اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCumulative Tsallis Entropy for Maximum Ranked Set Sampling with Unequal Samples
88
0
0.0
(
0
)
نشر من قبل
Maria Longobardi Prof.Dr.
تاريخ النشر
2020
مجال البحث
الاحصاء الرياضي
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a nonadditive generalization of Shannon entropy. We obtain several results of Tsallis entropy including bounds, monotonic properties, stochastic orders, and sharp bounds under some assumptions. We also compare the uncertainty and information content of MRSSU with its counterpart in the simple random sampling (SRS) data. Finally, we develop some characterization results in terms of cumulative Tsallis entropy and residual Tsallis entropy of MRSSU and SRS data.
قيم البحث
اقرأ أيضاً
We prove that any implementation of pivotal sampling is more efficient than multinomial sampling. This property entails the weak consistency of the Horvitz-Thompson estimator and the existence of a conservative variance estimator. A small simulation study supports our findings.
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannons or Tsallis entropies in the concomitant variational problem. It is shown that the two variations
lead to equivalent solutions that take different appearances but contain the same information. These solutions are linked by our transformation.
We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the sampling cos
ts, and one important question is how many to sample for optimal gain (worth minus costs). If, in addition, the assessment of worth for each sample is associated with some measurement error, the perceived best out of $n$ might not be the actual best, complicating the issue. Situations like this are typical in mate selection, job hiring, and food foraging, to name just a few. We tackle the problem by standard order statistics, yielding suggestions for optimal strategies, as well as some unexpected insights.
Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffdings inequality that use weaker assu
mptions but produce much looser (wider) intervals. In 1969, Anderson (1969) proposed a mean confidence interval strictly better than or equal to Hoeffdings whose only assumption is that the distributions support is contained in an interval $[a,b]$. For the first time since then, we present a new family of bounds that compares favorably to Andersons. We prove that each bound in the family has {em guaranteed coverage}, i.e., it holds with probability at least $1-alpha$ for all distributions on an interval $[a,b]$. Furthermore, one of the bounds is tighter than or equal to Andersons for all samples. In simulations, we show that for many distributions, the gain over Andersons bound is substantial.
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing observati
ons. Using the Stochastic Block Model as a parametric proxy, we bound the risk of the maximum likelihood estimator of network connections probabilities , and show that it is minimax optimal. When risk is measured in Frobenius norm, no estimator running in polynomial time has been shown to attain the minimax optimal rate of convergence for this problem. Thus, maximum likelihood estimation is of particular interest as computationally efficient approximations to it have been proposed in the literature and are often used in practice.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
