Approximations for two-dimensional discrete scan statistics in some block-factor type dependent models

We consider the two-dimensional discrete scan statistic generated by a block-factor type model obtained from i.i.d. sequence. We present an approximation for the distribution of the scan statistics and the corresponding error bounds. A simulation study illustrates our methodology.Comment: 17 pages, 9 figure

Approximation for the Distribution of Three-dimensional Discrete Scan Statistic

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan statistics. Importance sampling algorithm is used to obtains sharp bounds for the simulation error. Simulation results and comparisons with other approximations are presented for the binomial and Poisson models

Resuscitating Old Forest Models to Meet Present Environmental Reporting Needs

A plethora of forest models were developed by transforming dependent variable, which introduces bias in estimation if appropriate correction are not applied when back-transforming to the original units. The need for accurate reporting of environmental statistics to national and international agencies lead to improvement of existing models or development of new ones. However, in many instances, not only were no original models established, but original data sets are no longer available, which recommends ad-hoc bias corrections of existing models. The present research presents a procedure for bias correction based on information extracted from summary statistics, specifically coefficient of determination and standard error. The transformations considered in this study are trigonometric (i.e. sine, cosine, tangent, arcsine, and arctangent), hyperbolic (i.e., sine, secant, and tangent), power, and logarithm. The method was applied to site index equations of Douglas Fir and Ponderosa Pine [Hann and Scrivani, 1987], and tree volume of 27 species from Romania [Giurgiu, 1974]. Using only the information describing the models, such as variance or range, the proposed method corrected the bias, and proved that estimates can change from 1% (the site index equations of Hann and Scrivani) to 40% (the tree volumes of Giurgiu)

Scan statistics for some dependent models.Applications.

International audienc

Approximations pour la statistique de scan discrète multi-dimensionnelle

In this thesis, we derive accurate approximations and error bounds for the probability distribution of the multidimensional discrete scan statistics.We start by improving some existing results concerning the estimation of the distribution of extremes of 1-dependent stationary sequences of random variables, both in terms of range of applicability and sharpness of the error bound. These estimates play the key role in the approximation process of the multidimensional discrete scan statistics distribution.The presented methodology has two main advantages over the existing ones found in the literature: first, beside the approximation formula, an error bound is also established and second, the approximation does not depend on the common distribution of the observations. For the underlying random field under which the scan process is evaluated, we consider two models: the classical model, of independent and identically distributed observations and a dependent framework, where the observations are generated by a block-factor.In the i.i.d. case, in order to illustrate the accuracy of our results, we consider the particular settings of one, two and three dimensions. A simulation study is conducted where we compare our estimate with other approximations and inequalities derived in the literature. The numerical values are efficiently obtained via an importance sampling algorithm discussed in detail in the text.Finally, we consider a block-factor model for the underlying random field, which consists of dependent data and we show how to extend the approximation methodology to this case. Several examples in one and two dimensions are investigated. The numerical applications accompanying these examples show the accuracy of our approximation.All the methods presented in this thesis leaded to a Graphical User Interface (GUI) software, implemented in Matlab®.Dans cette thèse nous obtenons des approximations et les erreurs associées pour la distribution de la statistique de scan discrète multi-dimensionnelle. La statistique de scan est vue comme le maximum d'une suite de variables aléatoires stationnaires 1-dépendante. Dans ce cadre, nous présentons un nouveau résultat pour l'approximation de la distribution de l'extremum d'une suite de variables aléatoire stationnaire 1-dépendante, avec des conditions d'application plus larges et des erreurs d'approximations plus petites par rapport aux résultats existants en littérature. Ce résultat est utilisé ensuite pour l'approximation de la distribution de la statistique de scan. L'intérêt de cette approche par rapport aux techniques existantes en littérature est du à la précision d'une erreur d'approximation, d'une part, et de son applicabilité qui ne dépend pas de la distribution du champ aléatoire sous-adjacent aux données, d'autre part.Les modèles considérés dans ce travail sont le modèle i.i.d et le modèle de dépendance de type block-factor.Pour la modélisation i.i.d. les résultats sont détaillés pour la statistique de scan uni, bi et tri-dimensionnelle. Un algorithme de simulation de type "importance sampling" a été introduit pour le calcul effectif des approximations et des erreurs associées. Des études de simulations démontrent l'efficacité des résultats obtenus. La comparaison avec d'autres méthodes existantes est réalisée.La dépendance de type block-factor est introduite comme une alternative à la dépendance de type Markov. La méthodologie développée traditionnellement dans le cas i.i.d. est étendue à ce type de dépendance. L'application du résultat d'approximation pour la distribution de la statistique de scan pour ce modèle de dépendance est illustrée dans le cas uni et bi-dimensionnel.Ces techniques, ainsi que celles existantes en littérature, ont été implémentées pour la première fois à l'aide des programmes Matlab® et une interface graphique

Scan statistics for some dependent models.Applications.

International audienc

Two Decades of Research Collaboration: A Keyword Scopus Evaluation

One issue that has become more important over the years is to evaluate the capability for worldwide research networks on different areas of research, especially in the areas that are identified as being worldwide significant. The study investigated the research output, citations impact and collaborations on publications listed in Scopus authored by researchers all over the world, research published between 1999-2014, selected by a group of keywords identified by authors. The results of the analysis identified an increasing trend in scientific publications starting with 2006, especially on three of the analyzed keywords. We also found differences in the citations patterns for the Black Sea and Danube Delta keywords in the contributing countries. The results of this study revealed a steady increase of the collaboration output and an increasing trend in the collaboration behavior, both at the European and national level. Additionally, at the national level the study identified the collaboration network between Romanian institutions per counties

One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems

International audienceThe one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with accuracy and sharp bounds are provided. The longest increasing run statistics is related to the scan statistics and its distribution is studied. The moving average process is a particular case of block factor and the distribution of the associated scan statistics is approximated. Numerical results are presented

Development of Nonlinear Parsimonious Forest Models Using Efficient Expansion of the Taylor Series: Applications to Site Productivity and Taper

The parameters of nonlinear forest models are commonly estimated with heuristic techniques, which can supply erroneous values. The use of heuristic algorithms is partially rooted in the avoidance of transformation of the dependent variable, which introduces bias when back-transformed to original units. Efforts were placed in computing the unbiased estimates for some of the power, trigonometric, and hyperbolic functions since only few transformations of the predicted variable have the corrections for bias estimated. The approach that supplies unbiased results when the dependent variable is transformed without heuristic algorithms, but based on a Taylor series expansion requires implementation details. Therefore, the objective of our study is to investigate the efficient expansion of the Taylor series that should be included in applications, such that numerical bias is not present. We found that five functions require more than five terms, whereas the arcsine, arccosine, and arctangent did not. Furthermore, the Taylor series expansion depends on the variance. We illustrated the results on two forest modeling problems, one at the stand level, namely site productivity, and one at individual tree level, namely taper. The models that are presented in the paper are unbiased, more parsimonious, and they have a RMSE comparable with existing less parsimonious models