scholarly journals ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

2019 ◽  
Vol 36 (4) ◽  
pp. 559-582
Author(s):  
James A. Duffy
Keyword(s):  
Unit Root ◽  
Regression Models ◽  
Asymptotic Theory ◽  
Kernel Density ◽  
Nonparametric Tests ◽  
Moderate Deviations ◽  
Autoregressive Processes ◽  
Predictive Regression ◽  
Asymptotic Size ◽  
Rejection Probability

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

Influence of alloying systems on the properties of single crystal nickel-based superalloys

2021 ◽  
Vol 112 (10) ◽  
pp. 794-799
Author(s):  
Alexander Glotka ◽  
Vadim Ol’shanetskii
Keyword(s):  
Single Crystal ◽  
Regression Models ◽  
Strength Properties ◽  
Term Limits ◽  
Alloying Elements ◽  
Structure Stability ◽  
Plastic Properties ◽  
Crystal Lattices ◽  
Predictive Regression ◽  
First Time

Abstract The purpose of the investigation was to obtain the predictive regression models that help correct the calculation of the mechanical properties of single crystal nickel-based superalloys without conducting prior experiments. The paper considers the influence of alloying elements on their tendency to form phases in foundry nickel-based superalloys. Using the elements influence on the phase formation, the coefficient Kc’ of the ratio of alloying elements for this class of alloys was set for the first time. We have revealed the short correlation of the ratio Kc’ with the dimensional misfit of γ and γ’ crystal lattices. Also, a high probability to predict the misfit for multicomponent nickel systems is shown, which significantly affected the strength properties. The regression models of correlation dependencies on the dimensional γ/γ’- misfit were offered to predict the short-term and long-term limits of the strength of alloys. We determined the operating temperature at which the misfit value should decrease to zero. The structure stability should increase because of the structural stresses minimizing. This has a positive effect on strength and plastic properties.

scholarly journals Properties of nickel-based superalloys of equiaxial crystallization

2021 ◽  
pp. 19-23
Author(s):  
O. Glotka ◽  
V. Olshanetskii
Keyword(s):  
Mechanical Properties ◽  
Chemical Composition ◽  
Regression Models ◽  
Computational Prediction ◽  
Integrated Approach ◽  
Experimental Data Processing ◽  
Predictive Regression ◽  
Heat Resistant ◽  
First Time ◽  
Thermodynamic Processes

Purpose. The aim of the work is to obtain predictive regression models, with the help of which, it is possible to adequately calculate the mechanical properties of nickel-based superalloys of equiaxial crystallization, without carrying out preliminary experiments. Research methods. To find regularities and calculate  the latest CALPHAD method was chosen, and modeling of thermodynamic processes of phase crystallization was performed. Results. As a result of experimental data processing, the ratio of alloying elements Kg¢ was proposed for the first time, which can be used to assess the mechanical properties, taking into account the complex effect of the main alloy components. The regularities of the influence of the composition on the properties of heat-resistant nickel alloys of equiaxial crystallization are established. The analysis of the received dependences in comparison with practical results is carried out. The relations well correlated with heat resistance, mismatch and strength of alloys are obtained. Scientific novelty. It is shown that for multicomponent nickel systems it is possible with a high probability to predict a mismatch, which significantly affects the strength characteristics of alloys of this class. The regularities of the influence of the chemical composition on the structure and properties of alloys are established. A promising and effective direction in solving the problem of predicting the main characteristics of heat-resistant materials based on nickel is shown Practical value. On the basis of an integrated approach for multicomponent heat-resistant nickel-based alloys, new regression models have been obtained that make it possible to adequately predict the properties of the chemical composition of the alloy, which made it possible to solve the problem of computational prediction of properties from the chemical composition of the alloy. This allows not only to design new nickel-based alloys, but also to optimize the composition of existing brands.

scholarly journals Environmental Factors Associated With Loa loa Microfilaria Prevalence and Intensity in Diverse Bioecological Zones of Cameroon

2021 ◽  
Vol 2 ◽  
Author(s):  
Xavier Badia-Rius ◽  
Hannah Betts ◽  
Samuel Wanji ◽  
David Molyneux ◽  
Mark J. Taylor ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Regression Models ◽  
Polynomial Regression ◽  
Canopy Cover ◽  
Nonparametric Tests ◽  
Tree Canopy ◽  
Mean Annual Temperature ◽  
Loa Loa ◽  
Factors Associated ◽  
Tree Canopy Cover

Loiasis (African Eye Worm) is a filarial infection caused by Loa loa and transmitted by Chrysops vectors, which are confined to the tropical rainforests of Central and West Africa. Loiasis is a major impediment to control and elimination programmes that use the drug ivermectin due to the risk of serious adverse events. There is an urgent need to better refine and map high-risk communities. This study aimed to quantify and predict environmental factors associated with loiasis across five bioecological zones in Cameroon. The L. loa microfilaria (mf) prevalence (%) and intensity (mf number/ml) data from 42 villages within an Equatorial Rainforest and Savannah region were examined in relation to climate, topographic and forest-related data derived from satellite remote sensing sources. Differences between zones and regions were examined using nonparametric tests, and the relationship between L. loa mf prevalence, mf intensity, and the environmental factors using polynomial regression models. Overall, the L. loa mf prevalence was 11.6%, L. loa intensity 927.4 mf/ml, mean annual temperature 23.7°C, annual precipitation 2143.2 mm, elevation 790 m, tree canopy cover 46.7%, and canopy height 19.3m. Significant differences between the Equatorial Rainforest and Savannah region were found. Within the Equatorial Rainforest region, no significant differences were found. However, within the Savannah region, significant differences between the three bioecological zones were found, and the regression models indicated that tree canopy cover and elevation were significant predictors, explaining 85.1% of the L. loa mf prevalence (adjusted R2 = 0.851; p<0.001) and tree cover alone was significant, explaining 58.1% of the mf intensity (adjusted R2 = 0.581; p<0.001). The study highlights that environmental analysis can help delineate risk at different geographical scales, which may be practical for developing larger scale operational plans for mapping and implementing safe effective interventions.

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust
Keyword(s):  
Unit Root ◽  
Sufficient Conditions ◽  
Unit Root Test ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Test Procedures ◽  
Asymptotic Size ◽  
Finite Sample Size ◽  
Topological Sense

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

scholarly journals UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION

2011 ◽  
Vol 27 (6) ◽  
pp. 1117-1151 ◽  
Author(s):  
Chirok Han ◽  
Peter C. B. Phillips ◽  
Donggyu Sul
Keyword(s):  
Normal Distribution ◽  
Rate Of Convergence ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Signal Strength ◽  
Rates Of Convergence ◽  
Moment Conditions ◽  
First Order ◽  
The Cost ◽  
Artificial Shrinkage

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

LSTUR regression theory and the instability of the sample correlation coefficient between financial return indices

2020 ◽  
Author(s):  
Tim Ginker ◽  
Offer Lieberman
Keyword(s):  
Correlation Coefficient ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Financial Return ◽  
Spurious Regression ◽  
Root Model ◽  
Sampling Window ◽  
Sample Correlation ◽  
Underlying Processes ◽  
Regression Theory

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application reveals that the new theory explains very well the instability, in both sign and scale, of the sample correlation coefficient between gold, oil, and stock return price indices. In addition, we establish spurious regression theory for LSTUR variables, which generalises the results known hitherto, as well as a theory for balanced regression in this setting.

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