Detailed Statistical Inference—An Alternative Non-Bayesian Approach : Two-Decision Problem

1992 ◽  
Vol 42 (1-2) ◽  
pp. 41-74
Author(s):  
Shoutir Kishore Chatterjee ◽  
Gaurangadeb Chattopadhyay
Keyword(s):  
Statistical Inference ◽  
Bayesian Approach ◽  
Decision Problem ◽  
Utility Functions ◽  
Subject Classification ◽  
New Approach ◽  
Ams Subject Classification ◽  
Actual Application ◽  
Betting Odds

In this paper we propose a new approach to detailed inference for any two-decision problem under the frequentist framework, based on a somewhat different interpretation of the confidence coefficients in terms of betting odds. We first elaborate this interpretation with reference to summary inference and enlarge the interpretation to the needs of detailed inference. The actual application of the proposed technique requires the choice of some suitable utility functions. We illustrate our ideas through some examples. AMS Subject Classification: 62 A 99.

Detailed Statistical Inference – From Multiple Decisions to Confidence Sets – A Non­Bayesian Approach

2000 ◽  
Vol 50 (1-2) ◽  
pp. 17-32
Author(s):  
Gaurangadeb Chattopadhyay
Keyword(s):  
Utility Function ◽  
Statistical Inference ◽  
Parameter Space ◽  
Decision Problem ◽  
Confidence Set ◽  
Truncated Form ◽  
Confidence Sets ◽  
New Approach ◽  
Multiple Decision Problem ◽  
Betting Odds

A new approach to detailed statistical inference for the two-decision and multiple decision problem was developed by Chatterjee and Chattopadhyay (1992, 1993). The procedure developed for the multipledecision case is used here to find a solution to, what may be called, the problem of estimation by a ‘confidence set’ when the parameter space is finite. The confidence set problem in which we are required to state a datadependent measure of ‘confidence’ which can be interpreted in terms of betting odds that are ‘optimal’ under repeated experimentation, is considered. A truncated form of utility function is introduced. The case of the truncated form of logarithmic utility function is considered in detail. AMS {2000} Subject Classification: 62A01, 62F99.

Detailed Statistical Inference-multiple Decision Problem

1993 ◽  
Vol 43 (3-4) ◽  
pp. 155-180
Author(s):  
Shoutir Kishore Chatterjee ◽  
gaurangadeb Chattopadhyay
Keyword(s):  
Utility Function ◽  
Statistical Inference ◽  
Decision Problem ◽  
Numerical Examples ◽  
Mathematical Result ◽  
Logarithmic Utility ◽  
Actual Solution ◽  
Case Application ◽  
Multiple Decision Problem ◽  
Betting Odds

The procedure for detailed statistical inference developed by the authors in an earlier paper (1992) for the two-decision case, is extended here to the case of several decisions. Alongwith the rule for choosing the decision, the problem of stating data dependent measures of confidence in terms of betting odds, is considered. The extension involves generalization oftlie coneept of legitimacy of betting odds introduced in the earlier paper and the choice of a suitable utility function for bets. The actual solution is worked out in the case of logarithmic utility. A rather intricate mathematical result requires to be established to prove the existence of an optimum rule in this case. Application of the procedure is illustrated through some numerical examples.

Comparison of Judgment Scales of the Analytical Hierarchy Process — A New Approach

2019 ◽  
Vol 18 (02) ◽  
pp. 445-463 ◽  
Author(s):  
Klaus D. Goepel
Keyword(s):  
Analytical Hierarchy Process ◽  
Analytic Functions ◽  
Decision Problem ◽  
Decision Criteria ◽  
Maximum Weight ◽  
Analytic Hierarchy ◽  
New Approach ◽  
Scale Functions ◽  
Decision Method ◽  
Hierarchy Process

The analytic hierarchy process (AHP) remains a popular multi-criteria decision method. One topic under discussion of AHP is the use of different scales to translate judgments into ratios. The author makes a new approach to compare different scale functions and to derive a recommendation for the application of scales. The approach is based on simple analytic functions and takes into consideration the number of criteria of the decision problem. A generalization of the so-called balanced scale is proposed, and a new adaptive-balanced scale is introduced. Scales are then categorized and compared based on weight boundaries and weight ratios, weight uncertainties, weight dispersion and number of decision criteria. Finally, a practical example of a decision hierarchy is presented applying the different scales. The results show that the generalized balanced scale improves weight dispersion and weight uncertainty in comparison to the fundamental AHP scale. The proposed adaptive-balanced scale overcomes the problem of a change of the maximum weight depending on the number of decision criteria.

