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Papers by Paul Feigin

Advances in Applied Probability, 1973

to + 00 the limit behaviour of M; is similar to that of Sn, and we obtain a weak-convergence theo... more to + 00 the limit behaviour of M; is similar to that of Sn, and we obtain a weak-convergence theorem to this effect, thereby extending earlier work by Heyde. When oscillation occurs, Problems I and II are substantially (though not entirely) equivalent, the connection being provided by the continuous mapping theorem of weak convergence theory; again there are connections with earlier work by Heyde. A complete solution to Problem II is obtained when X is spectrally negative, by means of results of Zolotarev and the author (this contains the usual solution for the Wiener case). In general one cannot obtain even the one-dimensional distributions of Y explicitly, but we obtain complete asymptotic information on Yand Z. We find explicitly the process X(Z) giving the place of first exit from an interval. We also discuss the method of ladder-points in this context, note some open problems, and discuss some connections with related work.

Stochastic Processes and their Applications, May 1, 1986

This paper develops an approach to conditional inference for nonergodic stochastic process models... more This paper develops an approach to conditional inference for nonergodic stochastic process models by considering asymptotic properties. The context for most of the analysis is that of Le Cam's local asymptotic theory: in particular, the locally asymptotically mixed normal (LAMN) situation. An attempt has been made to evaluate local asymptotic properties of global procedures. locally asymptotically mixed normal * nonergodic stochastic processes * decision theory * approximate ancillarity * local ancillarity * asymptotic conditional risk * contiguity * conditional exponential families

Communications in statistics, 1992

Annals of Statistics, Dec 1, 1982

The New England Journal of Medicine, Sep 24, 2009

Journal of Time Series Analysis, 1985

Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general sta... more Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general state space have recently been developed. We illustrate their application to non-linear time series models and, in particular, to random coefficient autoregressive models. As well as ensuring the existence of a unique stationary distribution, geometric rates of convergence to stationarity are ensured. Moreover, sufficient conditions for the existence and convergence of moments can be determined by a closely related method. The latter conditions, in particular, are new.

Journal of Mathematical Sciences, Jun 1, 2005

Journal of the royal statistical society series b-methodological, 1978

CONSIDER a number n of judges, each of whom ranks the same set of k objects according to some par... more CONSIDER a number n of judges, each of whom ranks the same set of k objects according to some particular criterion. Assume that each judge ranks (stochastically) independently of the other judges so that we regard the situation as that of n rankings (Daniels, 1950; Kendall, 1970) or of n related samples (Conover, 1971, p. 246). We wish to say something about whether and to what degree the judges act concordantly (or homogeneously) with respect to a particular ranking which is not assumed known beforehand. More particularly we wish to estimate this underlying ranking and also consider a model for the proposed measure of concordance. In so doing we address ourselves to the problem of non-null modelling referred to in Kendall (1970, p. V). To place the suggested model in its proper setting it is appropriate to review briefly the relevant literature on modelling non-null distributions for rankings. These models may be, broadly speaking, divided into three classes: (I) parametric; (II) paired comparison; and (III) sampling. The parametric approach may be further subdivided into the categories: (Ia) multivariate; and (Ib) independent deviations. They may be described as follows:

Stochastic Processes and their Applications, 1978

concerning parameters of stochastic processes. Spxial at ttmti(w 1% 1 conditional exponential fam... more concerning parameters of stochastic processes. Spxial at ttmti(w 1% 1 conditional exponential families of stochastic processes and tc! three tc\t\ hard 1~ the' ~DI;I~E likelihood estimate as well as to the likelihood ratio tc\t. A contiguit! c';bi~:lnl;ttu~n trr. UW$ try that a previously suggested criterion is inadequate and itself provtdcx a par:iai scab problem. A heuristic argument is also put forward to support a propoGticrn rr optimality of the maximum iikelihood estimate in a certain WW. Two examples *isi< the theory are discussed. asymptotic efficiency contiguity .: 'l~~itional exponential families hypothesis testing

Springer eBooks, 1975

A general definition of efficiency for stochastic process estimation is proposed and some of its ... more A general definition of efficiency for stochastic process estimation is proposed and some of its ramifications are explored. Of particular importance in the definition is the form of the derivative of the logarithm of the likelihood. The question of the simplest possible form for this leads on to a discussion of extensions of the concepts of sufficiency and exponential families, the latter in a Markov process context. The paper concludes with several illustrative examples.

Annals of Probability, May 1, 1984

Journal of Applied Probability, Jun 1, 1979

We provide a probabilistic proof of the characterization of point processes (on the real line) wi... more We provide a probabilistic proof of the characterization of point processes (on the real line) with the order statistic property. The characterization is used to investigate the homogeneity of such processes and is also related to the martingale theory associated with point processes.

Journal of Applied Probability, Jun 1, 1979

Consider the maximum likelihood estimation of θ based on continuous observation of the process X,... more Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt. Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

Annals of Statistics, May 1, 1981

Advances in Applied Probability, Jun 1, 1978

Advances in Applied Probability, Jun 1, 1977

convergence theorem in the theoretical framework of the so-called distancediminishing models whic... more convergence theorem in the theoretical framework of the so-called distancediminishing models which gives a straightforward application to conditional probabilities related to partially observed events. Finally we prove a Shannon-McMillan-type theorem finding application to classification procedures. A note on identification characterisation of the Gaussian distribution and time reversibility in linear stochastic processes

