Neyman, J. and Elisabeth L. Scott, 1948, Consistent Estimates Based on Partially Consistent Observations, Econometrica, 16, 1-32.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Since we are interested in the position and orientation of the structure but not the exact orientation of each emission, the variables for the former are called the structural parameters while the latter the nuisance parameters [2] This type of formulation is called the Neyman Scott problem [14]. A similar mathematical structure is also found in what is known as the errors in variables model [4] In the above example, an optimal solution can be obtained by introducing a parametric model for the laser emission orientations and regarding the actual emissions as randomly sampled from it. ....

J. Neyman and E. L. Scott, Consistent estimates based on partially consistent observations, Econometrica, 16-1 (1948-1), 1--32.

....parameters. However, this type of modeling causes various difculties. The main difculty in such modeling arises since the number of unknown parameters increases with the number of samples. The family of problems which are characterized by this property was rst presented by Neyman and Scott [7]. Their goal was to nd Consistent estimates based on partially consistent observations . In their classic paper they show that sometimes maximum likelihood (ML) estimation fails to provide consistent estimates. They also give examples in which ML estimates are consistent but not optimal in the ....

J. Neyman and E. L. Scott. Consistent estimates based on partially consistent observations. Econometrica, 16(1):1--32, January 1948.

....# as the size of the data matrix increases. As the number of legislators n l grows by one so does the size of #. Similarly,asn v grows so does the size of #. This proliferation of parameters as the sample size increases is well known to undermine the standard consistency results for ML estimators #Neyman and Scott 1948#. One way around this problem has been to show that estimates of # will be consistent under a so called #triple asymptotic condition #Haberman 1977#. In these cases, # can be consistently estimated if the following three conditions hold: #1# the number of roll calls goes to in#nity, #2# the ....

Neyman, J. and Elizabeth L. Scott. 1948. #Consistent estimates based on partially consistent observations." Econometrics. 16#1#:1#32.

....a density function ( Then, the x i are regarded as independent observations from the semiparametric model p(x; Z q(x; d; 2:7) where ( is the nuisance parameter of function degrees of freedom. This model is called the mixture model. This type of problems was studied by Neyman and Scott (1948) and has attracted many researchers (Andersen (1970) Lindsay (1982) Kumon and Amari (1984) Amari and Kumon (1988) Pfanzagl (1990) etc. There are a lot of interesting and important examples in this class. A typical example is the following class of distributions of the form, q(x; expf ....

Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica 32, 1 -- 32.

....the simplest likelihood approach to eliminating nuisance parameters is to replace them with their conditional maximize likelihood estimates, leading to the profile likelihood in (2) this can then be used as an ordinary likelihood. Many examples of misleading behavior of the profile likelihood (Neyman and Scott, 1948; Cruddas, Cox and Reid, 1989) have given rise to various corrections of the profile, which aim to account for the error in simply replacing by a point estimate. Among the advances in this area are the modified profile likelihood (Barndorff Nielsen 1983, 1988) and the conditional profile ....

Neyman, J. and Scott, E.L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1--32.

....the u it is a random error. We now consider the nature of a i , which may be treated as fixed or random. If it is treated as fixed, we cannot obtain consistent estimates of a i since the number of a i increases with the sample size. This is the familiar incidental parameter problem addressed by Neyman and Scott (1948). In the case of fixed effects, an assumption of a logistic distribution for u it produces a computationally simple maximum likelihood estimator. This is the conditional maximum likelihood estimator, where the conditioning is carried out with respect to the minimal sufficient statistics in order ....

Neyman, J. and Scott, E. L. (1948) - `Consistent estimates based on partially consistent observations', Econometrics, 16, 1-32.

....even when the repeated measurements (Y ij ; j = 1; p) at the point X i are available. In this case, the pro le 3 likelihood becomes pl n ( 1 p 2 ) np exp n X i=1 fY ij (X i )g 2 =2 2 ; where (X i ) p 1 P p j=1 Y ij . This case corresponds to the famous Neyman Scott (1948) problem. In both cases, the pro le likelihood method does not even give a consistent estimator of . What distinguishes this from the Cox proportional hazards model The entropy of the nuisance parameter space in the nonparametric regression model is much larger without further restrictions on ....

Neyman, J. and Scott, Elizabeth L. (1948) Consistent estimates based on partially consistent observations. Econometrica, 16, 1 - 32.

....logit model to estimate both the locations of legislators ideal points and the locations of legislative bills in a unidimensional attribute space. Heckman and Snyder (1997) noted that the Poole Rosenthal estimator is inconsistent due to the incidental parameters problem rst identi ed by Neyman and Scott (1948). In particular, the bill locations are inconsistently estimated because only one observation (vote) is possible for each 3 Anderson, De Palma, and Thisse (1992) refer to the ideal point model as the address model. 4 Estimation of the covariance matrix, however, would not be possible if the ....

Neyman, J. and Scott, E.L. (1948), \Consistent Estimates Based on Partially Consistent Observations, " Econometrica, 16, 1-32.

