On the confidence region comparison of some solutions for the multivariate behrens-fisher problem

1975 ◽  
Vol 4 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Kathleen Subrahmaniam ◽  
Kocherlakota Subrahmaniam
Keyword(s):  
Confidence Region

Constraints on kinematic model from Pantheon SNIa, OHD and CMB shift parameter measurements

2021 ◽  
Vol 36 (08) ◽  
pp. 2150049
Author(s):  
Abdulla Al Mamon
Keyword(s):  
Confidence Region ◽  
Kinematic Model ◽  
Hubble Constant ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Shift Parameter ◽  
Redshift Range ◽  
Data Points ◽  
Text Model ◽  
Good Agreement

In this paper, we reconstruct the late-time cosmological dynamics using a purely kinematic approach. In particular, considering a divergence-free parametrization for deceleration parameter [Formula: see text], we first derive the jerk parameter [Formula: see text] and then confront it with combination of various cosmological datasets. We use the most recent observational datasets consisting of the 1048 Pantheon Supernovae Ia data points in the redshift range [Formula: see text], the 51 data points of observational Hubble parameter (OHD) measurements in the redshift range [Formula: see text], the Hubble constant [Formula: see text] (R19) and the CMB shift parameter measurements. We study the evolution of different cosmological quantities for the present model and compare it with the concordance [Formula: see text]CDM model. We find that only the combined Pantheon+OHD+R19 data shows good agreement with the [Formula: see text]CDM [Formula: see text] model within [Formula: see text] confidence region. We also find that our model successfully generates late time cosmic acceleration along with a decelerated expansion in the past.

scholarly journals A Confidence Region for Zero-Gradient Solutions for Robust Parameter Design Experiments

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Aili Cheng ◽  
John Peterson ◽  
Pallavi Chitturi
Keyword(s):  
Confidence Region ◽  
Control Variable ◽  
Critical Values ◽  
Parameter Design ◽  
Feasible Region ◽  
Robust Parameter Design ◽  
Control Variables ◽  
Controllable Factors ◽  
Key Issues ◽  
Robust Parameter

One of the key issues in robust parameter design is to configure the controllable factors to minimize the variance due to noise variables. However, it can sometimes happen that the number of control variables is greater than the number of noise variables. When this occurs, two important situations arise. One is that the variance due to noise variables can be brought down to zero The second is that multiple optimal control variable settings become available to the experimenter. A simultaneous confidence region for such a locus of points not only provides a region of uncertainty about such a solution, but also provides a statistical test of whether or not such points lie within the region of experimentation or a feasible region of operation. However, this situation requires a confidence region for the multiple-solution factor levels that provides proper simultaneous coverage. This requirement has not been previously recognized in the literature. In the case where the number of control variables is greater than the number of noise variables, we show how to construct critical values needed to maintain the simultaneous coverage rate. Two examples are provided as a demonstration of the practical need to adjust the critical values for simultaneous coverage.

scholarly journals Natural inflation after Planck 2018

2022 ◽  
Vol 2022 (01) ◽  
pp. 022
Author(s):  
Nina K. Stein ◽  
William H. Kinney
Keyword(s):  
Symmetry Breaking ◽  
High Precision ◽  
Confidence Region ◽  
Hubble Constant ◽  
Current Data ◽  
Electroweak Symmetry Breaking ◽  
Observational Constraints ◽  
Electroweak Symmetry ◽  
History Of ◽  
The Universe

Abstract We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on r and n S, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95% confidence out by current data. If we assume protracted reheating characterized by w̅>1/3, Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68% confidence region requires values of T re below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant H 0 only worsens the fit.

scholarly journals Block Empirical Likelihood for Longitudinal Single-Index Varying-Coefficient Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yunquan Song ◽  
Ling Jian ◽  
Lu Lin
Keyword(s):  
Longitudinal Data ◽  
Empirical Likelihood ◽  
Coverage Probability ◽  
Confidence Region ◽  
Asymptotic Covariance Matrix ◽  
Varying Coefficient Model ◽  
Varying Coefficient ◽  
Single Index ◽  
Asymptotic Covariance ◽  
Normal Approximations

In this paper, we consider a single-index varying-coefficient model with application to longitudinal data. In order to accommodate the within-group correlation, we apply the block empirical likelihood procedure to longitudinal single-index varying-coefficient model, and prove a nonparametric version of Wilks’ theorem which can be used to construct the block empirical likelihood confidence region with asymptotically correct coverage probability for the parametric component. In comparison with normal approximations, the proposed method does not require a consistent estimator for the asymptotic covariance matrix, making it easier to conduct inference for the model's parametric component. Simulations demonstrate how the proposed method works.

scholarly journals The partial banana mapping: a robust linear method for impact probability estimation

2019 ◽  
Vol 492 (3) ◽  
pp. 4546-4552
Author(s):  
Dmitrii E Vavilov
Keyword(s):  
Coordinate System ◽  
Confidence Region ◽  
Linear Method ◽  
Probability Estimation ◽  
Curvilinear Coordinate System ◽  
The Earth ◽  
Curvilinear Coordinate ◽  
Near Earth Asteroids ◽  
The Impact ◽  
Confidence Ellipsoid

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

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