scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

1994 ◽  
Vol 10 (5) ◽  
pp. 821-848 ◽  
Author(s):  
Joel L. Horowitz ◽  
Wolfgang Härdle

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.


2018 ◽  
Vol 19 (4) ◽  
pp. 341-361 ◽  
Author(s):  
Paul Wilson ◽  
Jochen Einbeck

Abstract: While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.


2000 ◽  
Vol 16 (4) ◽  
pp. 576-601 ◽  
Author(s):  
Pascal Lavergne ◽  
Quang Vuong

A procedure for testing the significance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has an nhp2/2 standard normal limiting distribution, where p2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detects local alternatives approaching the null at rate slower than n−1/2h−p2/4. Our Monte-Carlo experiments indicate that it outperforms the test proposed by Fan and Li (1996, Econometrica 64, 865–890).


Author(s):  
Jack P. C. Kleijnen ◽  
Wim C. M. van Beers

Kriging or Gaussian process models are popular metamodels (surrogate models or emulators) of simulation models; these metamodels give predictors for input combinations that are not simulated. To validate these metamodels for computationally expensive simulation models, the analysts often apply computationally efficient cross-validation. In this paper, we derive new statistical tests for so-called leave-one-out cross-validation. Graphically, we present these tests as scatterplots augmented with confidence intervals that use the estimated variances of the Kriging predictors. To estimate the true variances of these predictors, we might use bootstrapping. Like other statistical tests, our tests—with or without bootstrapping—have type I and type II error probabilities; to estimate these probabilities, we use Monte Carlo experiments. We also use such experiments to investigate statistical convergence. To illustrate the application of our tests, we use (i) an example with two inputs and (ii) the popular borehole example with eight inputs. Summary of Contribution: Simulation models are very popular in operations research (OR) and are also known as computer simulations or computer experiments. A popular topic is design and analysis of computer experiments. This paper focuses on Kriging methods and cross-validation methods applied to simulation models; these methods and models are often applied in OR. More specifically, the paper provides the following; (1) the basic variant of a new statistical test for leave-one–out cross-validation; (2) a bootstrap method for the estimation of the true variance of the Kriging predictor; and (3) Monte Carlo experiments for the evaluation of the consistency of the Kriging predictor, the convergence of the Studentized prediction error to the standard normal variable, and the convergence of the expected experimentwise type I error rate to the prespecified nominal value. The new statistical test is illustrated through examples, including the popular borehole model.


2006 ◽  
Vol 19 (24) ◽  
pp. 6353-6370 ◽  
Author(s):  
Charles Jones ◽  
Leila M. V. Carvalho

Abstract The Madden–Julian oscillation (MJO) is the most prominent mode of tropical intraseasonal variability. This study investigates the following questions. Is there statistical evidence of linear trends in MJO activity since the mid-1970s? Does the MJO exhibit changes in regimes of high and low activity? Are there significant seasonal differences in the activity of the MJO on time scales longer than interannual? Positive linear trends are observed in zonal wind anomalies at 200 (U200) and 850 (U850) hPa during summer and winter seasons. Positive trends are also observed in the number of summer MJO events. Resampling statistical tests indicate that positive trends in summer U200 and U850 anomalies are statistically different from random occurrences at a 5% significance level. A methodology based on the number of events is used to characterize low-frequency (LF) changes in MJO activity. Mean winter LF activity was characterized by nearly uniform variability from the early 1960s until the mid-1990s. In contrast, mean summer LF changes showed a regime of high activity from the mid-1960s until the late 1970s, a low regime from 1980 to 1988, and a regime of high activity from the early 1990s to early 2000. Fourier analysis of the mean summer LF index indicates that regimes of high MJO activity were separated by 18.5 yr. The substantial changes in summer MJO regimes do not appear to be related to increases in observational samplings due to satellite-derived winds assimilated in the NCEP–NCAR reanalysis. Monte Carlo experiments indicate that the observed changes in regimes of MJO activity in summer are statistically different from random occurrences at the 10% significance level only.