....class of problems being considered here, Section 2 also gives a natural generalization, termed the C bootstrap, of an approach that involves resampling the estimator. Section 3 considers a number of examples involving a single parameter including the classical problem of estimating a common mean (Neyman Scott 1948). In Section 4, the multiparameter case is considered explicitly. Methods based on generalized score statistics are developed to estimate subsets or functions of the parameters, or to test hypotheses specified in various ways. The methods are exemplified in an example on binary logistic ....

....are k independent strata and, in the ith stratum, y ij # N ( # 2 i ) j =1, n i , independently where n i # 3andi=1, k. The variances # 2 i are unknown and interest centers on the estimation of . This problem has received much attention in the literature; cf. e.g. Bartlett (1936) Neyman Scott (1948), Kalbfleisch Sprott (1970) Barndor# Nielsen (1983) and Cox Reid (1987) Neyman and Scott showed that the maximum likelihood estimator can be ine#cient. They (and many others) proposed the estimating equation k # i=1 n i (n i 2) y i ) T i ( 0 (9) where T i ( # n i j=1 (y ....

J. Neyman & E. L. Scott (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1--32.

....8. A particularly simple case is the following. 2. 6) Definition Let us call a family (P j ) simple structured if p ( j) q ( v(T ( j) 2 INTRODUCTION 8 and if for every 2 Theta the statistic T is complete for the family (P j : j 2 ) The famous example of Neyman and Scott, [12], is simple structured. If the family (P j ) is simple structured then h Gamma does not depend on Gamma and it is possible to construct asymptotically efficient estimator sequences by means of the conditional maximum likelihood method. For details confer Pfanzagl, 13] Remark 7.10. ....

J. Neyman and E. Scott. Consistent estimates based on partially consistent observations. Econometrica, 16:1--32, 1948.

....#v i u e (# i )# 2 . 5 Large sample asymptotics This section studies the behavior of the least squares estimators of the small circle parameters as the sample size goes to infinity, when the errors are bounded away from 0. The least squares estimators are, in this situation, inconsistent. Neymann and Scott (1948) showed that too many nuisance parameters can jeopardize the convergence of the maximum likelihood estimator. For the small circle model, the problem comes from estimating the # i s. Assume that v i has a rotationally symmetric distribution with mean direction u(# i ) whose density with respect ....

Neymann, J. and Scott, E.L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1-32.

....property wrt a one to one differential transformation, a property not shared by the unbiased minimum variance estimators. Now assume that Omega Gamma OE) is unknown, and collect the parameters as = fi; OE) where fi are parameters of interest and OE are the nuisance parameters. The so called Neyman and Scott (1948) problem is that the ML estimator obtained by ignoring nuisance parameters OE can be inefficient and inconsistent. Though this was published as a lead article in Econometrica, it is rarely, if ever, cited in econometric literature. The EF literature shows how to avoid the Neyman Scott problem. Let ....

Neyman, J. and E. L. Scott (1948). Consistent estimates based on partially consistent observations. Econometrica 16, 1-32.

....F 0 is a continuous distribution, the ELT is surprising because the number of parameters, p i in the previous section, is equal to the number of data points n. There are n Gamma 1 free parameters because P i p i = 1. Parametric MLE s are not necessarily consistent under these conditions (Neyman and Scott, 1948). Also, in the finite discrete case it is eventually true that R(F 0 ) 0, but for the continuous case, R(F 0 ) 0 no matter how large n is. The degrees of freedom in the chisquare is d, unless the distribution of X is completely restricted to a hyperplane of dimension q d. The error in the ....

Neyman, J. & Scott, E.L. (1948). Consistent Estimates Based on Partially Consistent Observations. Econometrica 16, 1--16.

....modelling can, at its worst, be thought of as a problem for which the number of parameters to be estimated grows with the data. It is well known that Maximum Likelihood can become inconsistent (or very inefficient) with such problems, e.g. multiple factor analysis[35] and the Neyman Scott problem[24, 16]. 5 Alternative Bayesian methods In doing inductive inference of mixture models from data, there are several levels of inference that we might conceivably wish to make. We might wish simply to infer the most likely number of components. Or, alternatively, we might wish to infer the number of ....

....and Poisson distributions. In general, with problems such as mixture modelling or multiple factor analysis where the number of parameters to be estimated increases with (and is potentially proportional to) the amount of data, one must beware Maximum Likelihood and MAP methods, which are both liable[24, 16] to give inconsistent results. 7 Snob (and MML) Applications Earlier applications of Snob include several to medical, psychological, biological and exploratory geological data, with a survey in [41] The Poisson module seems to be accurately able to discriminate between pseudorandomly generated ....

J. Neyman and E.L. Scott. Consistent estimates based on partially consistent observations. Econometrika, 16:1--32, 1948.

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Neyman, J. and Elisabeth L. Scott, 1948, Consistent Estimates Based on Partially Consistent Observations, Econometrica, 16, 1-32.

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Neyman, J. and Scott, E. (1948) Consistent Estimates Based on Partially Consistent Observations. Econometrica, 16, 1-32 Institut de Statistique, Universit'e de Louvain, 20 Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium.

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Neyman, J. and Scott, E.L., (1948). Consistent estimates based on partially consistent observations. Econometrica 16, 1--32.

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Neyman, J. and Scott, E.L. (1948), \Consistent Estimates Based on Partially Consistent Observations, " Econometrica, 16, 1-32.

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