Theory Of Statistical Hypothesis Testing Research Articles

Analysis of the results of preventive testing of bushings using elements of the theory of statistical hypothesis testing

The article presents the results of a study of the dependence of insulation indicators on the duration of operation for serviceable and faulty high-voltage oil-filled bushings, both of hermetic and non-hermetic construction. The results of periodic tests of oil-filled bushings, with a voltage of 110 kV of hermetic design with paper-oil insulation of the capacitor type, as well as non-hermetic construction, were used as initial data. Three statistical criteria were used to form statistically homogeneous data sets: the Wilcoxon rank test, the Z-test, and the Fisher-Snedecor test. The values of the sample mean, sample variance, as well as coefficients of asymmetry and excess of insulation indicators of high-voltage bushings were obtained for the array of initial data and arrays obtained during statistical processing. The values of the sample averages for the arrays obtained as a result of the statistical processing procedure differ significantly. There is a significant decrease in the sample variance values for tgd1 compared to the original arrays. To check the homogeneity of the data in the obtained arrays, the one-factor variance analysis model is used. The practical use of this algorithm made it possible to significantly reduce the heterogeneity of the results of periodic tests of the state of insulation of high-voltage bushings. The analysis of the composition of the arrays with homogeneous values of the indicators made it possible to establish that the values of the indicators of bushings from different regions of Ukraine, of different types and made with different numbers of factory drawings, got into the homogeneous data arrays. It is noted that for high-voltage bushings that do not have insulation defects, the values of the mathematical expectation of the same indicator for different arrays of preventive tests of capacitor-type insulation have a shift relative to each other. From this it follows that the load factor and the operating time of the transformer significantly affect the determination of the maximum allowable value of the insulation index of the high-voltage bushing.

Статистические характеристики сигнала на выходе оптимальной радиолокационной системы распознавания подвижных воздушных объектов

This work can be considered as a continuation of the article, or as separate materials devoted to the recognition of moving air objects based on the theory of testing statistical hypotheses. In the future, when presenting the materials of this article, the terminology proposed in [1] will be used. The relevance of this article is due to the events taking place on the European continent, indicating the need for further development of radar systems for various purposes and the transition from radar to radio vision, which will significantly improve the effectiveness of air defense and airspace control in general. The construction of a radar portrait and further automatic recognition of moving air objects, as an element of artificial intelligence, will eliminate human error, as well as significantly reduce the time it takes to make a decision on the necessary measures to influence the detected aircraft. Studying the freely available scientific works of various scientists devoted to such a direction of research and development of artificial intelligence as the statistical theory of pattern recognition, one can note the absence of such an important element as the function of the dependence of the probability of correct recognition on the quality and noise of the image. Within the framework of this article, a variant of solving this problem in the form of a mathematical model will be proposed. Since in [1] a recognition method is considered that uses the correlation coefficient between the current image and the reference one, and the probability of correct recognition is estimated using the Neumann-Pearson criterion, it is proposed to plot the dependence of the probability of correct recognition on the ratio of the image energy EI to the spectral noise density (R = 2EI/N0R), for a given false recognition probability . In the future, in the presented work, this dependence will be called recognition characteristics. Graphs will also be considered, in this paper referred to as the distribution density of the recognition probability.

РЕШЕНИЕ ЗАДАЧИ ОПТИМАЛЬНОГО РАДИОЛОКАЦИОННОГО РАСПОЗНАВАНИЯ ПОДВИЖНЫХ ВОЗДУШНЫХ ОБЪЕКТОВ НА ОСНОВЕ ТЕОРИИ ПРОВЕРКИ СТАТИСТИЧЕСКИХ ГИПОТЕЗ

