Testing conditional independence with data missing at random

It is known that conditional independence is a quite basic assumption in many fields of statistics. How to test its validity is of great importance and has been extensively studied by the literature. Nevertheless, all of the existing methods focus on the case that data are fully observed, but none of them seems having taken into account of the scenario when missing data are present. Motivated by this, this paper develops two testing statistics to handle such a situation relying on the idea of inverse probability weighted and augmented inverse probability weighted techniques. The asymptotic distributions of the proposed statistics are also derived under the null hypothesis. The simulation studies indicate that both testing statistics perform well in terms of size and power.

Conditional Independence Leads to Satisfaction of the Bell Inequality without Assuming Non-Locality or Non-Reality

The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy the particles, the physical realization of three variables from an experiment producing two particles per trial requires two separate trial runs. One assumed variable value (for particle 1) occurs at a fixed instrument setting in both trial runs while a second variable (for particle 2) occurs at alternative instrument settings in the two trial runs. Given that measurements on the two particles occurring in each trial are themselves correlated, measurements from independent realizations at mutually exclusive settings on particle 2 are conditionally independent, i.e., conditionally dependent on particle 1, through probability. This situation is realized from variables defined by Bell using entangled particle pairs. Two correlations have the form that Bell computed from entanglement, but a third correlation from conditionally independent measurements has a different form. When the correlations are computed using quantum probabilities, the Bell inequality is satisfied without recourse to assumptions of non-locality, or non-reality.

The Researches on Path Independence Problem

Rationality condition is imposed in Arrow's General Possibility Theorem in order for social choice to be independent of the path of choice. In this Paper, emphasis is laid on the analysis of the relevance of path independence and rationality condition. Two kinds of Path independence, i.e., Plott's path independence and Bandyopadhyay's sequential path independence, are shown, and their meanings with respect to the problem are investigated.

LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS

In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.

The Use of Field Dependence/Independence in Language Acquisition

Field dependence/independence in Language Acquisition are discussed by many language learners.In this article,we will mainly focus on talking about the cognitive style,including the concept of Field-dependence/independence,their character istics and differences and functions in language acquisition.

The Independence-Separation Problem on the 3-D Rook’s Graph

Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

CONSISTENCY BETWEEN INDEPENDENCE THEOREMS AND GENERALIZED SELF-CONSISTENT METHOD

Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.

On the connotation, challenge and significance of China’s “energy independence” strategy

The world’s energy is in the "third major transformation period" from fossil energy to new energy, and all countries in the world have formulated energy development strategies. Through advanced deployment, the United States is about to achieve "energy independence" relying on "unconventional oil and gas revolution". China’s energy development is faced with four challenges:(1) The population base and economic development scale determine the "totally huge amount" of energy consumption;(2) the "coal rich but oil and gas insufficient" resource structure determines the "unclean" energy consuming structure;(3) the increasing dependence on imported oil and gas determines the "unsafe" energy supply;and(4) the unconventional oil and gas endowment makes it impossible to achieve energy independence by copying the American model. From the perspective of the world energy trend and the unique situation of China’s energy, we put forward a "three-step" strategy for China to achieve "energy independence": From 2020 to 2035, "energy supply security" will be addressed by "cleaning coal, stabilizing oil and gas production and vigorously developing new alternative energy";from 2035 to 2050, the vision of "production independence" will be realized by relying on "domestic production and overseas oil and gas mining rights";from 2050 to 2100, "intelligent energy and new energy" will help China realize "energy independence". The two important signs of China’s "energy independence" are that domestic production accounts for more than 90% of the domestic consumption and clean energy production accounts for more than 70%, and energy security realizes "independence and self-control" and "long-term security". The strategic significance of "energy independence" is to ensure national energy security, drive the development of relevant major industries, achieve energy management reform, and implement the environmental protection goal of zero carbon emissions. The "energy independence" of China is a strategic mission, it might be fulfilled in the future with the growth of the state’s power, even when the domestic energy production does not catch up with the domestic consumption. Perhaps the world’s new technological revolution will exceed expectations, and China’s "energy independence" dream will eventually come true.

Sub-independence-spaces

聪明地使用独立空格和 B-matroids 的关系，这份报纸第一处理一个独立空格的闭合操作员的性质，由介绍定义并且在电路的帮助下解决一些相对性质一个独立空格的亚独立空格列在后面。

A View on Independence of Grammar——Extracts from Syntactic Structures

According to Chomsky,the grammar of Language is a device that generates all of the grammatical sequences of Language and none of the ungrammatical ones.However,as the foundation of Universal Grammar,independence of grammar is strongly criticized by many other linguists.This paper aims at reviewing the literature and illustrating different ideas towards Universal Grammar.

The Criterion of weighting the independence of non-executive directors

Non-executive directors are now very well established in Chinese business. The uniform and final criterion of weighting the independence of non-executive directors is not available. It will be valuable to draw an analogy with the criterion of weighting the independence of non-executive directors in the UK, where over a dozen different criterions are applied.

