Reducing bias of the maximum-likelihood estimation for the truncated Pareto distribution

The Pareto distribution is an important distribution in statistics, which has been widely used in finance, physics, hydrology, geology, astronomy, and so on. Even though the parameter estimation for the Pareto distribution has been well established in the literature, the estimation problem for the truncated Pareto distribution becomes complex. This article investigates the bias and mean-squared error of the maximum-likelihood estimation for the truncated Pareto distribution, and some useful results are obtained.     

Determining Process Death Based on Censored Activity Data

This article addresses the problem of estimating the time of apparent death in a binary stochastic process. We show that, when only censored data are available, a fitted logistic regression model may estimate the time of death incorrectly. We improve this estimation by utilizing discrete-event simulation to produce simulated complete time series data. The proposed methodology may be applied to situations where time of death cannot be formally determined and has to be estimated based on prolonged inactivity. As an illustration, we use observed monthly activity patterns from 300 real Open Source Software development projects sampled from Sourceforge.net.     

Testing the Equality of the Noncentrality Parameters of Two Noncentral t-Distributions with Identical Degrees of Freedom

The problem of testing the equality of the noncentrality parameters of two noncentral t-distributions with identical degrees of freedom is considered, which arises from the comparison of two signal-to-noise ratios for simple linear regression models. A test procedure is derived that is guaranteed to maintain Type I error while having only minimal amounts of conservativeness, and comparisons are made with several other approaches to this problem based on variance stabilizing transformations. The new procedure derived in this article is shown to have good properties and will be useful for practitioners.     

Semiparametric multiple kernel estimators and model diagnostics for count regression functions

Abstract

This study concerns semiparametric approaches to estimate discrete multivariate count regression functions. The semiparametric approaches investigated consist of combining discrete multivariate nonparametric kernel and parametric estimations such that (i) a prior knowledge of the conditional distribution of model response may be incorporated and (ii) the bias of the traditional nonparametric kernel regression estimator of Nadaraya-Watson may be reduced. We are precisely interested in combination of the two estimations approaches with some asymptotic properties of the resulting estimators. Asymptotic normality results were showed for nonparametric correction terms of parametric start function of the estimators. The performance of discrete semiparametric multivariate kernel estimators studied is illustrated using simulations and real count data. In addition, diagnostic checks are performed to test the adequacy of the parametric start model to the true discrete regression model. Finally, using discrete semiparametric multivariate kernel estimators provides a bias reduction when the parametric multivariate regression model used as start regression function belongs to a neighborhood of the true regression model.     

Modeling of Discrete HNBUE Class with Hypothesis Testing Application

A new model is proposed to test whether an equipment whose life is measured in discrete time units fails due to uncontrollable chance factors alone against the alternatives that it degrades over time in the sense of discrete HNBUE (harmonic new better than used in expectation) aging. The test is shown to be consistent and the asymptotic distribution of the test statistic has been obtained. The critical points and the power of the test against various alternatives from discrete HNBUE class have been studied by means of simulation. Finally, the test is applied to a discrete reliability data to examine the performance.     

Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit

In the quest to model various phenomena, the foundational importance of parameter identifiability to sound statistical modeling may be less well appreciated than goodness of fit. Identifiability concerns the quality of objective information in data to facilitate estimation of a parameter, while nonidentifiability means there are parameters in a model about which the data provide little or no information. In purely empirical models where parsimonious good fit is the chief concern, nonidentifiability (or parameter redundancy) implies overparameterization of the model. In contrast, nonidentifiability implies underinformativeness of available data in mechanistically derived models where parameters are interpreted as having strong practical meaning. This study explores illustrative examples of structural nonidentifiability and its implications using mechanistically derived models (for repeated presence/absence analyses and dose–response of Escherichia coli O157:H7 and norovirus) drawn from quantitative microbial risk assessment. Following algebraic proof of nonidentifiability in these examples, profile likelihood analysis and Bayesian Markov Chain Monte Carlo with uniform priors are illustrated as tools to help detect model parameters that are not strongly identifiable. It is shown that identifiability should be considered during experimental design and ethics approval to ensure generated data can yield strong objective information about all mechanistic parameters of interest. When Bayesian methods are applied to a nonidentifiable model, the subjective prior effectively fabricates information about any parameters about which the data carry no objective information. Finally, structural nonidentifiability can lead to spurious models that fit data well but can yield severely flawed inferences and predictions when they are interpreted or used inappropriately.     

Modeling time series data with semi-reflective boundaries

Time series data are increasingly common in many areas of the health sciences, and in some instances, may have natural boundaries serving as performance guidelines or as thresholds associated with adverse outcomes. Such boundaries may be labeled as semi-reflective, in that the time series values have an increased chance of returning towards middle levels as the boundaries are approached, but boundaries can still be breached. In this paper we review a model that was previously proposed for such data and we investigate its statistical properties. Specifically, this model consists of a third-order auto-regressive projection component, parameterized as a constrained linear combination of linear, flat, and quadratic trends, and an error term that uses a logistic regression model for its sign. We describe and compare a previously-proposed estimation method with a modified version thereof, using computer simulations, as well as data examples from heart monitoring and from a driving simulator. We find that the two methods tend to give different results, with the modified technique having lower bias and more accurate confidence intervals than the previously-proposed method.     

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

The hyper‐Poisson distribution can handle both over‐ and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation‐specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper‐Poisson distribution in analyzing motor vehicle crash count data. The hyper‐Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway‐highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness‐of‐fit measures indicated that the hyper‐Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper‐Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway‐Maxwell‐Poisson model previously developed for the same data set. The advantages of the hyper‐Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper‐Poisson model can handle both over‐ and underdispersed crash data. Although not a major issue for the Conway‐Maxwell‐Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.     

Time varying long memory parameter estimation for locally stationary long memory processes

The semiparametric estimators of time varying long memory parameter are investigated for locally stationary long memory processes. The GPH estimator and the local Whittle estimator are considered. Under some mild regularity assumptions, the weak consistency and the asymptotic normality of the estimators are obtained. The finite sample performance of the estimators is discussed through a small simulation study.