2016 ◽  
Vol 5 (11) ◽  
pp. 5041
Author(s):  
Farkhondeh Jamshidi ◽  
Ahmad Ghorbani ◽  
Sina Darvishi*

The abuse of some pesticides especially to suicide is one of the current problems of pesticides. Aluminum phosphide induced poisoning usually happens to suicide and sometimes it is due to accidental occupational exposure and in a few cases it has some criminal intensions. This study is conducted to evaluate patients poisoned with aluminum phosphide. In the present study the medical records of cases of poisoning with rice tablets (aluminum phosphide) hospitalized in Ahvaz Razi hospital is studied. Accordingly, a checklist is prepared that included demographic information of patients (age, gender) and information on patient records (information on poisoning) are completed using the patients’ medical records. The analysis of data is done by SPSS V22. 18 patients poisoned with rice tablet (aluminum phosphide) are studied. Results of the study show that 11 patients are male and seven are female. The mean patient age is 27.06 ±8.04 years that is 28 ±9 and 25 ±6.02 in men and women respectively. Statistical tests show no statistically significant difference in mean age in both genders (P> 0.05). Among patients, 11 subjects took aluminum phosphide to attempt suicide and 3 cases took it unintentionally and of course the reason is not mentioned in four cases. Among the patients who tried to commit suicide by taking aluminum phosphide, 6 cases are male and 5 cases are female that no statistically significant difference is observed between the genders in this respect (P> 0.05). In addition to the study of the complications caused by this poisoning and its mortality, it is recommended to responsible authorities to provide the necessary educations and treatments to prevent this type of poisoning.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 497.2-497
Author(s):  
J. Arroyo Palomo ◽  
M. Arce Benavente ◽  
C. Pijoan Moratalla ◽  
B. A. Blanco Cáceres ◽  
A. Rodriguez

Background:Musculoeskeletal ultrasound (MSUS) is frequently used in several rheumatology units to detect subclinical inflammation in patients with joint symptoms suspected for progression to inflammatory arthritis (IA). Synovitis grade I (EULAR-OMERACT combined score) is known to be a casual finding in healthy individuals, but studies headed to unravel its possible role on rheumatic diseases are sparse.Objectives:To investigate the correlation between synovitis grade I, and the diagnosis of IA made after a year follow-up period since MSUS findings, in patients of an MSUS-specialized unit of a Rheumatology Department.Methods:We conducted a descriptive, retrospective and unicentric study. 30 patients were selected from the MSUS-specialized unit of our Rheumatology Department from July-18 to January-19. Patients presenting synovitis grade 0 (exclusively), 2 and/or 3 on combined score were excluded. Data collection at baseline included age, sex, immunological profile and previous physical examination to the MSUS findings, as well as the diagnosis made by the rheumatologist in 1-year visit follow-up: dividing the patient sample into two groups: those who were diagnosed with IA and those not. Non-parametric statistical tests for comparing means were used.Results:The mean age was 51,6 years and 70% were females. 6 (20%) patients were diagnosed with inflammatory arthritis after a year follow-up: 2 (4,8%) psoriatic arthritis, 1 (3,3%) undifferentiated arthritis, 1 (3,3%) rheumatoid arthritis, 1 (3,3%) Sjögren’s syndrome. Non-inflammatory arthropathies were also found 24 (80%), of which, 12 (40%) were non-specific arthralgias and 8 (19%) osteoarthritis.In the group of patients who did not developed an IA the mean C-reactive protein (CPR) value was 3,12 mg/L and erythrocyte sedimentation rate (ESR) was 8,2 mm; all of them were rheumatoid factor (RF) positive and ACPA-negative except one patient. 5 (31,3%) patients presented low antinuclear antibodies (ANAs) levels. In those who HLA B-27 and Cw6 were tested (4,25%); both were negative except for one that was HLA B-27 positive. The median number of swollen and painful joint count was 0, and the mean of joints with MSUS involvement was 3,5; the mean involved metacarpophalangeal (MCP) joints was 1,83; proximal interphalangeal (PIP) joints was 1,48 and distal interphalangeal (DIP) joints 0,21.Among the group of patients that developed an IA the mean of CPR and ESR was 9,27 mg/L and 14,17 mm respectively; 2 (33%) patients were RF- positive, and 1 ACPA-positive. ANAs were positive in 3 cases (50%). The median of swollen joint count was 2 and for painful joint count was 0, the median of joints with MSUS involvement was 4,5. The mean of MSUS involvement was for MCP, PIP and DIP joints: 1,67, 2 and 0. Comparing the means of CPR values in the two groups with Student’s t-test we obtained a statistically significant difference (p=0,023). No other significant differences were found.Conclusion:Despite the limitations and possible statistical bias, the presence of MSUS-defined synovitis grade I and elevated CRP levels could be related to further diagnoses of inflammatory arthropathy. Besides, the absence of synovitis in DIP joints might have a diagnostic role. Normal physical exploration and normal levels of CRP might suggest low MSUS value. However, further research is needed to clarify the role of MSUS-defined synovitis grade I.References:[1]D’Agostino MA et al. Scoring ultrasound synovitis in rheumatoid arthritis: a EULAR-OMERACT ultrasound taskforce-Part 1: definition and development of a standardized, consensus-based scoring system. RMD Open. 2017;3(1):e000428.[2]Van den Berg R et al. What is the value of musculoskeletal ultrasound in patients presenting with arthralgia to predict inflammatory arthritis development? A systematic literature review. Arthritis Research & Therapy (2018) 20:228.Disclosure of Interests:None declared


