Conditional independence, conditional mixing and conditional association

@article{Rao2009ConditionalIC,
  title={Conditional independence, conditional mixing and conditional association},
  author={B. L. S. Prakasa Rao},
  journal={Annals of the Institute of Statistical Mathematics},
  year={2009},
  volume={61},
  pages={441-460}
}
  • B. Rao
  • Published 1 June 2009
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hajek-Renyi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional… 
Some conditional results for conditionally strong mixing sequences of random variables
The relation between strong mixing and conditionally strong mixing is answered by examples, that is, the strong mixing property of random variables does not imply the conditionally strong mixing
Conditional versions of limit theorems for conditionally associated random variables
Abstract Relation between association and conditional association is answered, several examples show that the association of random variables does not imply the conditional association, and vice
Conditional limit theorems for conditionally negatively associated random variables
From the ordinary notion of negative association for a sequence of random variables, a new concept called conditional negative association is introduced. The relation between negative association and
From Conditional Independence to Conditionally Negative Association: Some Preliminary Results
Conditional moment estimates on the cumulative sum of conditionally independent random variables are derived, conditional prophet inequalities for conditionally independent random variables are
Some preliminary results on conditionally ψ-mixing sequences of random variables
From the ordinary notion of -mixing for a sequence of random variables, a new concept called conditionally -mixing is proposed. That conditionally -mixing neither implies nor is implied by -mixing is
On inequalities for conditional probabilities of unions of events and the conditional Borel–Cantelli lemma
New sharp upper and lower bounds for conditional (given a σ-algebra A) probabilities of unions of events and for a generalization of the conditional Borel–Cantelli lemma are obtained. Averaging the
Conditional limit theorems for conditionally linearly negative quadrant dependent random variables
From the ordinary notion of linearly negative quadrant dependence for a sequence of random variables, a new concept called conditionally linearly negative quadrant dependence is introduced. The
A conditional version of the extended Kolmogorov-Feller weak law of large numbers ✩
A conditional version of the extended Kolmogorov–Feller weak law of large numbers is established, which generalizes the existing results and is actually adapted to a sequence of exchangeable random
THE CONDITIONAL BOREL-CANTELLI LEMMA AND APPLICATIONS
In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of F -independent random variables sequences,
Conditional mean convergence theorems of conditionally dependent random variables under conditions of integrability
We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 32 REFERENCES
Probability theory: Independence, interchangeability, martingales
1 Classes of Sets, Measures, and Probability Spaces.- 1.1 Sets and set operations.- 1.2 Spaces and indicators.- 1.3 Sigma-algebras, measurable spaces, and product spaces.- 1.4 Measurable
Moment inequalities for mixing sequences of random variables
In this work, sequences of random variables are considered satisfying certain mixing conditions. After the relevant definitions are presented, some alternative characterizations are discussed. Also,
ON THE APPLICATION OF THE BOREL-CANTELLI LEMMA
The celebrated Borel-Cantelli lemma asserts that (A) If ~P(E,,) < 00, then P (lim sup Ek) =O; (B) If the events Es are independent and if xP(Ek) = m, then P(lim sup Eh) = 1. In intuitive language
Asymptotic optimal inference for non-ergodic models
0. An Over-view.- 1. Introduction.- 2. The Classical Fisher-Rao Model for Asymptotic Inference.- 3. Generalisation of the Fisher-Rao Model to Non-ergodic Type Processes.- 4. Mixture Experiments and
CHARACTERIZATION OF PROBABILITY MEASURES BY LINEAR FUNCTIONS DEFINED ON A HOMOGENEOUS MARKOV CHAIN
Let ζ 1 , ζ 2 , ζ 3 be three independent random variables and Z 1 = ζ 1 −ζ 2 and Z 2 = ζ 2 −ζ 3 . It is known that if the characteristic function of (Z 1 , Z 2 ) does not vanish, then the
Associated sequences and related inference problems
The concept of association of random variables was introduced by Esary et al. (1967). In several situations, for example, in reliability and survival analysis, the random variables of lifetimes
Statistical inference for diffusion type processes
Semimartingales exponential families of stochastic processes asymptotic likelihood theory asymptotic likelihood theory for diffusion processes quasi-likelihood and semimartingales local asymptotic
On mixing for flows of σ -algebras
The notion of mixing is extended to flows of σ-algebras. Suppose a stochastic process is mixing in some sense. Conditions under which this process, observed at random times, inherits mixing property
Semimartingales and their Statistical Inference
Semimartingales Introduction Stochastic Processes Doob-Meyer Decomposition Stochastic Integration Local Martingales Semimartingales Girsanov's Theorem Limit Theorems for Semimartingales Diffusion
...
1
2
3
4
...