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     

Book Reviews

Books reviewed:
M Hollander and D Wolfe, Nonparametric Statistical Methods
T Leonard and J.S.J Hsu, Bayesian Methods     

Quadratic estimators of covariance components in a multivariate mixed linear model

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

ABSTRACT.  This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non-compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.     

Mapping water quality by local scoring

The mean density of bacteria in a water body is commonly monitored using quantal assay. This paper describes the use of local scoring in estimating the spatial distribution of mean density from quantal assay results at a set of point locations. An application to estimating the mean density of fecal conform bacteria in a coastal pond is presented. Model diagnostics based on a parametric bootstrap are also presented.     

Two phase parametric and probabilistic NPV calculations, with possible deferral of disposal of UK nuclear waste as an example

This paper illustrates the value of several particular features of a first phase parametric approach to discounted cash flow (DCF) decision analysis when significant uncertainty is involved. It also illustrates the value of second phase probabilistic approaches to selected parameters for five quite different example reasons. The most controversial example reason concerns the discount rate. The particular example used to illustrate both phases may stimulate general interest because of the important issues involved, but it is argued that the two phase approach as a whole has a wide range of applications for decisions large and small.     

我国环境刑罚轻缓化探析

毋庸置疑,在整个国际社会对环境犯罪处以轻缓刑罚的背景下,我国亦应该对环境刑罚采用轻缓化的原则。诚然,我国的环境刑罚制度与其他国家相比还有许多亟待完善的地方,但这并不妨碍我们在借鉴其他国家先进的立法经验的基础上构建适合我国具体国情的环境刑罚制度。在环境刑罚中要突出自由刑的适用,扩大并完善财产刑的适用,明确财产刑中过于模糊的规定,逐步改善环境犯罪的刑事处罚措施过于单一的缺点和功能上的不足,同时提高对辅助刑罚措施的关注。在环境犯罪方面,在适用传统刑罚措施惩治的基础上配合适用辅助刑罚措施,使我国环境刑罚轻缓化实践不至于成为一纸空谈。     

A bootstrap control chart for inverse Gaussian percentiles

The conventional Shewhart-type control chart is developed essentially on the central limit theorem. Thus, the Shewhart-type control chart performs particularly well when the observed process data come from a near-normal distribution. On the other hand, when the underlying distribution is unknown or non-normal, the sampling distribution of a parameter estimator may not be available theoretically. In this case, the Shewhart-type charts are not available. Thus, in this paper, we propose a parametric bootstrap control chart for monitoring percentiles when process measurements have an inverse Gaussian distribution. Through extensive Monte Carlo simulations, we investigate the behaviour and performance of the proposed bootstrap percentile charts. The average run lengths of the proposed percentage charts are investigated.