The materials of this article are devoted to the development of one of the main aspects of artificial intelligence systems - pattern recognition. The relevance of the materials is due to the rapid development of radar systems for various purposes and the transition in some directions from radar to radio vision. Currently, much attention is paid to the development of radar systems with synthesizing the antenna aperture, for remote sensing of the earth and recognition of stationary ground objects, however, according to the author, radar recognition of mobile aerial objects is an important issue. The purpose of this article is to propose a solution to the problem of recognizing moving aerial objects by their radar portraits, based on the theory of statistical hypothesis testing. At the moment there are many methods of pattern recognition, this article discusses an algorithm that implements the function of matching the current image and the reference from a pre-formed catalog. As the current image, an azimuth-range radar portrait is considered, which is formed by super-resolution in azimuth, by synthesizing the aperture of the antenna and in range, using ultra-wideband signal. The author suggests, with a statistical approach to solving the problem of radar recognition, not to be tied to finding the probability of an object belonging to each of the pre-formed classes using a selected feature with a known probability distribution density of values, but to consider this process from the position of the signal at the output of the optimal recognition system to a specific image. A new approach to the description of probabilistic events when making a recognition decision is proposed. As a statistical classifier, it is proposed to use the Neumann-Pearson theory of statistical solutions.

Development of modern models and methods of the theory of statistical hypothesis testing

Typical problems of the theory of statistical hypothesis testing are considered. All these problems belong to the same object area and are formulated in a single system of axioms and assumptions using a common linguistic thesaurus. However, different approaches are used to solve each of these problems and a unique solution method is developed. In this regard, the work proposes a unified methodological approach for formulating and solving these problems. The mathematical basis of the approach is the theory of continuous linear programming (CLP), which generalizes the known mathematical apparatus of linear programming for the continuous case. The mathematical apparatus of CLP allows passing from a two-point description of the solution of the problem in the form {0; 1} to a continuous one on the segment [0; 1]. Theorems justifying the solution of problems in terms of CLP are proved. The problems of testing a simple hypothesis against several equivalent or unequal alternatives are considered. To solve all these problems, a continuous function is introduced that specifies a randomized decision rule leading to continuous linear programming models. As a result, it becomes possible to expand the range of analytically solved problems of the theory of statistical hypothesis testing. In particular, the problem of making a decision based on the maximum power criterion with a fixed type I error probability, with a constraint on the average risk, the problem of testing a simple hypothesis against several alternatives for given type II error probabilities. The method for solving problems of statistical hypothesis testing for the case when more than one observed controlled parameter is used to identify the state is proposed

Application of Cluster Analysis with Fuzzy Logic Elements for Ground Environment Assessment of Robotic Group

Emergency situations, that cause risks for human life and health, dictate elevated requirements to completeness and accuracy of the presentation of information about current ground environment. Modern robotic systems include sensors, that operate on different physical principles. This causes incrementation of information entering control system. Computing resources and technical capabilities of robotic systems are limited in range and detection probabilities of appearing objects. In case of insufficient performance of the on-board computer system and high uncertainties of ground environment, robotic systems are not able to perform without combining information from robotic group and producing a single view of ground environment. Complex information from a group of robotic systems occurs in real time and a non-deterministic environment.
 To solve the problem of identifying attribute vectors related to a single object, as well as to evaluate the effectiveness of obtained solutions, is possible using known formulas of the theory of statistical hypothesis testing and probability theory only under the normal distribution law with the known mathematical expectation of an attribute vector and a correlation matrix. However, these conditions are usually not met in practice. Problems also arise when methods of nonparametric statistics are used with an unknown law of probability distribution.
 The new method of identifying attribute vectors is proposed, that does not rely on a statistical approach and, therefore, does not require knowledge of the type of distribution law and the values of its parameters. Proposed method is based on the idea of combining cluster analysis and fuzzy logic, and is relatively simple to the basic methods of multidimensional nonparametric statistics.
 The results of modeling information processes are presented. The advantages of proposed method are shown. The comparative values for the number of false recognitions are given. The recommendations are given for constructing fuzzy inference rules when creating an expert system knowledge base.

