A necessary and sufficient condition for the strong consistency of a family of estimators of the common odds ratio

1995 ◽  
Vol 23 (2) ◽  
pp. 215-225
Author(s):  
Kai Fun Yu
Keyword(s):  
Odds Ratio ◽  
Strong Consistency ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Common Odds Ratio ◽  
The Common ◽  
Necessary And Sufficient

A non-uniform rate of convergence in a local limit theorem

1978 ◽  
Vol 84 (2) ◽  
pp. 351-359 ◽  
Author(s):  
Sujit K. Basu
Keyword(s):  
Limit Theorem ◽  
Rate Of Convergence ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Standard Normal ◽  
The Common ◽  
Necessary And Sufficient

AbstractLet {Xn} be a sequence of iid random variables. If the common charac-teristic function is absolutely integrable in mth power for some integer m ≥ 1, then Zn = n−½(X1 + … + Xn) has a pdf fn for all n ≥ m. Here we give a necessary and sufficient condition for sup as n. → ∞, where φ (x) is the standard normal pdf and M(x) is a non-decreasing function of x ≥ 0 such that M(0) > 0 and M(x)/xδ is non-increasing for 0 < δ ≤ 1.

scholarly journals A Novel Necessary and Sufficient Condition for the Positivity of a Binary Quartic Form

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yang Guo
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pencil Of Conics ◽  
Quartic Form ◽  
The Common ◽  
Necessary And Sufficient

In this paper, by considering the common points of two conics instead of the roots of the binary quartic form, we propose a novel necessary and sufficient condition for the positivity of a binary quartic form using the theory of the pencil of conics. First, we show the degenerate members of the pencil of conics according to the distinct natures of the common points of two base conics. Then, the inequalities about the parameters of the degenerate members are obtained according to the properties of the degenerate conics. Last, from the inequalities, we derive a novel criterion for determining the positivity of a binary quartic form without the discriminant.

State-Transition Computation Models and Program Correctness Thereon

2007 ◽  
Vol 11 (10) ◽  
pp. 1250-1261 ◽  
Author(s):  
Kiyoshi Akama ◽  
◽  
Ekawit Nantajeewarawat ◽  
Keyword(s):  
General Theory ◽  
State Transition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Program Correctness ◽  
Common Framework ◽  
The Common ◽  
Correct Program ◽  
Necessary And Sufficient ◽  
Mapping Concept

The common framework for formalizing state-transition computation models we present is based on a general theory for studying the interrelationship of specifications, programs, computation, and program correctness. We establish a necessary and sufficient condition for program correctness for this class of computation models and demonstrate framework application by formalizing, as its instances, two concrete examples of state-transition computation models – NAT and D-rule. We compare their correct-program spaces by introducing the embedding mapping concept.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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