Bayesian penalized spline modelbased inference for finite population proportion in unequal probability sampling qixuanchen,michaelr. Recall, a statistical inference aims at learning characteristics of the population from a sample. With respect to research design and statistical analysis, a population is the entire collection of entities one seeks to understand or, more formally, about which one seeks to draw an inference consequently, defining clearly the population of interest is a fundamental component of research design because the way in which the population is defined dictates the scope of the inferences. Lucie leon, marie jauffretroustide, yann le strat, designbased inference in timelocation sampling, biostatistics, volume 16, issue 3. Sep 24, 2014 real populations are finite and the branch of statistics which treats sampling of such populations is called survey sampling. Modelbased inference is not predicated on probability sampling so it is a potentially attractive option for using vgi data that did not ori ginate from a probability sampling design.
Alternative modelbased and designbased frameworks for. Hence, in addition to stratum structure, it induces an additional ranking structure within stratum samples. A prediction approach presents for the first time a unified treatment of sample design and estimation for finite populations from a prediction point of view, providing readers with access to a wealth of theoretical results, including many new results and, a variety of practical applications. Iconstruct and implement a probability sampling design. Design and inference in finite population sampling wiley series in survey methodology. Statistical inference using stratified ranked set samples. Randomness comes from sampling alone unbiasedness over repeated sampling. Get a printable copy pdf file of the complete article 534k, or click on a page image below to browse page by page. Strategies based on probability proportional to size schemes of. Bootstrap inference for the finite population total under complex sampling designs. Get a printable copy pdf file of the complete article 534k, or click on a page image below.
Design and inference in finite population sampling wiley series in. For many years survey sampling remained the province of survey samplers with very little input from statisticians involved in the more traditional aspects of the subject. Simple random sampling, systematic sampling, stratified sampling fall into the category of simple sampling techniques. Finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution, rather than on statistical models for the measured variables. Randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling. Full text full text is available as a scanned copy of the original print version. Finite and infinite populations in biological statistics. We first select a simple random sample srs of size n and identify their population ranks. However, modelbased sampling can make use of randomization, and, further, the form of a designbased sample can be guided by the modeling of data. However, modelbased sampling can make use of randomization, and, further, the form of a design based sample can be guided by the modeling of data. Raj, p4 all these four steps are interwoven and cannot be considered isolated from one another.
Evaluation and development of strategies for sample. Inference for the population total from probability proportional to size pps sampling provides a comparison of design based and modelbased approac we use cookies to enhance your experience on our website. Most studies about bootstrapbased inference are developed under simple random sampling and stratified random sampling. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. Sampling distributions and statistical inference sampling distributions population the set of all elements of interest in a particular study.
This latter point is an important part of the material found in cochran 1977. L ittle 1 abstract we propose a bayesian penalized spline predictive bpsp estimator for a finite population proportion in an unequal probability sampling setting. The corresponding numbers for the sample are n, m and k respectively. Causal inference in rebuilding and extending the recondite. Modelbased prediction theory for finite population sampling and inference valliant et al.
Bayesian finite population survey sampling sudipto banerjee division of biostatistics school of public health university of minnesota. If valid estimates of the parameters of a finite population are to be produced, the finite population needs to be defined very precisely and the sampling method needs to be carefully designed and implemented. In brief, designbased inference is the classical approach to inference in survey sampling. Design and inference in finite population sampling book, 1991.
Sampling from finite populations encyclopedia of mathematics. Design and inference in finite population sampling journal. Pdf file of the complete article 534k, or click on a page image below to browse page by page. In chaudhuri and stenger 1992, we see treatment of both designbased and modelbased sampling and inference. Bootstrap inference for the finite population total under complex. Strategies based on probability proportional to size schemes of sampling. Design and inference in finite population sampling ncbi nih. Designbased inference also known as randomization inference is concerned with infer ences about a finite population of size n, with fixed values for element i.
Using standard tools from finite population sampling to improve. It is shown that if the finite population variables have a dirichletmultinomial prior, then the posterior distribution of the inobserved variables given a sample is also dirichletmultinomial. Design and inference in finite population sampling wiley series in survey methodology sinha, b. Designbased inference in timelocation sampling lucie leon. Srss is constructed from a finite population using a without replacement sampling design.
