scholarly journals Approximation, characterization, and continuity of multivariate monotonic regression functions

2021 ◽  
pp. 1-39
Author(s):  
Jochen Schmid
Keyword(s):  
Approximation Error ◽  
Likelihood Estimation ◽  
Rectangular Domain ◽  
Distance Measures ◽  
Regression Formula ◽  
Regression Functions ◽  
Simple Bounds ◽  
Regression Problems ◽  
The Mean ◽  
Monotonic Regression

We deal with monotonic regression of multivariate functions [Formula: see text] on a compact rectangular domain [Formula: see text] in [Formula: see text], where monotonicity is understood in a generalized sense: as isotonicity in some coordinate directions and antitonicity in some other coordinate directions. As usual, the monotonic regression of a given function [Formula: see text] is the monotonic function [Formula: see text] that has the smallest (weighted) mean-squared distance from [Formula: see text]. We establish a simple general approach to compute monotonic regression functions: namely, we show that the monotonic regression [Formula: see text] of a given function [Formula: see text] can be approximated arbitrarily well — with simple bounds on the approximation error in both the [Formula: see text]-norm and the [Formula: see text]-norm — by the monotonic regression [Formula: see text] of grid-constant functions [Formula: see text]. monotonic regression algorithms. We also establish the continuity of the monotonic regression [Formula: see text] of a continuous function [Formula: see text] along with an explicit averaging formula for [Formula: see text]. And finally, we deal with generalized monotonic regression where the mean-squared distance from standard monotonic regression is replaced by more complex distance measures which arise, for instance, in maximum smoothed likelihood estimation. We will see that the solution of such generalized monotonic regression problems is simply given by the standard monotonic regression [Formula: see text].

scholarly journals Subcritical Transmission in the Early Stage of COVID-19 in Korea

2021 ◽  
Vol 18 (3) ◽  
pp. 1265
Author(s):  
Yong Sul Won ◽  
Jong-Hoon Kim ◽  
Chi Young Ahn ◽  
Hyojung Lee
Keyword(s):  
Incubation Period ◽  
Early Stage ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Contact Tracing ◽  
Statistical Characterization ◽  
Serial Interval ◽  
Imported Cases ◽  
The Mean ◽  
Reporting Delays

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

scholarly journals ОПТИМІЗАЦІЯ ВИМІРЮВАЛЬНИХ ЗАСОБІВ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ЗА ДОПОМОГОЮ ТЕНЗОДАТЧИКІВ

2019 ◽  
pp. 50-56
Author(s):  
Людмила Володимирівна Кузьмич ◽  
Дмитро Петрович Орнатський ◽  
Володимир Павлович Квасніков
Keyword(s):  
Strain Gauge ◽  
Strain State ◽  
Approximation Error ◽  
Strain Gauges ◽  
Mean Square ◽  
Stress Strain ◽  
Stress Strain State ◽  
Destabilizing Factors ◽  
Mechanical Factors ◽  
The Mean

In the article, the principles of construction, design and mathematical modeling of deformation and stresses of complex technical constructions are developed with the help of strain gauges and strain gauges taking into account destabilizing factors, which allows to significantly reduce the level of errors in relation to existing measurement methods and known analogs.The method of digital compensation provides a more significant reduction in the errors of measuring transducers compared with the method of analog compensation. Features and technical indicators of this method are considered on an example of measuring pressure transducer with foil strain gauges.This method is universal, allows us to adjust not only the errors of the measurement channel nonlinearity and additional errors but also the errors associated with the effect of interferences of the general type due to ground resistance, which induces the connection between the measuring channels of the main and destabilizing factor.The disadvantages of this method include a significant amount of computations, which sharply increases with increasing order of approximating polynomials.The purpose is to develop a method and means of measuring stress-strain state using strain gauge, free from the above - mentioned shortcomings.The main destabilizing factors that limit the measurement accuracy using strain gauge are:- random processes (noises, obstacles, etc.);- changes in parameters of measuring transducers due to aging and physical degradation;- effects of external climatic and mechanical factors (temperature, humidity, etc.).The influence of the main destabilizing factors limiting the accuracy of the measurement of the stress-strain state of complex technical constructions with the help of strain gauges was analyzed, among which the influences of external climatic and mechanical factors are one of the most important ones. Regarding the systematic components, the most important in statistical measurements are the errors of nonlinearity and the temperature component of the error.For the study, two main alloys were taken, which today has the widest use as a material for strain gauges - it is constantan and karma. For these materials, the influence of the range of temperature changes, the spread of the values of temperature error on the mean-square value of the error of approximation by power polynomials was investigated.Using the NUMERY package, the dependence of the approximation error on the order of the approximating polyphony was determined. It is established that the mean square error value in the wide temperature range for both constantan and karma has a weak correlation with the order of a polynomial.

