Books on the topic 'Heteroscedastic Multivariate Linear Regression'

This article presents a unifying classification for functional regression modeling, and more specifically for modeling the link between two variables X and Y, when the explanatory variable (X) is of a functional nature. It first provides a background on the proposed classification of regression models, focusing on the regression problem and defining parametric, semiparametric, and nonparametric models, and explains how semiparametric modeling can be interpreted in terms of dimension reduction. It then gives four examples of functional regression models, namely: functional linear regression model, additive functional regression model, smooth nonparametric functional model, and single functional index model. It also considers a number of new models, directly adapted to functional variables from the existing standard multivariate literature.

Habitat is crucial to the survival and reproduction of individual organisms as well as persistence of populations. As such, species-habitat relationships have long been studied, particularly in the field of wildlife ecology and to a lesser extent in the more encompassing discipline of ecology. The habitat requirements of a species largely determine its spatial distribution and abundance in nature. One way to recognize and appreciate the over-riding importance of habitat is to consider that a young organism must find and settle into the appropriate type of habitat as one of the first challenges of life. This process can be cast in a probabilistic framework and used to better understand the mechanisms behind habitat preferences and selection. There are at least six distinctly different statistical approaches to conducting a habitat analysis – that is, identifying and quantifying the environmental variables that a species most strongly associates with. These are (1) comparison among group means (e.g., ANOVA), (2) multiple linear regression, (3) multiple logistic regression, (4) classification and regression trees, (5) multivariate techniques (Principal Components Analysis and Discriminant Function Analysis), and (6) occupancy modelling. Each of these is lucidly explained and demonstrated by application to a hypothetical dataset. The strengths and weaknesses of each method are discussed. Given the ongoing biodiversity crisis largely caused by habitat destruction, there is a crucial and general need to better characterize and understand the habitat requirements of many different species, particularly those that are threatened and endangered.

Hard coal mining is characterised by features that pose numerous challenges to its current operations and cause strategic and operational problems in planning its development. The most important of these include the high capital intensity of mining investment projects and the dynamically changing environment in which the sector operates, while the long-term role of the sector is dependent on factors originating at both national and international level. At the same time, the conditions for coal mining are deteriorating, the resources more readily available in active mines are being exhausted, mining depths are increasing, temperature levels in pits are rising, transport routes for staff and materials are getting longer, effective working time is decreasing, natural hazards are increasing, and seams with an increasing content of waste rock are being mined. The mining industry is currently in a very difficult situation, both in technical (mining) and economic terms. It cannot be ignored, however, that the difficult financial situation of Polish mining companies is largely exacerbated by their high operating costs. The cost of obtaining coal and its price are two key elements that determine the level of efficiency of Polish mines. This situation could be improved by streamlining the planning processes. This would involve striving for production planning that is as predictable as possible and, on the other hand, economically efficient. In this respect, it is helpful to plan the production from operating longwalls with full awareness of the complexity of geological and mining conditions and the resulting economic consequences. The constraints on increasing the efficiency of the mining process are due to the technical potential of the mining process, organisational factors and, above all, geological and mining conditions. The main objective of the monograph is to identify relations between geological and mining parameters and the level of longwall mining costs, and their daily output. In view of the above, it was assumed that it was possible to present the relationship between the costs of longwall mining and the daily coal output from a longwall as a function of onerous geological and mining factors. The monograph presents two models of onerous geological and mining conditions, including natural hazards, deposit (seam) parameters, mining (technical) parameters and environmental factors. The models were used to calculate two onerousness indicators, Wue and WUt, which synthetically define the level of impact of onerous geological and mining conditions on the mining process in relation to: —— operating costs at longwall faces – indicator WUe, —— daily longwall mining output – indicator WUt. In the next research step, the analysis of direct relationships of selected geological and mining factors with longwall costs and the mining output level was conducted. For this purpose, two statistical models were built for the following dependent variables: unit operating cost (Model 1) and daily longwall mining output (Model 2). The models served two additional sub-objectives: interpretation of the influence of independent variables on dependent variables and point forecasting. The models were also used for forecasting purposes. Statistical models were built on the basis of historical production results of selected seven Polish mines. On the basis of variability of geological and mining conditions at 120 longwalls, the influence of individual parameters on longwall mining between 2010 and 2019 was determined. The identified relationships made it possible to formulate numerical forecast of unit production cost and daily longwall mining output in relation to the level of expected onerousness. The projection period was assumed to be 2020–2030. On this basis, an opinion was formulated on the forecast of the expected unit production costs and the output of the 259 longwalls planned to be mined at these mines. A procedure scheme was developed using the following methods: 1) Analytic Hierarchy Process (AHP) – mathematical multi-criteria decision-making method, 2) comparative multivariate analysis, 3) regression analysis, 4) Monte Carlo simulation. The utilitarian purpose of the monograph is to provide the research community with the concept of building models that can be used to solve real decision-making problems during longwall planning in hard coal mines. The layout of the monograph, consisting of an introduction, eight main sections and a conclusion, follows the objectives set out above. Section One presents the methodology used to assess the impact of onerous geological and mining conditions on the mining process. Multi-Criteria Decision Analysis (MCDA) is reviewed and basic definitions used in the following part of the paper are introduced. The section includes a description of AHP which was used in the presented analysis. Individual factors resulting from natural hazards, from the geological structure of the deposit (seam), from limitations caused by technical requirements, from the impact of mining on the environment, which affect the mining process, are described exhaustively in Section Two. Sections Three and Four present the construction of two hierarchical models of geological and mining conditions onerousness: the first in the context of extraction costs and the second in relation to daily longwall mining. The procedure for valuing the importance of their components by a group of experts (pairwise comparison of criteria and sub-criteria on the basis of Saaty’s 9-point comparison scale) is presented. The AHP method is very sensitive to even small changes in the value of the comparison matrix. In order to determine the stability of the valuation of both onerousness models, a sensitivity analysis was carried out, which is described in detail in Section Five. Section Six is devoted to the issue of constructing aggregate indices, WUe and WUt, which synthetically measure the impact of onerous geological and mining conditions on the mining process in individual longwalls and allow for a linear ordering of longwalls according to increasing levels of onerousness. Section Seven opens the research part of the work, which analyses the results of the developed models and indicators in individual mines. A detailed analysis is presented of the assessment of the impact of onerous mining conditions on mining costs in selected seams of the analysed mines, and in the case of the impact of onerous mining on daily longwall mining output, the variability of this process in individual fields (lots) of the mines is characterised. Section Eight presents the regression equations for the dependence of the costs and level of extraction on the aggregated onerousness indicators, WUe and WUt. The regression models f(KJC_N) and f(W) developed in this way are used to forecast the unit mining costs and daily output of the designed longwalls in the context of diversified geological and mining conditions. The use of regression models is of great practical importance. It makes it possible to approximate unit costs and daily output for newly designed longwall workings. The use of this knowledge may significantly improve the quality of planning processes and the effectiveness of the mining process.