Advances in Applied Probability, Sep 1, 1997

Journal of Mathematical Sciences, Jun 1, 2005

Mathematical proceedings of the Cambridge Philosophical Society, May 1, 1989

IEEE Transactions on Engineering Management, 2022

Advances in Applied Probability, 1973

to + 00 the limit behaviour of M; is similar to that of Sn, and we obtain a weak-convergence theo... more to + 00 the limit behaviour of M; is similar to that of Sn, and we obtain a weak-convergence theorem to this effect, thereby extending earlier work by Heyde. When oscillation occurs, Problems I and II are substantially (though not entirely) equivalent, the connection being provided by the continuous mapping theorem of weak convergence theory; again there are connections with earlier work by Heyde. A complete solution to Problem II is obtained when X is spectrally negative, by means of results of Zolotarev and the author (this contains the usual solution for the Wiener case). In general one cannot obtain even the one-dimensional distributions of Y explicitly, but we obtain complete asymptotic information on Yand Z. We find explicitly the process X(Z) giving the place of first exit from an interval. We also discuss the method of ladder-points in this context, note some open problems, and discuss some connections with related work.

Stochastic Processes and their Applications, May 1, 1986

This paper develops an approach to conditional inference for nonergodic stochastic process models... more This paper develops an approach to conditional inference for nonergodic stochastic process models by considering asymptotic properties. The context for most of the analysis is that of Le Cam's local asymptotic theory: in particular, the locally asymptotically mixed normal (LAMN) situation. An attempt has been made to evaluate local asymptotic properties of global procedures. locally asymptotically mixed normal * nonergodic stochastic processes * decision theory * approximate ancillarity * local ancillarity * asymptotic conditional risk * contiguity * conditional exponential families

Communications in statistics, 1992

Annals of Statistics, Dec 1, 1982

The New England Journal of Medicine, Sep 24, 2009

Journal of Time Series Analysis, 1985

Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general sta... more Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general state space have recently been developed. We illustrate their application to non-linear time series models and, in particular, to random coefficient autoregressive models. As well as ensuring the existence of a unique stationary distribution, geometric rates of convergence to stationarity are ensured. Moreover, sufficient conditions for the existence and convergence of moments can be determined by a closely related method. The latter conditions, in particular, are new.

Journal of Mathematical Sciences, Jun 1, 2005

Journal of the royal statistical society series b-methodological, 1978

CONSIDER a number n of judges, each of whom ranks the same set of k objects according to some par... more CONSIDER a number n of judges, each of whom ranks the same set of k objects according to some particular criterion. Assume that each judge ranks (stochastically) independently of the other judges so that we regard the situation as that of n rankings (Daniels, 1950; Kendall, 1970) or of n related samples (Conover, 1971, p. 246). We wish to say something about whether and to what degree the judges act concordantly (or homogeneously) with respect to a particular ranking which is not assumed known beforehand. More particularly we wish to estimate this underlying ranking and also consider a model for the proposed measure of concordance. In so doing we address ourselves to the problem of non-null modelling referred to in Kendall (1970, p. V). To place the suggested model in its proper setting it is appropriate to review briefly the relevant literature on modelling non-null distributions for rankings. These models may be, broadly speaking, divided into three classes: (I) parametric; (II) paired comparison; and (III) sampling. The parametric approach may be further subdivided into the categories: (Ia) multivariate; and (Ib) independent deviations. They may be described as follows:

Stochastic Processes and their Applications, 1978

concerning parameters of stochastic processes. Spxial at ttmti(w 1% 1 conditional exponential fam... more concerning parameters of stochastic processes. Spxial at ttmti(w 1% 1 conditional exponential families of stochastic processes and tc! three tc\t\ hard 1~ the' ~DI;I~E likelihood estimate as well as to the likelihood ratio tc\t. A contiguit! c';bi~:lnl;ttu~n trr. UW$ try that a previously suggested criterion is inadequate and itself provtdcx a par:iai scab problem. A heuristic argument is also put forward to support a propoGticrn rr optimality of the maximum iikelihood estimate in a certain WW. Two examples *isi< the theory are discussed. asymptotic efficiency contiguity .: 'l~~itional exponential families hypothesis testing

Springer eBooks, 1975

A general definition of efficiency for stochastic process estimation is proposed and some of its ... more A general definition of efficiency for stochastic process estimation is proposed and some of its ramifications are explored. Of particular importance in the definition is the form of the derivative of the logarithm of the likelihood. The question of the simplest possible form for this leads on to a discussion of extensions of the concepts of sufficiency and exponential families, the latter in a Markov process context. The paper concludes with several illustrative examples.

Annals of Probability, May 1, 1984

Journal of Applied Probability, Jun 1, 1979

We provide a probabilistic proof of the characterization of point processes (on the real line) wi... more We provide a probabilistic proof of the characterization of point processes (on the real line) with the order statistic property. The characterization is used to investigate the homogeneity of such processes and is also related to the martingale theory associated with point processes.

Journal of Applied Probability, Jun 1, 1979

Consider the maximum likelihood estimation of θ based on continuous observation of the process X,... more Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt. Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

Annals of Statistics, May 1, 1981

Advances in Applied Probability, Jun 1, 1978

Advances in Applied Probability, Jun 1, 1977

convergence theorem in the theoretical framework of the so-called distancediminishing models whic... more convergence theorem in the theoretical framework of the so-called distancediminishing models which gives a straightforward application to conditional probabilities related to partially observed events. Finally we prove a Shannon-McMillan-type theorem finding application to classification procedures. A note on identification characterisation of the Gaussian distribution and time reversibility in linear stochastic processes

Advances in Applied Probability, Sep 1, 1997

Journal of Mathematical Sciences, Jun 1, 2005

Mathematical proceedings of the Cambridge Philosophical Society, May 1, 1989

IEEE Transactions on Engineering Management, 2022