Bootstrap inference for the finite population total under. In the designbased or randomization approach cochran 2007, y pop is treated as fixed, and inferences are based on the distribution of i i 1,i n. By continuing to use our website, you are agreeing to our use of cookies. In this paper, we consider statistical inference based on poststratified samples from a finite population. There are different terms that are used to describe the population, but the most commonly used is the target population, which is a finite set of elements to be studied. Littley abstract we study bayesian inference for the population total in probabilityproportionaltosize pps sampling. Design and inference in finite population sampling wiley series in survey methodology b. Models in the practice of survey sampling revisited scb. Alternative estimation method for a threestage cluster sampling in finite population. Modelbased ideas in finitepopulation sampling have received renewed discussion in recent years. Rubin indian institute of management calcutta department of statistics, harvard university abstract. Inference is constructed under both randomized design and a super population model. Uses of auxiliary size measures in survey sampling. Self and other in literary structure by rene girard 0pm.
Real populations are finite and the branch of statistics which treats sampling of such populations is called survey sampling. This approach automatically takes features of the survey design into. We contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan. Nov 01, 2009 the sampling frame is a list of primary sampling units in the finite population. The main feature of the proposed method is that the finite population is bootstrapped based on a multinomial distribution by incorporating the sampling weights. Estimation of population mean design based inference key idea. In the case of finite population sampling, the statistician is free to choose his own sampling design and is not confined to independent and identically distributed observations as is often the case with traditional statistical inference. The two inferential paradigms are constrasted, andexplanations are supplemented. Modelbased ideas in finite population sampling have received renewed discussion in recent years. Imputations may then be performed assuming iid data. Full text is available as a scanned copy of the original print version. Strategiesbased on probability proportional to size schemes ofsampling. Designbased and modelbased inference in survey sampling. This entry focuses on the estimation of such finite population parameters using what is known as the randomization or designbased approach.
Design and inference in finite population sampling core. Finite population sampling and inference a prediction approach richard valliant alan h. The first page of the pdf of this article appears above. New york chichester weinheim brisbane singapore toronto. Methodology for informative sampling we describe the bayesian model and inference in section 2. Get a printable copy pdf file of the complete article 534k. This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Design and inference in finite population sampling springerlink.
We look at the correspondence between the sampling design and the sampling scheme. The two inferential paradigms are constrasted, andexplanations. Design and inference in finite population sampling. Sorry, we are unable to provide the full text but you may find it at the following locations.
Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results in survey sampling if the sampling design is ignored. Bayesian inference for the finite population total from a. Bayesian penalized spline modelbased inference for finite. In this work, we propose a new bootstrap method applicable to some complex sampling designs, including poisson sampling and probability proportional to size sampling. Causal inference in rebuilding and extending the recondite bridge between finite population sampling and experimental design rahul mukerjee, tirthankar dasgupta and donald b. Design and inference in finite population sampling book. Inference is constructed under both randomization theory and a super population model. The next and generally final step in computing adjusted design weights is to calibrate the nonresponse adjusted weights for responding units to sum to known. Model for informative sampling and inference we have observed i. We propose different variations of the weighted fpbb for different sampling designs, and evaluate these methods using three studies. Their relationship to the classical ideas in sampling theorydo not appear to be universally well understood by samplers in applied disciplines such as forestry, and ecology more broadly. Statistical inference using stratified judgment post.
Little finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution, rather than on statistical models for the measured variables. Competing modes of inference for finite population sampling roderick j. In both approaches, the paper shows that the estimators of population mean and total are unbiased. Offers some important topics not found in other texts on sampling such as the superpopulation approach and randomized response, nonresponse and resampling techniques. Modelbased inference re quires specification of a model that relates y u to a set of covariates predictors. This entry focuses on the estimation of such finite population parameters using what is known as the randomization or design based approach. Bayesian predictive inference for finite population. The sampling frame is a list of primary sampling units in the finite population. However, the term population of inference or inferential population is used more often during the conceptualization stage of research studies and surveys.
To make inference in the population from the random sample, a sampling weight is assigned to each surveyed individual. For most finitepopulation sampling schemes, estimators for simple population parameters, like mean or proportion, are different from those for. Finitepopulationsampling samplingofindependentobservations interestingfactsi i underindependentsamplingin. The sampling design does not play a critical role in modelbased inference although certain design structures such as clusters and strata may be represented in the model. Design and inference in finite population sampling wiley. The most common finite population studies are those related to official statistics. An evaluation of modeldependent and probabilitysampling. Finite population sampling and inference request pdf. Nonprobability sampling for finite population inference.
It is assumed that the observed data set is sampled from a larger population inferential statistics can be contrasted with descriptive. Bayesian statistical inference for sampling a finite. Bias, finite population, optimal estimation, prediction, random effects. We first select a simple random sample srs of size n. A prediction approach presents for the first time a unified treatment of sample design and estimation for finite. Bayesian predictive inference for finite population quantities under informative sampling. Pdf an introduction to sampling from a finite population. In chaudhuri and stenger 1992, we see treatment of both design based and modelbased sampling and inference. Note that a finite population may be considered in several occasions. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.
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