Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Validation of a semi-Lagrangian, canonical regression model of climates in the southwestern United States

EXTRACT (SEE PDF FOR FULL ABSTRACT): A local climate model (LCM) has been developed to simulate the modern and 18 ka climate of the southwestern United States. ... LCM solutions indicate summers were about 1°C cooler and winters 11°C cooler at 18 ka. Annual PREC increased 68% at 18 ka, with large increases in spring and fall PREC and diminished summer monsoonal PREC. ... Validation of simulations of 18 ka climate indicate general agreement with proxy estimates of climate for that time. However, the LCM estimates of summer temperatures are about 5 to 10°C higher than estimates from proxy reconstructions.

The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purching Power Parity.

This paper studies seemingly unrelated linear models with integrated regressors and stationary errors. By adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by feasible generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. Simulation results suggest that this new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of purchasing power parity (PPP) among the G-7 countries. The test based on the efficient estimates rejects the PPP hypothesis for most countries.

Aerosol indirect effects – general circulation model intercomparison and evaluation with satellite data

Aerosol indirect effects continue to constitute one of the most important uncertainties for anthropogenic climate perturbations. Within the international AEROCOM initiative, the representation of aerosol-cloud-radiation interactions in ten different general circulation models (GCMs) is evaluated using three satellite datasets. The focus is on stratiform liquid water clouds since most GCMs do not include ice nucleation effects, and none of the model explicitly parameterises aerosol effects on convective clouds. We compute statistical relationships between aerosol optical depth (τa) and various cloud and radiation quantities in a manner that is consistent between the models and the satellite data. It is found that the model-simulated influence of aerosols on cloud droplet number concentration (Nd ) compares relatively well to the satellite data at least over the ocean. The relationship between �a and liquid water path is simulated much too strongly by the models. This suggests that the implementation of the second aerosol indirect effect mainly in terms of an autoconversion parameterisation has to be revisited in the GCMs. A positive relationship between total cloud fraction (fcld) and �a as found in the satellite data is simulated by the majority of the models, albeit less strongly than that in the satellite data in most of them. In a discussion of the hypotheses proposed in the literature to explain the satellite-derived strong fcld–�a relationship, our results indicate that none can be identified as a unique explanation. Relationships similar to the ones found in satellite data between �a and cloud top temperature or outgoing long-wave radiation (OLR) are simulated by only a few GCMs. The GCMs that simulate a negative OLR - �a relationship show a strong positive correlation between �a and fcld. The short-wave total aerosol radiative forcing as simulated by the GCMs is strongly influenced by the simulated anthropogenic fraction of �a, and parameterisation assumptions such as a lower bound on Nd . Nevertheless, the strengths of the statistical relationships are good predictors for the aerosol forcings in the models. An estimate of the total short-wave aerosol forcing inferred from the combination of these predictors for the modelled forcings with the satellite-derived statistical relationships yields a global annual mean value of −1.5±0.5Wm−2. In an alternative approach, the radiative flux perturbation due to anthropogenic aerosols can be broken down into a component over the cloud-free portion of the globe (approximately the aerosol direct effect) and a component over the cloudy portion of the globe (approximately the aerosol indirect effect). An estimate obtained by scaling these simulated clearand cloudy-sky forcings with estimates of anthropogenic �a and satellite-retrieved Nd–�a regression slopes, respectively, yields a global, annual-mean aerosol direct effect estimate of −0.4±0.2Wm−2 and a cloudy-sky (aerosol indirect effect) estimate of −0.7±0.5Wm−2, with a total estimate of −1.2±0.4Wm−2.

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

A national satellite-based land-use regression model for air pollution exposure assessment in Australia

Land-use regression (LUR) is a technique that can improve the accuracy of air pollution exposure assessment in epidemiological studies. Most LUR models are developed for single cities, which places limitations on their applicability to other locations. We sought to develop a model to predict nitrogen dioxide (NO2) concentrations with national coverage of Australia by using satellite observations of tropospheric NO2 columns combined with other predictor variables. We used a generalised estimating equation (GEE) model to predict annual and monthly average ambient NO2 concentrations measured by a national monitoring network from 2006 through 2011. The best annual model explained 81% of spatial variation in NO2 (absolute RMS error=1.4 ppb), while the best monthly model explained 76% (absolute RMS error=1.9 ppb). We applied our models to predict NO2 concentrations at the ~350,000 census mesh blocks across the country (a mesh block is the smallest spatial unit in the Australian census). National population-weighted average concentrations ranged from 7.3 ppb (2006) to 6.3 ppb (2011). We found that a simple approach using tropospheric NO2 column data yielded models with slightly better predictive ability than those produced using a more involved approach that required simulation of surface-to-column ratios. The models were capable of capturing within-urban variability in NO2, and offer the ability to estimate ambient NO2 concentrations at monthly and annual time scales across Australia from 2006–2011. We are making our model predictions freely available for research.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Estimation for the general sample selection models

Consider a general regression model with an arbitrary and unknown link function and a stochastic selection variable that determines whether the outcome variable is observable or missing. The paper proposes U-statistics that are based on kernel functions as estimators for the directions of the parameter vectors in the link function and the selection equation, and shows that these estimators are consistent and asymptotically normal.

