A Simulation Study of Some Biasing Parameters for the Ridge Type Estimation of Poisson Regression

This article proposes several estimators for estimating the ridge parameter k based on Poisson ridge regression (RR) model. These estimators have been evaluated by means of Monte Carlo simulations. As performance criteria, we have calculated the mean squared error (MSE), the mean value, and the standard deviation of k. The first criterion is commonly used, while the other two have never been used when analyzing Poisson RR. However, these performance criteria are very informative because, if several estimators have an equal estimated MSE, then those with low average value and standard deviation of k should be preferred. Based on the simulated results, we may recommend some biasing parameters that may be useful for the practitioners in the field of health, social, and physical sciences.     

Price bias and common practice in option pricing

Generally, the semiclosed-form option pricing formula for complex financial models depends on unobservable factors such as stochastic volatility and jump intensity. A popular practice is to use an estimate of these latent factors to compute the option price. However, in many situations this plug-and-play approximation does not yield the appropriate price. This article examines this bias and quantifies its impacts. We decompose the bias into terms that are related to the bias on the unobservable factors and to the precision of their point estimators. The approximated price is found to be highly biased when only the history of the stock price is used to recover the latent states. This bias is corrected when option prices are added to the sample used to recover the states' best estimate. We also show numerically that such a bias is propagated on calibrated parameters, leading to erroneous values. The Canadian Journal of Statistics 48: 8–35; 2020 © 2019 Statistical Society of Canada     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

Markov chain Monte Carlo methods for high dimensional inversion in remote sensing

Summary.  We discuss the inversion of the gas profiles (ozone, NO₃, NO₂, aerosols and neutral density) in the upper atmosphere from the spectral occultation measurements. The data are produced by the 'Global ozone monitoring of occultation of stars' instrument on board the Envisat satellite that was launched in March 2002. The instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10–20 km. The new feature is that these data allow the inversion of the gas concentration height profiles. A short introduction is given to the present operational data management procedure with examples of the first real data inversion. Several solution options for a more comprehensive statistical inversion are presented. A direct inversion leads to a non-linear model with hundreds of parameters to be estimated. The problem is solved with an adaptive single-step Markov chain Monte Carlo algorithm. Another approach is to divide the problem into several non-linear smaller dimensional problems, to run parallel adaptive Markov chain Monte Carlo chains for them and to solve the gas profiles in repetitive linear steps. The effect of grid size is discussed, and we present how the prior regularization takes the grid size into account in a way that effectively leads to a grid-independent inversion.     

Adaptive Management: A Paradigm for Remediation of Public Facilities Following a Terrorist Attack

Terrorist actions are aimed at maximizing harm (health, psychological, economical, and political) through the combined physical impacts of the act and fear. Immediate and effective response to a terrorist act is critical to limit human and environmental harm, effectively restore facility function, and maintain public confidence. Though there have been terrorist attacks in public facilities that we have learned from, overall our experiences in restoration of public facilities following a terrorist attack are limited. Restoration of public facilities following a release of a hazardous material is inherently far more complex than in industrial settings and has many unique technical, economic, social, and political challenges. For example, there may be a great need to quickly restore the facility to full operation and allow public access even though it was not designed for easy or rapid restoration, and critical information is needed for quantitative risk assessment and effective restoration must be anticipated to be incomplete and uncertain. Whereas present planning documents have substantial linearity in their organization, the “adaptive management” paradigm provides a constructive parallel paradigm for restoration of public facilities that anticipates and plans for uncertainty, inefficiencies, and stakeholder participation. Adaptive management grew out of the need to manage and restore natural resources in highly complex and changing environments with limited knowledge about causal relationships and responses to restoration actions. Similarities between natural resource management and restoration of a public facility after a terrorist attack suggest that integration of adaptive management principles explicitly into restoration processes will result in substantially enhanced and flexible responses necessary to meet the uncertainties of potential terrorist attacks.     

PATTERN RECOGNITION VIA ROBUST SMOOTHING WITH APPLICATION TO LASER DATA

Nowadays airborne laser scanning is used in many territorial studies, providing point data which may contain strong discontinuities. Motivated by the need to interpolate such data and preserve their edges, this paper considers robust nonparametric smoothers. These estimators, when implemented with bounded loss functions, have suitable jump‐preserving properties. Iterative algorithms are developed here, and are equivalent to nonlinear M‐smoothers, but have the advantage of resembling the linear Kernel regression. The selection of their coefficients is carried out by combining cross‐validation and robust‐tuning techniques. Two real case studies and a simulation experiment confirm the validity of the method; in particular, the performance in building recognition is excellent.     

Learning in experiments: Dynamic interaction of policy variables designed to deter tax evasion

While neoclassical economic theory sheds insight into the way that audit rates and penalty rates interact when individuals decide to declare income for taxation, it predicts far lower levels of compliance than observed levels of compliance. This paper analyses experimental responses to explore a dynamic interaction between audit and penalty rates as individuals learn how to comply with taxation. It compares the responses of subjects in experiments with responses that are predicted when individuals rely on an adaptive learning process (that offers information feedback about decision payoffs). This comparison suggests that learning is an important consideration when explaining differences between predicted and observed levels of tax compliance.     

C14. Moments of the kolmogorov-smirnov one-sample statistic

In adaptive estimation, it is often considered that an estimator has made a mistake if the component estimator chosen for use is not the most efficient for the distribution sampled. Theoretical and simulation results point to a fallacy in this line of thought. The Monte Carlo study involves extension of the Princeton Swindle to distributions conditional on a location and scale-free statistic, and to the uniform. The results give a partial explanation for the sometimes surprising robustness of adaptive L-estimators.     

Revisiting retesting in the estimation of proportions by group testing

In the estimation of a proportion p by group testing (pooled testing), retesting of units within positive groups has received little attention due to the minimal gain in precision compared to testing additional units. If acquisition of additional units is impractical or too expensive, and testing is not destructive, we show that retesting can be a useful option. We propose the retesting of a random grouping of units from positive groups, and compare it with nested halving procedures suggested by others. We develop an estimator of p for our proposed method, and examine its variance properties. Using simulation we compare retesting methods across a range of group testing situations, and show that for most realistic scenarios, our method is more efficient.     

Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data

In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out.