An Improved Method of Estimating an Integer-Parameter by Maximum Likelihood

Abstract

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Capture–Recapture When Time and Behavioral Response Affect Capture Probabilities

“…The second part of maximization is equivalent to estimating the size in a binomial case for a given trial probability 1 -Q. Thus, the CMLE is the integer part of Mt+l/(l -Q) (cf., Dahiya, 1981). For easy interpretation, the nearly exact solution M t + l / ( l -Q) instead of its integer part (error is less than unity) will be used and referred to as the CMLE throughout this article.…”

“…If N is treated as an integer, maximization is possible (Otis et al, 1978;Dahiya, 1981;Lindsay and Roeder, 1987) but the numerical manipulations become less tractable. Since the likelihood (2.1) is meaningful for any real N , we treat N as a real number in this article.…”

Integer estimation methods for GPS ambiguity resolution: an applications oriented review and improvement

“…As a result, (6) is also called the closest point problem in integer programming (see, e.g., [22]). If we further set y in (6) to 0, the corresponding problem is alternatively called the shortest vector problem (see, e.g., [22]). We should note, however, that integer programming is concerned with finding the optimal numerical solution(s) to an objective function with integer variables.…”

“…The estimation of real-valued and integer unknown parameters β and z in (1) is essentially a statistical inference problem. However, almost nothing can be found in any statistical literature and/or statistical journals, except for the maximum likelihood estimation of a single integer parameter that is associated with the binomial and/or Poisson distribution (see, e.g., [6], [21], [32]), as can be readily seen after a quick web search or a quick look at scientific journals on statistics. Although the integer linear model (2) is important in many different areas of science and engineering, likely due to the barrier of different languages used in different subject areas, researchers from different disciplines seem to be hardly aware of theory and methods developed and used beyond his or her own field of study.…”

The Capture-Recapture approach for population estimation in computer networks

“…Such terminology has been widely exploited in the 19 computer networks literature by analogy with similar esti-20 mation problems in biological environments [65]. 21 As a matter of fact, statistical approaches dealing with the 22 estimation of the population size are based on sampling, i.e., 23 on analyzing a subset of the entire population. The biometric 24 community developed many approaches [63,65], some as 25 old as the nineteenth century [44,51], to face the trade-off 26 between the effectiveness of estimation methods and their 27 computational complexity.…”