scholarly journals Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

2018 ◽  
Vol 28 (1) ◽  
pp. 141-154 ◽  
Author(s):  
Alexander Zeifman ◽  
Rostislav Razumchik ◽  
Yacov Satin ◽  
Ksenia Kiseleva ◽  
Anna Korotysheva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Queueing Systems ◽  
Approximation Error ◽  
Linear Operators ◽  
Upper And Lower Bounds ◽  
Logarithmic Norm ◽  
Batch Arrivals ◽  
State Dependent ◽  
The Mean ◽  
Number Of Customers

AbstractIn this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

scholarly journals Willingness to Pay for Teledermoscopy Services at a University Health Center

2018 ◽  
Vol 5 (3) ◽  
pp. 212-218 ◽  
Author(s):  
T S Raghu ◽  
James Yiannias ◽  
Nita Sharma ◽  
Allan L Markus
Keyword(s):  
Willingness To Pay ◽  
Health Center ◽  
Contingent Valuation Method ◽  
Cost Savings ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
College Health ◽  
Study Objective ◽  
Valuation Method ◽  
The Mean

Background: The study objective was to investigate the willingness to pay (WTP) for teledermoscopy services among students at a university health center. The hypothesis was that WTP for teledermoscopy among students would exceed the costs for traditional consultation. Methods: Between November 2013 and May 2014, students at a university health center were surveyed for their perceptions of teledermoscopy. One set of responses was collected from students visiting the health center for any reason (anonymous sample). An additional set of responses was collected from students visiting for dermatologic lesions (in-person sample). A contingent valuation method with a maximum likelihood estimation procedure was used to estimate the WTP distribution. Results: A total of 214 surveys were collected for the anonymous sample and 41 responses for the in-person sample. The mean (standard deviation [SD]) WTP for the anonymous sample was $55.27 ($39.11; 95% confidence interval [CI]: $49.99-$60.55). The mean (SD) WTP for the in-person sample was $52.37 ($26.56; 95% CI: $43.99-$60.75). Median WTP for the 2 samples was similar: $48.84 and $48.01. Conclusions: We conclude that students would be willing to pay for teledermoscopy services that would provide the potential for significant system cost savings. This may be especially true in college health or similar settings where dermatology services may not be available.

A New Approach to Length–Frequency Analysis: Growth Structure

1980 ◽  
Vol 37 (9) ◽  
pp. 1337-1351 ◽  
Author(s):  
Jon Schnute ◽  
David Fournier
Keyword(s):  
Frequency Analysis ◽  
Likelihood Estimation ◽  
Von Bertalanffy ◽  
Length Frequency ◽  
New Approach ◽  
New Methods ◽  
The Mean ◽  
Standard Deviations ◽  
Using Data ◽  
Length Frequency Analysis

This paper presents a new approach to length–frequency analysis which takes account of biological structure in the mean lengths and standard deviations in length for various age-classes of fish. The new methods help determine biologically meaningful solutions, even when earlier methods lead to an ambiguous set of competing solutions. The structure of the standard deviations turns out to be especially important. For describing the means, new parameters are defined for von Bertalanffy growth which prove to have greater biological meaning and numerical stability than L∞, K, and t0. These new parameters can often be estimated easily from the raw data in cases where the species experiences a slowing of growth with age. This paper also presents χ2 methods which can be used to rank competing solutions, although the results are not definitive. All methods are illustrated using data previously published for pike and abalone. An appendix describes in detail the computer programs required for the analysis.Key words: length–frequency analysis, aging of samples, von Bertalanffy growth, growth, maximum likelihood estimation, nonlinear estimation

Sign in / Sign up

Export Citation Format

Share Document