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Statistical Inference for Discrete Time Stochastic Processes

Part of the SpringerBriefs in Statistics Book Series

DOI: 10.1007/978-81-322-0763-4

ISBN: 978-81-322-0762-7

Publisher: Springer India - Springer Journals

Oct 5, 2012

Available

CAN Estimators from Dependent Observations

Rajarshi, M. B.

Pages: 1 –18

[ In this chapter, we review some basic properties of stationary stochastic processes. Results on martingale limit theorems and laws of large numbers for mixing sequences, as well as central limit theorems for sums of dependent random variables have been discussed. We then discuss weak...
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Markov Chains and Their Extensions

Rajarshi, M. B.

Pages: 19 –38

[This chapter deals with likelihood-based inference for ergodic finite as well as infinite Markov chains. We also consider extensions of Markov chain models, such as Hidden Markov chain, Markov chains based on polytomous regression, and Raftery’s Mixture Transition Density model. These models...
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Non-Gaussian ARMA Models

Rajarshi, M. B.

Pages: 39 –54

[We discuss stationary AR and ARMA time series models for sequences of integer-valued random variables and continuous random variables. Stationary distribution of these models is non-Gaussian. Such models can be broadly described as extensions of Gaussian ARMA models, which have been very widely...
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Estimating Functions

Rajarshi, M. B.

Pages: 55 –75

[In this chapter, we discuss methods of estimation of parameters which assume that the conditional expectation and conditional variance of an observable given the past observations have been specified. These constitute semi-parametric methods for stochastic models. We begin with Conditional Least...
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Estimation of Joint Densities and Conditional Expectation

Rajarshi, M. B.

Pages: 77 –83

[This chapter deals with estimation of joint density and conditional expectation when observations form a stationary time series. We describe kernel density estimation under the assumption that the time series satisfies the strong mixing condition. We give examples wherein kernel density...
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Bootstrap and Other Resampling Procedures

Rajarshi, M. B.

Pages: 85 –110

[In this chapter, we discuss various resampling procedures, such as bootstrap, jackknife, and sample re-use procedures for discrete time stochastic processes. Our discussion begins with bootstrap procedures for finite and infinite Markov chains. Further, bootstrap for stationary real valued...

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