Обеспечение достоверности методической поддержки управления объектов электроэнергетических систем

Enhancing the validity of methodical recommendations is one of the main problems that have to be solved in developing intelligent systems for managing maintenance and repair of electric power system equipment and devices. A risk of making an erroneous decision exists mainly due to availability of gross errors and abnormal values in statistical data on operation. The difficulty of solving this problem becomes still more obvious obvious if this risk is taken together with the fact that non-random samples of statistical data on operation differ from the theoretical representative samples of random quantities from the general totality of data, the need to consider a multidimensional nature of statistical data on operation, and lack of methods for analyzing scanty samples of multidimensional data. A method that allows abnormal realizations to be revealed based on the fiducial approach and statistical hypothesis testing theory is developed. By applying express methods for calculating the fiducial interval critical values for the selected significance level, this problem can be solved without using special tables and a computer.

Statistical Models and the Theory of Hypothesis Testing in Medicine

Purpose: The purpose of this work is to develop statistical approaches for treatment efficiency analysis on a medical case. These methods include the effect evaluation method performed with various preparations in regards to several factors such as the patient‘s blood state and his/her biochemical values. Design/Methodology/Approach: The results of this survey were divided into three groups: the first included the blood biochemistry values before the test, the second — an hour after the test, the the third — two hours after the test. When visually comparing the results of the analyses of the three groups, it was possible to assume that the load of FLC did not significantly affect the biochemistry of the patients' blood. To test this medical assumption, various statistical criteria of the theory of testing statistical hypotheses have been applied. Findings: Statistical analysis of changes in the level of lipase and triglycerides in the biochemical analysis of the blood of patients with chronic pancreatitis after ingestion of food containing medium-chain fatty acids showed that there is no overall disruption in the functioning of the pancreas. Practical implications: Clinical practice has shown that more than 85% of patients tolerated testing with medium chain fatty acids, not experiencing a painful abdominal symptom and other negative consequences of a violation of external secretion of the pancreas. Originality/Value: In clinical practice, the Russian Academy of Medical Sciences for the first time took into account the results of a statistical analysis.

Adaptive Soft Sensor Development for Multi-Output Industrial Processes Based on Selective Ensemble Learning

Soft sensors are vital for online predictions of quality-related yet difficult-to-measure variables in process industry. In this paper, an adaptive soft sensing approach based on selective ensemble learning is proposed for multi-output nonlinear and time-varying industrial processes, which we refer to as the selective ensemble learning for multi-outputs (SEL-MO). Specifically, an adaptive localization approach is developed for dealing with the process nonlinearity based on the statistical hypothesis testing theory, which can construct redundancy-free local model set. At the online operation stage, these constructed local models are partially combined under an adaptive selective ensemble learning framework, where the weightings of local models are query-sample-oriented such that both gradual and abrupt changes in the process characteristics can be handled. In addition, an insensitivity strategy is proposed to enhance the online computational efficiency of the SEL-MO by avoiding the unnecessary search of the historical data set. Case studies are carried out on a simulated fed-batch penicillin process and a real-life industrial primary reformer, and the results obtained demonstrate the effectiveness of the proposed method.

Fold-up derivatives of set-valued functions and the change-set problem: A Survey

We give a survey on fold-up derivatives, a notion which was introduced by Khmaladze (J Math Anal Appl 334:1055–1072, 2007) and extended by Khmaladze and Weil (J Math Anal Appl 413:291–310, 2014) to describe infinitesimal changes in a set-valued function. We summarize the geometric background and discuss in detail applications in statistics, in particular to the change-set problem of spatial statistics, and show how the notion of fold-up derivatives leads to the theory of testing statistical hypotheses about the change-set. We formulate Poisson limit theorems for the log-likelihood ratio in two versions of this problem and present also the route to a central limit theorem.