Designs Robust Against Aberrations

1993 ◽  
Vol 43 (1-2) ◽  
pp. 95-108 ◽  
Author(s):  
N. K. Mandal ◽  
K. R. Shah
Keyword(s):  
Sufficient Conditions ◽  
Subject Classification ◽  
Alternative Formulation ◽  
Block Designs ◽  
Ams Subject Classification ◽  
Secondary 62K05

In this paper, we obtain sufficient conditions for a design to be robust against aberrations in the sense of Box and Draper. Block designs, row-column designs and fractional designs are considered here. An alternative formulation of robustness is also presented. AMS Subject Classification: Primary 62K99; Secondary 62K05.

scholarly journals Two Higher Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 14 (1) ◽  
pp. 179-187
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Higher Order ◽  
Secant Method ◽  
Subject Classification ◽  
Numerical Examples ◽  
Ams Subject Classification

 The main purpose of this paper is to derive two higher order iterative methods for solving nonlinear equations as variants of Mir, Ayub and Rafiq method. These methods are free from higher order derivatives. We obtain these methods by amalgamating Mir, Ayub and Rafiq method with standard secant method and modified secant method given by Amat and Busquier. The order of convergence of new variants are four and six. Also, numerical examples are given to compare the performance of newly introduced methods with the similar existing methods. 2010 AMS Subject Classification: 65H05 Journal of the Institute of Engineering, 2018, 14(1): 179-187

A Bayesian approach to statistical inference in stochastic DEA

Omega ◽  
2010 ◽  
Vol 38 (5) ◽  
pp. 309-314 ◽  
Author(s):  
Efthymios G. Tsionas ◽  
Emmanuel N. Papadakis
Keyword(s):  
Statistical Inference ◽  
Bayesian Approach ◽  
Stochastic Dea

scholarly journals Reinforcement Number of a Graph with respect to Half-Domination

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
G. Muhiuddin ◽  
N. Sridharan ◽  
D. Al-Kadi ◽  
S. Amutha ◽  
M. E. Elnair
Keyword(s):  
Upper Bounds ◽  
Subject Classification ◽  
Ams Subject Classification

In this paper, we introduce the concept of reinforcement number with respect to half-domination and initiate a study on this parameter. Furthermore, we obtain various upper bounds for this parameter. AMS subject classification: 05C38, 05C40, 05C69.

scholarly journals AMS subject classification:30C45 Meromorphically p-valent functions defined by integral operator involving ȴ-Function in new subclasses

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Ahmed Khalaf Radhi ◽  
Thamer Khalil Al-Khafaji
Keyword(s):  
Integral Operator ◽  
Convex Set ◽  
Subject Classification ◽  
Partial Sums ◽  
Coefficient Inequality ◽  
Ams Subject Classification ◽  
Distortion Bounds

Some relations in this paper we using  in  new subclass of meromorphically p-valent functions TK( ) defined by integral operator involving  -function  We derived some properties, like, coefficient inequality  , growth and distortion bounds by theorems (2) and (3), Partial sums, convex set, radii of starlikeness and radii  convexity.

Inverse Sampling for Bivariate Nonparametric Two-Sample Problems Against Restricted Alternatives

1992 ◽  
Vol 42 (3-4) ◽  
pp. 221-236 ◽  
Author(s):  
Uttam Bandyopadhyay ◽  
Gopaldeb Chattopadhyay
Keyword(s):  
Nonparametric Tests ◽  
Bivariate Distribution ◽  
Distribution Functions ◽  
Subject Classification ◽  
Fixed Size ◽  
Inverse Sampling ◽  
Large Sample ◽  
Ams Subject Classification

The object of the present investigation is to provide suitable nonparametric tests for testing the identity of two bivariate distribution functions F1 and F2 against a class of restricted alternatives when there is sample of fixed size m from F1 and the observations from F2 are drawn sequentially. Various large sample results of the proposed tests are formulated and examined. AMS Subject Classification: Primary 62010, Secondary 62020.

Sign in / Sign up

Export Citation Format

Share Document