# 统计代写|抽样调查作业代写sampling theory of survey代考|STAT41020

## 统计代写|抽样调查作业代写sampling theory of survey代考|A Few Indirect Questioning Techniques Other than RRT’s

Certain general objections against the virtues of RRT’s are being sounded now-a-days from various quarters. RRT’s are hard to be clearly understood and correctly applied by average respondents, so for them face-to-face interviews are unavoidable; once RR’s are gathered they cannot be reproduced; complaints are common that RRT’s are tricky and are laughable leading to frequent disapprovals. Raghavarao and Federer (1979), Miller (1984), Miller, Cisim and Harrel (1986), Droitcour, Caspar, Hubbard, Parsley, Visscher and Ezzati (1991) are some of the proponents of an alternative indirect questioning technique called Item Count Technique. My collaborative involvement in the multifarious development of the subject is documented in the papers and monographs by Chaudhuri and Christofides $(2007,2008,2013)$, Chaudhuri (2011a), Shaw (2015,2016) and besides, Christofides (2015) has also added substantially. Other prominent contributors include Hussain, Shah and Shabbir (2012) and Tian, Tang, Wu and Liu (2014) among several others.

Briefly, Item Count Technique works as follows. Suppose $T$ stands for a stigmatizing or ‘tainted’ attribute and our object is to estimate in a finite population the proportion $\theta$ that bears it as is usual in RRT’s. But here two independent samples $s_1$ and $s_2$ say, are drawn from a population following a given design $p$ with probabilities and positive inclusion-probabilities $\pi_i$ for $i$ and for every pair $i, j(i \neq j)$ the value $\pi_{i j}, i, j \in U=(1, \cdots N)$. In the first sample a respondent is given a card on which $G(>1)$ innocuous items appear and the tainted attribute $T$ is added as the $(G+1)$ st item and the person is to report the number $K$ out of these $(G+1)$ items that apply to him/her. In the other independently drawn sample $s_2$ a person is presented a list of the above $G$ innocuous items and on request is to announce the number out of them that apply to him/her. Before the present author stepped in, the samples were taken according to the SRSWR method alone. But since 2007 as documented the samples were chosen with general unequal probabilities and essentially without replacement.

## 统计代写|抽样调查作业代写sampling theory of survey代考|Adaptive Sampling

As we understand, vide Chaudhuri $(2000,2015)$, adaptive sampling was introduced by Thompson (1990) and later further developed by Thompson (1992), Thompson and Seber (1996), Salehi and Seber (1997, 2002, 2013), Chaudhuri (2000, 2015) among others including Chaudhuri and Saha (2004), Chaudhuri, Bose and Dihidar (2005), Chaudhuri, Bose and Ghosh $(2004,2005)$ et al.

Suppose we intend to suitably estimate the numbers of people engaged in various types of small-scale industrial enterprises in the rural unorganized sector in certain under-developed or developing countries. This is necessary in assessing the magnitudes and values of gross and net domestic national products. In an Indian state many may earn their livelihoods as iron or goldsmiths or by manufacturing stone chips or metal screws in the villages as private craftsmen and craftswomen. Though in India there is a National Sample Survey Office (NSSO) every year conducting nationwide big surveys in both rural and urban areas in every Indian state or union territory (UT),

such surveys hardly capture such earners industry-wise in sufficient numbers. NSSO-sampled villages may not contain enough goldsmiths and so their contributions to GDP may be significantly underestimated.

A possible remedy is adaptive sampling with specific missions which may not be encouraged by a national survey at all. An adaptive sampling may provide a clue which we plan to discuss below.

As usual, let $U=(1, \cdots, i, \cdots N)$ be a finite population of units with $y$ values $y_i$ for respective $i$ in $U$. Also, let $s$ be a sample of units chosen with probability $p(s)$ according to a design $p$. But suppose that for most of the units $y_i$-values are zero or negligibly small but for certain unknown number of units in unknown locations forming unknowable clusters may be rather high-valued so that the population total $Y=\sum_1^N y_i$ may be quite sizeable in aggregated magnitudes. In a sample $s$ many of the $y_i$-values may be nil or negligible but a few may be adequately positive-valued. Then, it may be rational to suppose, or rather expect one or more neighboring units of such a positivevalued unit may be similarly valued but not in the sample. In such situations it may be worthwhile to extend the sample to cover them to capture useful units contributing to the sample-data helping to create a better estimation to render the estimator closer to the total. So, the following rationally profitable method starts developing.

Given a unit $i$ of $U$, a neighborhood is first uniquely defined. For example given a farmland, one to its left, one to its right, one above and one below it may be regarded as its four neighbors; the set of these five units including the initial unit $i$ itself may be called its neighborhood. When a sample $s$ is drawn, every sampled unit is to be scanned to note its value, doing nothing if it is nil or negligible-valued, but in case it is well-valued check the value of each of its neighbors, going no further if the neighbors are not well-valued but checking each of the neighbors for its value if it is well-valued and proceeding with this process and enhancing the sample and stopping as soon as the first time it is found that none of the units among the neighbors is well-valued. The set of units thus reached starting with a unit is called a cluster of that unit. Dropping from this cluster all the nil or negligible-valued units in it what is left out constitutes the network of the initial unit.

# 抽样调查代考

## 统计代写|抽样调查作业代写sampling theory of survey代考|Adaptive Sampling

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