Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model

2000 Mathematics Subject Classification: Primary: 62M10, 62J02, 62F12, 62M05, 62P05, 62P10; secondary: 60G46, 60F15.

Stochastic structure and individual-tree growth models

The majority of past and current individual-tree growth modelling methodologies have failed to characterise and incorporate structured stochastic components. Rather, they have relied on deterministic predictions or have added an unstructured random component to predictions. In particular, spatial stochastic structure has been neglected, despite being present in most applications of individual-tree growth models. Spatial stochastic structure (also called spatial dependence or spatial autocorrelation) eventuates when spatial influences such as competition and micro-site effects are not fully captured in models. Temporal stochastic structure (also called temporal dependence or temporal autocorrelation) eventuates when a sequence of measurements is taken on an individual-tree over time, and variables explaining temporal variation in these measurements are not included in the model. Nested stochastic structure eventuates when measurements are combined across sampling units and differences among the sampling units are not fully captured in the model. This review examines spatial, temporal, and nested stochastic structure and instances where each has been characterised in the forest biometry and statistical literature. Methodologies for incorporating stochastic structure in growth model estimation and prediction are described. Benefits from incorporation of stochastic structure include valid statistical inference, improved estimation efficiency, and more realistic and theoretically sound predictions. It is proposed in this review that individual-tree modelling methodologies need to characterise and include structured stochasticity. Possibilities for future research are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Stochastic time-concentration activity models for cytotoxicity in 3D brain cell cultures.

BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

Body mass index, abdominal adiposity and blood pressure: consistency of their association across developing and developed countries.

BACKGROUND: Obesity is increasing worldwide because developing countries are adopting Western high-fat foods and sedentary lifestyles. In parallel, in many of them, hypertension is rising more rapidly, particularly with age, than in Western countries. OBJECTIVE: To assess the relationship between adiposity and blood pressure (BP) in a developing country with high average BP (The Seychelles, Indian Ocean, population mainly of African origin) in comparison to a developed country with low average BP (Switzerland, population mainly of Caucasian origin). DESIGN: Cross-sectional health examination surveys based on population random samples. SETTING: The main Seychelles island (Mahé) and two Swiss regions (Vaud-Fribourg and Ticino). SUBJECTS: Three thousand one hundred and sixteen adults (age range 35-64) untreated for hypertension. MEASUREMENTS: Body mass index (BMI), waist circumference (WC), waist-to-hip ratio (WHR), systolic and diastolic blood pressure (SBP and DBP, mean of two measures). METHODS: Scatterplot smoothing techniques and gender-specific linear regression models. RESULTS: On average, SBP and DBP were found to increase linearly over the whole variation range of BMI, WHR and WC. A modest, but statistically significant linear association was found between each indicator of adiposity and BP levels in separate regression models controlling for age. The regression coefficients were not significantly different between the Seychelles and the two Swiss regions, but were generally higher in women than in men. For the latter, a gain of 1.7 kg/m(2) in BMI, of 4.5 cm in WC or of 3.4% in WHR corresponded to an elevation of 1 mmHg in SBP. For women, corresponding figures were 1.25 kg/m(2), 2.5 cm and 1.8% respectively. Regression coefficients for age reflected a higher effect of this variable on both SBP and DBP in the Seychelles than in Switzerland. CONCLUSION: These findings suggest a stable linear relation of adiposity with BP, independent of age and body fat distribution, across developed and developing countries. The more rapid increase of BP with age observed in the latter countries are likely to reflect higher genetic susceptibility and/or higher cumulative exposure to another risk factor than adiposity.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.

Uncertainty Quantification with Support Vector Regression Prediction Models

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. The paper considers a data driven approach in modelling uncertainty in spatial predictions. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic features and describe stochastic variability and non-uniqueness of spatial properties. It is able to capture and preserve key spatial dependencies such as connectivity, which is often difficult to achieve with two-point geostatistical models. Semi-supervised SVR is designed to integrate various kinds of conditioning data and learn dependences from them. A stochastic semi-supervised SVR model is integrated into a Bayesian framework to quantify uncertainty with multiple models fitted to dynamic observations. The developed approach is illustrated with a reservoir case study. The resulting probabilistic production forecasts are described by uncertainty envelopes.

Evolutionary synthesis of stochastic gene network models using feature-based search spaces

A feature-based fitness function is applied in a genetic programming system to synthesize stochastic gene regulatory network models whose behaviour is defined by a time course of protein expression levels. Typically, when targeting time series data, the fitness function is based on a sum-of-errors involving the values of the fluctuating signal. While this approach is successful in many instances, its performance can deteriorate in the presence of noise. This thesis explores a fitness measure determined from a set of statistical features characterizing the time series' sequence of values, rather than the actual values themselves. Through a series of experiments involving symbolic regression with added noise and gene regulatory network models based on the stochastic 'if-calculus, it is shown to successfully target oscillating and non-oscillating signals. This practical and versatile fitness function offers an alternate approach, worthy of consideration for use in algorithms that evaluate noisy or stochastic behaviour.