sunshine, windspeed and time of day, and to examine potential biases arising from variation in these factors.     

Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data

We analyse data on abortion rate (AR) in Italy with a particular focus on different behaviours in different regions in Italy. The aim is to try to reveal the relationship between the AR and several covariates that describe in some way the modernity of the region and the condition of the women there. The data are mostly underdispersed and the degree of underdispersion also varies with the covariates. To analyse these data, recent techniques for flexible modelling of a mean and dispersion function in a double exponential family framework are further developed now in a generalized additive model context for dealing with the multivariate set-up. The appealing unified framework and approach even allow to semi-parametric modelling of the covariates without any additional efforts. The methodology is illustrated on ozone-level data and leads to interesting findings in the Italian abortion data.