Land use regression model (LUR) for ultrafine particles in Brisbane

Traffic-related air pollution has been associated with a wide range of adverse health effects. One component of traffic emissions that has been receiving increasing attention is ultrafine particles(UFP, < 100 nm), which are of concern to human health due to their small diameters. Vehicles are the dominant source of UFP in urban environments. Small-scale variation in ultrafine particle number concentration (PNC) can be attributed to local changes in land use and road abundance. UFPs are also formed as a result of particle formation events. Modelling the spatial patterns in PNC is integral to understanding human UFP exposure and also provides insight into particle formation mechanisms that contribute to air pollution in urban environments. Land-use regression (LUR) is a technique that can use to improve the prediction of air pollution.

Mechanisms of formation of the Arabian Sea mini warm pool in a high-resolution Ocean General Circulation Model

An Ocean General Circulation Model of the Indian Ocean with high horizontal (0.25 degrees x 0.25 degrees) and vertical (40 levels) resolutions is used to study the dynamics and thermodynamics of the Arabian Sea mini warm pool (ASMWP), the warmest region in the northern Indian Ocean during January-April. The model simulates the seasonal cycle of temperature, salinity and currents as well as the winter time temperature inversions in the southeastern Arabian Sea (SEAS) quite realistically with climatological forcing. An experiment which maintained uniform salinity of 35 psu over the entire model domain reproduces the ASMWP similar to the control run with realistic salinity and this is contrary to the existing theories that stratification caused by the intrusion of low-salinity water from the Bay of Bengal into the SEAS is crucial for the formation of ASMWP. The contribution from temperature inversions to the warming of the SEAS is found to be negligible. Experiments with modified atmospheric forcing over the SEAS show that the low latent heat loss over the SEAS compared to the surroundings, resulting from the low winds due to the orographic effect of Western Ghats, plays an important role in setting up the sea surface temperature (SST) distribution over the SEAS during November March. During March-May, the SEAS responds quickly to the air-sea fluxes and the peak SST during April-May is independent of the SST evolution during previous months. The SEAS behaves as a low wind, heat-dominated regime during November-May and, therefore, the formation and maintenance of the ASMWP is not dependent on the near surface stratification.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds acid precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%-20% weaker than observed, The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a targe amount of high-frequency intraseasonal variations, While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency EI Nino-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15 degrees west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Indian Ocean dipole mode events in an ocean general circulation model

The evolution of the dipole mode (DM) events in the Indian Ocean is examined using an ocean model that is driven by the NCEP fluxes for the period 1975-1998. The positive DM events during 1997, 1994 and 1982 and negative DM events during 1996 and 1984-1985 are captured by the model and it reproduces both the surface and subsurface features associated with these events. In its positive phase, the DM is characterized by warmer than normal SST in the western Indian Ocean and cooler than normal SST in the eastern Indian Ocean. The DM events are accompanied by easterly wind anomalies along the equatorial Indian Ocean and upwelling-favorable alongshore wind anomalies along the coast of Sumatra. The Wyrtki jets are weak during positive DM events, and the thermocline is shallower than normal in the eastern Indian Ocean and deeper in the west. This anomaly pattern reverses during negative DM events. During the positive phase of the DM easterly wind anomalies excite an upwelling equatorial Kelvin wave. This Kelvin wave reflects from the eastern boundary as an upwelling Rossby wave which propagates westward across the equatorial Indian Ocean. The anomalies in the eastern Indian Ocean weaken after the Rossby wave passes. A similar process excites a downwelling Rossby wave during the negative phase. This Rossby wave is much weaker but wind forcing in the central equatorial Indian Ocean amplifies the downwelling and increases its westward phase speed. This Rossby wave initiates the deepening of the thermocline in the western Indian Ocean during the following positive phase of the DM. Rossby wave generated in the southern tropical Indian Ocean by Ekman pumping contributes to this warming. Concurrently, the temperature equation of the model shows upwelling and downwelling to be the most important mechanism during both positive events of 1994 and 1997. (C) 2002 Elsevier Science Ltd. All rights reserved.