Книги з теми "Linear estimation problems"

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.

This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressive processes as well as two issues related to the general estimation problem, namely: identifiability and the inverse problem. Finally, it examines convergence results for the autocorrelation operator and the predictor, extensions for the autoregressive Hilbertian (ARH) model, and some numerical aspects of prediction when the data are curves observed at discrete points.

This book is the first to make chi-squared model testing, one of the data analysis methods used to discover the Higgs boson and gravitational waves, accessible to undergraduate students in introductory physics laboratory courses. By including uncertainties in the curve fitting, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one- and two-parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics, requiring calculus, are addressed in an advanced topics chapter. This self-contained and student-friendly introduction to chi-squared analysis and model testing includes a glossary, end-of-chapter problems with complete solutions, and software scripts written in several popular programming languages, that the reader can use for chi-squared model testing. In addition to introductory physics lab students, this accessible introduction to chi-squared analysis and model testing will be of interest to all who need to learn chi-squared model testing, e.g. beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences.

The quality of data collected in official spatial databases is crucial in making strategic decisions as well as in the implementation of planning and design works. Awareness of the level of the quality of these data is also important for individual users of official spatial data. The author presents methods and models of description and evaluation of the quality of spatial data collected in public registers. Data describing the space in the highest degree of detail, which are collected in three databases: land and buildings registry (EGiB), geodetic registry of the land infrastructure network (GESUT) and in database of topographic objects (BDOT500) were analyzed. The results of the research concerned selected aspects of activities in terms of the spatial data quality. These activities include: the assessment of the accuracy of data collected in official spatial databases; determination of the uncertainty of the area of registry parcels, analysis of the risk of damage to the underground infrastructure network due to the quality of spatial data, construction of the quality model of data collected in official databases and visualization of the phenomenon of uncertainty in spatial data. The evaluation of the accuracy of data collected in official, large-scale spatial databases was based on a representative sample of data. The test sample was a set of deviations of coordinates with three variables dX, dY and Dl – deviations from the X and Y coordinates and the length of the point offset vector of the test sample in relation to its position recognized as a faultless. The compatibility of empirical data accuracy distributions with models (theoretical distributions of random variables) was investigated and also the accuracy of the spatial data has been assessed by means of the methods resistant to the outliers. In the process of determination of the accuracy of spatial data collected in public registers, the author’s solution was used – resistant method of the relative frequency. Weight functions, which modify (to varying degree) the sizes of the vectors Dl – the lengths of the points offset vector of the test sample in relation to their position recognized as a faultless were proposed. From the scope of the uncertainty of estimation of the area of registry parcels the impact of the errors of the geodetic network points was determined (points of reference and of the higher class networks) and the effect of the correlation between the coordinates of the same point on the accuracy of the determined plot area. The scope of the correction was determined (in EGiB database) of the plots area, calculated on the basis of re-measurements, performed using equivalent techniques (in terms of accuracy). The analysis of the risk of damage to the underground infrastructure network due to the low quality of spatial data is another research topic presented in the paper. Three main factors have been identified that influence the value of this risk: incompleteness of spatial data sets and insufficient accuracy of determination of the horizontal and vertical position of underground infrastructure. A method for estimation of the project risk has been developed (quantitative and qualitative) and the author’s risk estimation technique, based on the idea of fuzzy logic was proposed. Maps (2D and 3D) of the risk of damage to the underground infrastructure network were developed in the form of large-scale thematic maps, presenting the design risk in qualitative and quantitative form. The data quality model is a set of rules used to describe the quality of these data sets. The model that has been proposed defines a standardized approach for assessing and reporting the quality of EGiB, GESUT and BDOT500 spatial data bases. Quantitative and qualitative rules (automatic, office and field) of data sets control were defined. The minimum sample size and the number of eligible nonconformities in random samples were determined. The data quality elements were described using the following descriptors: range, measure, result, and type and unit of value. Data quality studies were performed according to the users needs. The values of impact weights were determined by the hierarchical analytical process method (AHP). The harmonization of conceptual models of EGiB, GESUT and BDOT500 databases with BDOT10k database was analysed too. It was found that the downloading and supplying of the information in BDOT10k creation and update processes from the analyzed registers are limited. An effective approach to providing spatial data sets users with information concerning data uncertainty are cartographic visualization techniques. Based on the author’s own experience and research works on the quality of official spatial database data examination, the set of methods for visualization of the uncertainty of data bases EGiB, GESUT and BDOT500 was defined. This set includes visualization techniques designed to present three types of uncertainty: location, attribute values and time. Uncertainty of the position was defined (for surface, line, and point objects) using several (three to five) visual variables. Uncertainty of attribute values and time uncertainty, describing (for example) completeness or timeliness of sets, are presented by means of three graphical variables. The research problems presented in the paper are of cognitive and application importance. They indicate on the possibility of effective evaluation of the quality of spatial data collected in public registers and may be an important element of the expert system.

Three successive parts are presented within this article, all intended to raise the visibility and show the utility of classical geopolitics as a deserving and separate international-relations model: (a) a common traditional definition, (b) relevant theories that correspond to that definition, and (c) applications of certain theories that will delve at some depth into three case studies (the Ukrainian shatterbelt, contemporary Turkish geopolitics, and a North American heartland).The placement of states, regions, and resources, as affecting international relations and foreign policies, defines classical geopolitics. This definition emphasizes the application of spatially composed unbiased theories that should bring insight into foreign-affairs events and policies. Specifically, a “model” contains theories that correspond to its description. A “theory” is a simple sentence of probability, with “A” happening to likely affect “B.” Importantly, models are passive; they merely hold theories. In contrast, theories possess their own titles and perform actively when taken from such models.Various methodological challenges are presented: (a) combining concepts with theories, (b) estimating probability for testing theories, (c) claiming the “scientific,” (d) accounting for determinism, (e) revealing a dynamic environment for geopolitics, (f) separating realism from geopolitics, and (g) drawing classical geopolitics away from the critical. Certain theories that are placed within the geopolitical model are examined next: (a) heartlands and rimlands, (b) land and sea power, (c) choke points and maritime lines of communication, (d) offshore balancing, (e) the Monroe doctrine, (f) balances of power, (g) checkerboards, (h) shatterbelts, (i) pan-regions, (j) influence spheres, (k) dependency, (l) buffer states, (m) organic borders, (n) imperial thesis, (o) borders/wars, (p) contagion, (q) irredentism, (r) demography, (s) fluvial laws, (t) petro-politics, and (u) catastrophic events in nature. Additional theories apply elsewhere in the article as well.Of the three case studies, the Ukrainian shatterbelt represents the sole contemporary geopolitical configuration of this type, a regional conflict coupling with a strategic rivalry. Here, partisans of the civil war between the eastern and the western sectors of the country have joined with the Russians against the Europeans and Americans, respectively. Next, Turkey’s pivotal location has afforded it both advantages and disadvantages, a topic discussed at some length earlier in the article. Its “zero-problems” strategy of seeking positive relations with neighbors has now been forced to change tactics, reflective of new forces within and beyond the country. Finally, a North American heartland compares nicely to Halford Mackinder’s earlier Eurasia heartland thesis, with the American perhaps proving more stable, wealthy, and enduring, based in large part on its stronger geopolitical features.