A statistical approach to combining multisource information in one‐class classifiers

A new method is introduced for combining information from multiple sources to support one‐class classification. The contributing sources may represent measurements taken by different sensors of the same physical entity, repeated measurements by a single sensor, or numerous features computed from a single measured image or signal. The approach utilizes the theory of statistical hypothesis testing, and applies Fisher's technique for combining p‐values, modified to handle nonindependent sources. Classifier outputs take the form of fused p‐values, which may be used to gauge the consistency of unknown entities with one or more class hypotheses. The approach enables rigorous assessment of classification uncertainties, and allows for traceability of classifier decisions back to the constituent sources, both of which are important for high‐consequence decision support. Application of the technique is illustrated in two challenge problems, one for skin segmentation and the other for terrain labeling. The method is seen to be particularly effective for relatively small training samples.

A NEYMAN-PEARSON PERSPECTIVE ON OPTIMAL REINSURANCE WITH CONSTRAINTS

AbstractThe formulation of optimal reinsurance policies that take various practical constraints into account is a problem commonly encountered by practitioners. In the context of a distortion-risk-measure-based optimal reinsurance model without moral hazard, this article introduces and employs a variation of the Neyman–Pearson Lemma in statistical hypothesis testing theory to solve a wide class of constrained optimal reinsurance problems analytically and expeditiously. Such a Neyman–Pearson approach identifies the unit-valued derivative of each ceded loss function as the test function of an appropriate hypothesis test and transforms the problem of designing optimal reinsurance contracts to one that resembles the search of optimal test functions achieved by the classical Neyman–Pearson Lemma. As an illustration of the versatility and superiority of the proposed Neyman–Pearson formulation, we provide complete and transparent solutions of several specific constrained optimal reinsurance problems, many of which were only partially solved in the literature by substantially more difficult means and under extraneous technical assumptions. Examples of such problems include the construction of the optimal reinsurance treaties in the presence of premium budget constraints, counterparty risk constraints and the optimal insurer–reinsurer symbiotic reinsurance treaty considered recently in Cai et al. (2016).

Analysis and simulation of the nonlinear kinetics of reacting chemical systems

A new scientific approach to the simulation of the nonlinear kinetics of chemically reacting systems has been devised in order to elucidate the stepwise mechanism of complex chemical reactions and to construct high-precision kinetic models describing this mechanism. A procedure has been developed for obtaining a finite set of kinetic models for given chemical reactions. Based on these models, kinetic models are constructed for estimating the subsets of the set of kinetic constants selected to solve particular scientific problems or for constructing high-precision kinetic models for a priori specified regimes of the chemical process. A relaxation method has been devised for kinetic models of the total number of estimable constants or their combinations. This method is based on the theory of testing statistical hypotheses and on experimental design theory. Procedures have been developed for point estimation of the constants of nonlinearly parameterized models and for additional construction of the distribution density function for the constants’ estimates and of the response vector of the chemical system. These data are used to precisely calculate the confidence intervals for the estimates of the constants and for the responses of the system and to validate the kinetic models and to discriminate between them.

Intelligently searching the slice of ambiguity function main ridge based on superiority inheritance

Extracting the novel signal parameters is an effective means to solve the sorting problems of complex radar emitter signals.The features of the slice of ambiguity function main ridge are one of the most feasible parameters among various characteristics.To search the slice of ambiguity function main ridge of signal more quickly,a smart search algorithm based on superiority inheritance was constructed and statistical hypothesis testing theory was used to analyze and test the obtained data.The results of simulation show that,the proposed method can reduce the search time to 28.6% that of original method while obtaining the right slice with higher success rate and higher accuracy.

Studying possibilities for the classification of infrasonic signals from different sources

Atmospheric infrasonic signals were classified on the basis of data obtained in the United States (University of Alaska, Fairbanks) and in the Antarctic region (Windless Bight) from 1980 to 1983. The data archive included five classes of signals from different sources: explosions, mountain associated waves, microbaroms, volcanic infrasound, and auroral infrasonic waves. This classification was based on the theory of testing statistical hypotheses. The possibilities of separating these classes were studied. It was shown that the signals (from the archive used) that are characteristic of explosions and volcanic activity can be rather easily separated from those characteristic of mountain associated waves, microbaroms, and auroral infrasonic waves.

