Vector calculus pdf nptel

Please forward this error screen to sharedip-1666228125. Descriptive statistics is solely concerned with properties vector calculus pdf nptel the obse

Please forward this error screen to sharedip-1666228125. Descriptive statistics is solely concerned with properties vector calculus pdf nptel the observed data, and does not assume that the data came from a larger population.

Kitagawa state, “The majority of the problems in statistical inference can be considered to be problems related to statistical modeling”. Any statistical inference requires some assumptions. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference. Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn. The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters. The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal. This term typically implies assumptions ‘in between’ fully and non-parametric approaches.

For example, one may assume that a population distribution has a finite mean. More generally, semi-parametric models can often be separated into ‘structural’ and ‘random variation’ components. One component is treated parametrically and the other non-parametrically. More complex semi- and fully parametric assumptions are also cause for concern. For example, incorrectly assuming the Cox model can in some cases lead to faulty conclusions.

Incorrect assumptions of Normality in the population also invalidates some forms of regression-based inference. In particular, a normal distribution “would be a totally unrealistic and catastrophically unwise assumption to make if we were dealing with any kind of economic population. Here, the central limit theorem states that the distribution of the sample mean “for very large samples” is approximately normally distributed, if the distribution is not heavy tailed. Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these.

Limiting results are not statements about finite samples, and indeed are irrelevant to finite samples. However, the asymptotic theory of limiting distributions is often invoked for work with finite samples. In frequentist inference, randomization allows inferences to be based on the randomization distribution rather than a subjective model, and this is important especially in survey sampling and design of experiments. Statistical inference from randomized studies is also more straightforward than many other situations. Objective randomization allows properly inductive procedures.