Composite Likelihood Inference by Nonparametric Saddlepoint Tests

The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strenght of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently inaccurate estimates of the Godambe information translate in inaccurate p-values. In this paper it is shown how accurate inference can be obtained by using a fully nonparametric saddlepoint test statistic derived from the composite score functions. The proposed statistic is asymptotically chi-square distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies

Empirical and Simulated Adjustments of Composite Likelihood Ratio Statistics

Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward asymptotic distribution. There are many proposals for adjusting composite likelihood ratio tests in order to recover an asymptotic chi square distribution, but they all depend on the sensitivity and variability matrices. The same is true for Wald-type and score-type counterparts. In realistic applications sensitivity and variability matrices usually need to be estimated, but there are no comparisons of the performance of composite likelihood based statistics in such an instance. A comparison of the accuracy of inference based on the statistics considering two methods typically employed for estimation of sensitivity and variability matrices, namely an empirical method that exploits independent observations, and Monte Carlo simulation, is performed. The results in two examples involving the pairwise likelihood show that a very large number of independent observations should be available in order to obtain accurate coverages using empirical estimation, while limited simulation from the full model provides accurate results regardless of the availability of independent observations.Comment: 15 page

Changepoint Detection over Graphs with the Spectral Scan Statistic

We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics and relate it to the problem of finding a sparsest cut in a graph. We develop a tractable relaxation of the GLR statistic based on the combinatorial Laplacian of the graph, which we call the spectral scan statistic, and analyze its properties. We show how its performance as a testing procedure depends directly on the spectrum of the graph, and use this result to explicitly derive its asymptotic properties on few significant graph topologies. Finally, we demonstrate both theoretically and by simulations that the spectral scan statistic can outperform naive testing procedures based on edge thresholding and $\chi^2$ testing

Participation in the Conservation Reserve Program and Off-Farm Work: Implications for Farm and Farm Household Productivity

Using a national survey of U.S farm households, we investigate the interrelationship between participation in the Conservation Reserve Program (CRP) and the decision to work off the farm. We go on examine the effects of these two decisions on farm and farm household efficiency and productivity by estimating stochastic frontier productions for farm output and multiple output-orientated distance functions that consider income from agricultural sales, the CRP and off-farm work as outputs of the farm household. We control for the effects of self selection in estimating both the frontier production and distance functions. It appears that operators' decisions to work off the farm have led to significant improvements in household resource allocation between farm and other productive activities by farm households -- leading to high technical efficiency for both farm and farm household activities. In contract, participation in the CRP alone leads to the reduction of the technical efficiency and productivity on farm as well as on combined household activities.Farm Management,

Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems

The Bayesian formulation of sequentially testing $M \ge 3$ hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most $M-1$ unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensor messages, multiple sensors, or composite hypotheses.Comment: 14 pages, 1 figure, submitted to IEEE Trans. Inf. Theor

On the Maximal Invariant Statistic for Adaptive Radar Detection in Partially-Homogeneous Disturbance with Persymmetric Covariance

This letter deals with the problem of adaptive signal detection in partially-homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the Maximal Invariant Statistic (MIS) is derived. Then, it is shown that the (Two-step) Generalized-Likelihood Ratio test, Rao and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a Constant False-Alarm Rate (CFAR).Comment: submitted for journal publicatio