We study in this paper some nonparametric inference problems where the nonparametric maximum likelihood estimator (NPMLE) are not well defined. However, if we enlarge the parameter space, the NPMLE will be well defined. We propose to gradually shrink the enlarged parameter space by placing more and more restrictions on the parameter space, producing a sequence of (envelope) estimators. The approach is a counter part of the sieve MLE (Grenander, 1981). Several different problems where this method can be applied effectively are discussed. The detailed treatment of 2-sample location problem is presented, including a Wilks type theorem for the empirical envelope likelihood ratio statistic and the asymptotic distribution of the empirical envelope MLE of location.

In this study we investigate maximum likelihood (ML) estimation and likelihood ratio (LR) tests for the multivariate normal distribution with mean vector ~ and covariance matrix k following the linear structures: 11 = Xr< and]:; = I T G, where X and G are properly defined ~ ~.- g g~g ~ ~g

Bootstrap LR tests of stationarity, common trends and cointegration

We investigate the Polyakov loop in different representations of SU(3) in pure gauge at finite T. We discuss Casimir scaling for the Polyakov loop in the deconfined phase and test and generalize the renormalization procedure for the Polyakov loop from [ 1] to arbitrary representations

Abstract: This paper presents the likelihood ratio (LR) test for the number of cointegrating and multi-cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the (multi-) cointegration ranks is identical to the asymptotic

In this paper, we use a maximal invariant likelihood (MIL) to construct two likelihood ratio (LR) tests. The first involves testing for the inclusion of a non-linear regressor and the second involves testing of a linear regressor against the alternative of a non-linear regressor. We report

Likelihood ratio (LR) tests for association and for interaction are examined for three-way contingency tables, in particular, the widely used 2 × 2 ×K table. Mutual information identities are used to characterize the information decomposition and the logical relationship between the omnibus LR test

In this note, we show that LR(k) testing of context-free grammars with respect to random instances is many-one complete for DistNP (Distributional NP). The same result holds for testing whether a context-free grammar is LL(k), strong LL(k), SLR(k), LC(k) or strong LC(k), respectively.

In this paper a Canonical Correlation Analysis CCA is used to test the hypothesis r r against the alternative r r Such a test ips the null and alternative hypotheses of Johansens LR test and can be used jointly with the LR test to construct a condence set for the cointegra tion rank

Likelihood ratio (LR) tests for the cointegrating rank of a vector autoregressive (VAR) process have been developed under different assumptions regarding deterministic terms. For instance, nonzero mean terms and linear trends have been accounted for in some of the tests. In this paper we provide a