An Analysis of Judy’s Personality of Independence in Daddy-Long-Legs

Daddy- Long- Legs written by Jane Webster in 1912 has been always well received since it was published. In the novel, Miss Webster portrays a female image Judy who remained positive although she grew up in asylum and bore the brunt of distressing time. She tried her best to improve her ideas and personality and become a writer and paid back to Daddy- Long-Legs.As a result, she got real love from Daddy- Long-Legs and she also became a typical representative of independent females. The author of the paper aims making more teenagers take Judy as an example and learn from her. What’s more, we can gradually develop our own independent spirit.

Changes and Trends in the Independence of the US Federal Reserve Following the Financial Crisis

In 2018, US President Donald Trump repeatedly and publicly criticized the US Federal Reserve for raising interest rates too quickly, breaking the long-established precedent for presidents to refrain from intervening in monetary policy and putting the independence of the Federal Reserve into question. However, this is only the latest development of a longer process: since the financial crisis, the Federal Reserve has been gradually losing its independence, in a quiet and perhaps permanent way. There are several reasons for this trend: the Federal Reserve’s performance during the financial crisis undermined its credibility, the consolidation of political factors arranged against its independence, and the consequences of the financial crisis weakened the economic foundation for its independence. Trump’s rise to power has only strengthened these factors, bringing an additional loss of independence, which will have a profound impact on the economy, society, and politics.

Study on Rank Reversal and Independence of Irrelevant Alternatives

Rank reversals appearing in AHP are discussed. It is proved with examples that they are in certain degree universal in the process of decision making. The mechanism of rank reversal is expounded. It is believed that rank reversal can not deny the reasonableness of AHP and the axioms of independences of irrelevant alternatives.

Independence Numbers in Trees

The independence number of a graph G is the maximum cardinality among all independent sets of G. For any tree T of order n ≥ 2, it is easy to see that . In addition, if there are duplicated leaves in a tree, then these duplicated leaves are all lying in every maximum independent set. In this paper, we will show that if T is a tree of order n ≥ 4 without duplicated leaves, then . Moreover, we constructively characterize the extremal trees T of order n ≥ 4, which are without duplicated leaves, achieving these upper bounds.

The Influence of the Empowerment of the Elderly Group on Independence of Activities Daily Living in Arjuna Village Bandung

The increasing number of the elderly in Indonesia as a result of the success of development has led to increasing problems in the elderly group whose natural life journey will experience an old age with all its limitations, especially in the health problems of the elderly who suffer from disabilities compared to younger people. The situation is also added that the elderly usually suffer from a variety of physiological disorders that are chronic, and biological aspect, psychological aspect, socio economic aspect will experience setback. The empowerment of elderly group is an effort to give power or strength so that elderly have independence, especially in aspects of intellectual ability, and aspects Physical, the empowerment of the elderly is done by improving ability through education. This study aims to analyze the influence of empowerment of the elderly group through health education on the independence of Activitiey Daily Living (ADL). The research design used quasi-experiment with the approach of pre post test group design without comparison (control), while the data analysis used t-test. The results of the study before being carried out empowerment through health education on the independence of the average value of independence were 9.9506 (SD 4.66074) and the result after being carried out empowerment through health education became 13.2716 (SD.4.61523) Research Results showed statistically significant influence on empowering the elderly group through health education to independence of the ADL with a p-value of 0.04. Based on this, it is recommended that empowerment for the elderly should be determined in Posbindu activities. The effect of empowering the elderly group through more effective health education can influence the level of independence by providing a guidebook (module) which is equipped with interesting pictures about the procedures for fulfilling the needs of daily activities, finished providing educational guidebooks. The guidebook is given to the elderly group can be read repeatedly so that it affects the elderly memory in a longer period of time.

Decomposition of Independence Using the Logit Uniform Association Model and Equality of Concordance and Discordance for Two-Way Classifications

For two-way contingency tables with ordered categories, the present paper gives a theorem that the independence model holds if and only if the logit uniform association model holds and equality of concordance and discordance for all pairs of adjacent rows and all dichotomous collapsing of the columns holds. Using the theorem, we analyze the cross-classification of duodenal ulcer patients according to operation and dumping severity.

Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method

For the system with the fuzzy failure state, the effects of the input random variables and the fuzzy failure state on the fuzzy probability of failure for the structural system are studied, and the moment-independence global sensitivity analysis（GSA） model is proposed to quantitatively measure these effects. According to the fuzzy random theory, the fuzzy failure state is transformed into an equivalent new random variable for the system, and the complementary function of the membership function of the fuzzy failure state is defined as the cumulative distribution function（CDF） of the new random variable. After introducing the new random variable, the equivalent performance function of the original problem is built. The difference between the unconditional fuzzy probability of failure and conditional fuzzy probability of failure is defined as the moment-independent GSA index. In order to solve the proposed GSA index efficiently, the Kriging-based algorithm is developed to estimate the defined moment-independence GSA index. Two engineering examples are employed to verify the feasibility and rationality of the presented GSA model, and the advantages of the developed Kriging method are also illustrated.

ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES

This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.