One-Step Estimation with Scaled Proximal Methods

We study statistical estimators computed using iterative optimization methods that are not run until completion. Classical results on maximum likelihood estimators (MLEs) assert that a one-step estimator (OSE), in which a single Newton-Raphson iteration is performed from a starting point with certain properties, is asymptotically equivalent to the MLE. We further develop these early-stopping results by deriving properties of one-step estimators defined by a single iteration of scaled proximal methods. Our main results show the asymptotic equivalence of the likelihood-based estimator and various one-step estimators defined by scaled proximal methods. By interpreting OSEs as the last of a sequence of iterates, our results provide insight on scaling numerical tolerance with sample size. Our setting contains scaled proximal gradient descent applied to certain composite models as a special case, making our results applicable to many problems of practical interest. Additionally, our results provide support for the utility of the scaled Moreau envelope as a statistical smoother by interpreting scaled proximal descent as a quasi-Newton method applied to the scaled Moreau envelope.

Using the EISTL Model to Structure Citation Trends of Research in JMIR mHealth and uHealth: Bibliometric Analysis (Preprint)

BACKGROUND The citation trend of research has frequently been applied to topical entities of interest in bibliographical studies. Although the burst spot and the corresponding burst strength can be highlighted in the traditional temporal bar graph (TBG) as viewing their evolutions of entities, no such growth trends were added to the TBG for a better understanding of future tremd (e.g., reading to rise, increasing, decreasing, or slowdown). A step-by-step scheme for constructing the bibliographical study is thus required to make data meaningful and fruitful. OBJECTIVE This article assesses (1) whether an EISTL model (i.e., identifying the topical entity, indicator, selection of top entities, TBG, and using the line-chart plot for verification) can be applied to display the trend analysis of article citations for entities and (2) whether the TBG can be enhanced to release more valuable information for readers. METHODS We obtained 2,151 abstracts indexed in PubMed by searching the keywords “JMIR mHealth and uHealth” (Journal) on November 11, 2021. The metadata was collected, including author names, research institutes, article identifiers (PMIDs), countries, and medical subject headings (MeSH terms). The burst spot and the growth trend were displayed along with the inflection point (IP) using the Newton–Raphson Iteration Method (NRIM) and the growth/share matrix (GSM). Cooccurrence analysis was performed to select the top-cited entities using social network analysis (SNA) and Sankey diagrams. The TBG plays a transitive role before drawing the line-chart plot in the EISTL model. Both choropleth map and Kano diagram were used to compare and classify research achievements (RA) for countries using the x-index. The differences in RAs were compared between two groups (i.e., participants of Summit for Democracy (SFD) 2021 and Non-SFD) using the forest plot. All animation-typed dashboards were laid on Google Maps for readers to manipulate entities of interest on their own. RESULTS The burst spot and citation trend for the top entities were selected and displayed on the TBG. The most cited entities were sequentially shown in the Sankey diagram, including Stoyan R Stoyanov (Australia), Queensland University of Technology (Australia), PMID=25760773, the US, and standards (MeSH). The top three most cited counties/regions were highlighted in a choropleth map and Kano diagram using the x-index to stratify in descending order: Australia, the UK, and Canada with x-indexes of 23.26, 22.21, and 21.42, respectively, when the US and China were divided into individual states and provinces for comparison. Differences in the six selective bibliometric metrics were not found (p>0.05) in countries between SFDs and non-SFDs. CONCLUSIONS We verified that (1) the EISTL model is viable and useful for presenting citation trends in bibliometric research, and (2) the improved TBG mode releases more information about citation trends. The EISTL model makes the bibliometrics clearer and easier to understand. As a corollary, the TBG with citation trends and burst spots is recommended for future bibliometrics and is not merely limited to the citation trends of the JMIR mHealth and uHealth, as we did in this study.

Willingness to Pay of Fishermen Insurance Using Logistic Regression with Parameter Estimated by Maximum Likelihood Estimation Based on Newton Raphson Iteration

The high risk of losing fishermen's life while at sea is inversely proportional to their low welfare. Fishermen are also unable to meet their daily needs when they are not going to sea. Fishermen welfare insurance can be a solution for them to meet their daily needs. Willingness to Pay (WTP) of fishermen to participate in fishermen welfare insurance can be analyzed using Logistic Regression with Newton Raphson and Genetic Algorithm approximations. Some of the main factors that can support their WTP to participate in fishermen welfare insurance, are fishermen education, membership in the fishing community, membership in fisherman business cards, and knowledge about the existence of fishermen insurance. From these four factors, Logistic Regression Model is generated which is expected to help the increase of fishermen’s WTP on fishermen insurance in Indonesia.

Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

Unconditional Applicability of Lehmer’s Measure to the Two-Term Machin-like Formula for π

Lehmer defined a measure depending on numbers beta_i used in a Machin-like formula for pi. When the beta_i are integers, Lehmer's measure can be used to determine the computational efficiency of the given Machin-like formula for pi. However, because the computations are complicated, it is unclear if Lehmer's measure applies when one or more of the beta_i are rational. In this article, we develop a new algorithm for a two-term Machin-like formula for pi as an example of the unconditional applicability of Lehmer's measure. This approach does not involve any irrational numbers and may allow calculating pi rapidly by the Newton-Raphson iteration method for the tangent function.

Calculation of Flight Data Fusion Coefficients Using Newton–Raphson Iterations

The problem of plotting the flight path of an aircraft based on flight data containing numerous measurement errors is investigated. A theoretical (continuous) model of the flight data fusion problem is proposed in the form of a boundary value problem for a system of differential equations with unknown coefficients. The application of the Newton–Raphson iteration method for calculating the sought-for coefficients is described.

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.