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Aristeidis A. Villias ◽  
Stefanos G. Kourtis ◽  
Hercules C. Karkazis ◽  
Gregory L. Polyzois

Abstract Background The replica technique with its modifications (negative replica) has been used for the assessment of marginal fit (MF). However, identification of the boundaries between prosthesis, cement, and abutment is challenging. The recently developed Digital Image Analysis Sequence (DIAS) addresses this limitation. Although DIAS is applicable, its reliability has not yet been proven. The purpose of this study was to verify the DIAS as an acceptable method for the quantitative assessment of MF at cemented crowns, by conducting statistical tests of agreement between different examiners. Methods One hundred fifty-one implant-supported experimental crowns were cemented. Equal negative replicas were produced from the assemblies. Each replica was sectioned in six parts, which were photographed under an optical microscope. From the 906 standardized digital photomicrographs (0.65 μm/pixel), 130 were randomly selected for analysis. DIAS included tracing the profile of the crown and the abutment and marking the margin definition points before cementation. Next, the traced and marked outlines were superimposed on each digital image, highlighting the components’ boundaries and enabling MF measurements. One researcher ran the analysis twice and three others once, independently. Five groups of 130 measurements were formed. Intra- and interobserver reliability was evaluated with intraclass correlation coefficient (ICC). Agreement was estimated with the standard error of measurement (SEM), the smallest detectable change at the 95% confidence level (SDC95%), and the Bland and Altman method of limits of agreement (LoA). Results Measured MF ranged between 22.83 and 286.58 pixels. Both the intra- and interobserver reliability were excellent, ICC = 1 at 95% confidence level. The intra- and interobserver SEM and SDC95% were less than 1 and 3 pixels, respectively. The Bland–Altman analysis presented graphically high level of agreement between the mean measurement of the first observer and each of the three other observers’ measurements. Differences between observers were normally distributed. In all three cases, the mean difference was less than 1 pixel and within ± 3 pixels LoA laid at least 95% of differences. T tests of the differences did not reveal any fixed bias (P > .05, not significant). Conclusion The DIAS is an objective and reliable method able to detect and quantify MF at ranges observed in clinical practice.


Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.


Sankhya B ◽  
2021 ◽  
Author(s):  
Stefan Bedbur ◽  
Thomas Seiche

AbstractIn step-stress experiments, test units are successively exposed to higher usually increasing levels of stress to cause earlier failures and to shorten the duration of the experiment. When parameters are associated with the stress levels, one problem is to estimate the parameter corresponding to normal operating conditions based on failure data obtained under higher stress levels. For this purpose, a link function connecting parameters and stress levels is usually assumed, the validity of which is often at the discretion of the experimenter. In a general step-stress model based on multiple samples of sequential order statistics, we provide exact statistical tests to decide whether the assumption of some link function is adequate. The null hypothesis of a proportional, linear, power or log-linear link function is considered in detail, and associated inferential results are stated. In any case, except for the linear link function, the test statistics derived are shown to have only one distribution under the null hypothesis, which simplifies the computation of (exact) critical values. Asymptotic results are addressed, and a power study is performed for testing on a log-linear link function. Some improvements of the tests in terms of power are discussed.


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