Intelligent design and mathematical statistics: a troubled alliance

The explanatory filter is a proposed method to detect design in nature with the aim of refuting Darwinian evolution. The explanatory filter borrows its logical structure from the theory of statistical hypothesis testing but we argue that, when viewed within this context, the filter runs into serious trouble in any interesting biological application. Although the explanatory filter has been extensively criticized from many angles, we present the first rigorous criticism based on the theory of mathematical statistics.

Practical Implementation of the Capability Index C pk Based on the Control Chart Data

ABSTRACT Process capability indices are used to measure the ability of the process to manufacture product that meets specification requirement. Since estimated capability index is a random variable with a distribution, most practitioners look at the value of the capability index calculated from the given sample and then make a conclusion on whether the given process as capable or not which will not be reliable. In this paper, based on the theory of statistical hypothesis testing, when the process is in a state of statistical control, we propose a procedure on assessing C pk index for practitioners to use in determining whether a given process as capable. We consider the case where process measurements are collected from the control chart data, as a sequence of independent samples. Applying Hamaker's approximation, the testing procedure can be adequately derived from a normal distribution approximation and that the more complicated distribution can be avoided. These proposed techniques would be especially applicable when the data are taken from X¯ and R, and X¯ and S control charts.

Using normal approximation for calculating the p-value in assessing process capability index Cpk

When a process is in a perfect state of statistical control, the process capability indices are widely used to measure the capability of the process to manufacture items within the required tolerance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. The index Cpk has been used in various manufacturing industries to provide a quantitative measurement of the performance of the manufacturing. In this paper, based on the theory of statistical hypothesis testing, we propose a procedure on assessing Cpk index for practitioners to use in determining whether a given process as capable. Applying Hamaker’s approximation, the testing procedure can be adequately derived from a normal distribution approximation, which avoids the more complicated non-central t-distribution. The provided approach is easy to use and the decision making is more reliable.

Testing process capability for one-sided specification limit with application to the voltage level translator

Process capability indices C PU and C PL have been widely used in the microelectronics manufacturing industry as capability measures for processes with one-sided specification limits. In this paper, the theory of statistical hypothesis testing is implemented for normal processes, using the uniformly minimum variance unbiased estimators of C PU and C PL. Efficient SAS computer programs are provided to calculate the critical values and the p-values required for making decisions. Useful critical values for some commonly used capability requirements are tabulated. Based on the test a simple but practical step-by-step procedure is developed for in-plant applications. An example on the voltage level translator manufacturing process is given to illustrate how the proposed procedure may be applied to test whether the process meets the preset capability requirement.

Joint Estimation of the Motion Coordinates and Parameters of the Robotic Space Module and Transferred Elastic Load

Consideration was given to the possibility of estimating jointly the motion coordinates and parameters of the elastic spacecraft using algorithms based on the discrete Kalman filtering and the theory of testing statistical hypotheses. These algorithms enable one to reduce the nonlinear stochastic equations to stochastic linear ones. Results of mathematical modeling of the designed algorithm were presented.

An elementary model for statistical lot inspection and its application to sampling by variables

Recently some critical papers have initiated a discussion on pros and cons of standard sampling by variables (sampling by measurement). This discussion demonstrates the need for clarification by a sound stochastic model of statistical lot inspection. On the basis of such a model, variables sampling for lot proportion nonconforming and attributes sampling can be compared in terms of the theory of statistical hypothesis testing. This comparison refutes the well-known dogma of “same protection at lower sample size with variables plans”. Sampling by measurement for lot means, however, emerges as a perfectly valid method of statistical lot inspection.