Analysis of binary spatial data by quasi-likelihood estimating equations

The goal of this paper is to describe the application of quasi-likelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov-Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses. The consistency and asymptotic normality for quasi-likelihood estimates can then be derived. By modeling spatial correlation with a variogram, we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well-known example based on data from Lansing Woods. The comparison of generalized estimating equations and the proposed approach is also discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000057 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal x(i) with Fourier transform X(ν) band-limited to |ν|<Θ/2 can be reconstructed from its samples x(T0n) with T0=2π/Θ. In the case that X(ν) consists of two bands and is band-limited to ν0<|ν|<ν0 +Θ/2, successful reconstruction of x(t) from x(T0n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T0n) and x(2T0n+d1), with average sampling period T0, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case

Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor

Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system