摘要:

For treatment comparisons in clinical cancer trials, the data often indicate absence or presence of response along with duration of response when it occurs. Response length is frequently truncated by death, loss of followup information, study termination, or other causes, and is usually a discrete variable (days, weeks, or months). A mixture of a binomial and truncated geometric probability is studied as an appropriate statistical model. Maximum likelihood estimators are derived for parameters of the model and a likelihood ratio statistic (-2 InA) is given for testing equality of treatments. Noncentrality parameters are given for power approximations under contiguous alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480342

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This paper establishes new ergodic theorems for population age structure. LetA1,A2, … be denumerable Leslie matrices, and for ℓ = 1,2, m(ℓ)(0) be age structures (vectors with elementsmi(ℓ)(0)), satisfying the assumptions of the Coale-Lopez theorem. Let {A(t, ωℓ)}∞t− 1 be sample paths of a discrete-time Markov chain with sample space {Ak}∞k− 1, and m(ℓ)(t) =A(t, ωℓ)A(t− 1, ωℓ) …A(1, ωℓ)m(ℓ)(0). Then forb= 1, 2, … (weak stochastic ergodicity) limt→∞(E(mi(1)(t)/mi(1)(t))b−E(mi(2)(t)/mi(2)(t))b) = 0 if the chain is finite and weakly ergodic (see [4]) or denumerable and weakly ergodic (see [13]). The limit holds and (strong stochastic ergodicity){m(ℓ)(t)}∞t − 1converge in distribution, if the chain is homogeneous, aperiodic, positive recurrent, and uniformly geometrically ergodic.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480343

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A new algorithm is presented for simulating stable random variables on a digital computer for arbitrary characteristic exponent α(0 < α ≤ 2) and skewness parameter β(-1 ≤ β ≤ 1). The algorithm involves a nonlinear transformation of two independent uniform random variables into one stable random variable. This stable random variable is a continuous function of each of the uniform random variables, and of α and a modified skewness parameter β' throughout their respective permissible ranges.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480344

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The principles of sufficiency and conditionality are shown by Birnbaum [1] to imply the principle of likelihood. But in his formulation it is necessary to adopt in the continuous case, a definition of sufficiency which differs from the conventional definition. The objections against the new definition are set out and it is shown that the conventional definition can be adhered to by taking into consideration that in practice there is always a finite limit to the accuracy with which the values assumed by a continuous random variable can be observed.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480345

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This article deals with the general qualitative response model involving several polytomous variables. An extension of Berkson's minimum chi-square estimator to this model is defined and shown to be not always asymptotically efficient, and the conditions under which it is so are derived. It is also shown that the nonlinear weighted least squares method proposed by Walker and Duncan [11] is equivalent to the method of scoring.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480346

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This article provides an alternative derivation of a maximum likelihood solution, due to Birch [1], which simplifies the algebra and characterizes Birch's solution as a special case of a result, due to Dolby [2], that has application to a variety of more complex structural models, including factor analysis.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480347

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

For nonlinear equation systems, the properties of the MLE commonly have been deduced from related but inapplicable results in the statistical and econometric literature. Under specific regularity conditions, we build on the nonlinear GLS results of Malinvaud to derive the large-sample properties of the MLE and the limiting distribution of the asymptotic likelihood ratio statistic. We discuss iterative convergence conditions under which the iterated Aitken estimator locates a consistent local maximum of the likelihood function, and we derive results permitting convenient estimation of the asymptotic covariance matrix of any subset of parameter estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480348

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

We assume a normal linear regression model. Amongkindependent variables, onlyxkare controllable, and the others are exogenous. The categorical control problem is: given the values of the exogenous variables, how should we controlxkso thatylies within a preassigned target interval (c1,c2)? The answer is to determine an interval (or union of intervals) on thexk-axis, the “regulation interval.” We require that the probability that the dependent variable falls within the target interval simultaneously for allxkin the regulation interval to be at leastPwith confidence 1 − α, wherePand α are preassigned constants.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480349

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

We are concerned with the problem of parameter estimation in normal regression when some of the observations are missing. A Bayesian approach with vague prior distributions is taken. No assumption is made about the independent variables for which no observations are missing, but the missing components are assumed to be normally distributed with a mean that can depend on the other variables. Joint estimators of the parameters are obtained as the joint mode of the posterior distribution.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480350

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Least-squares monotone regression (also known as least-squares isotone regression) is being used increasingly. Recently, an application arose in which the fitted values are restricted to be integers. We prove that a very simple procedure yields the optimum monotonic fit subject to this restriction, or to the more general restriction that the fitted values lie in some specified closed set. This procedure is to perform unrestricted monotone regression, and then to round off each resulting value to the nearest element of the closed set. When there are two nearest elements in the closed set, either one may be chosen, subject to the preservation of monotonicity and to one minor complication.

ISSN:0162-1459    

DOI:10.1080/01621459.1976.10480351

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor