Introduction to the Theory of Statistical Inference


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Since , she has taught Statistics for undergraduate and graduate students.

Her research interests have moved from theoretical statistics to computer intensive statistics. She is interested in consulting and was working in Astrometry.

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Skickas inom vardagar. Laddas ned direkt. Skickas inom vardagar specialorder. Based on the authors' lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles.

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Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems. Highlights Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form Classroom-tested and designed for students of mathematical statistics Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material Solutions provided for problems formulated at the end of each chapter Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models Theoretical, difficult, or frequently misunderstood problems are marked The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines.


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Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose.

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Introduction to the Theory of Statistical Inference : Hannelore Liero :

With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference. This data, therefore, provides some evidence against the claim. It is claimed that among drivers years of age our population there is no relationship between drunk driving and gender. A roadside survey collected data from a random sample of 5, drivers and recorded their gender and whether they were drunk. The collected data showed roughly the same percent of drunk drivers among males and among females.

Introduction to Probability Theory and Statistical Inference / Edition 3

These data, therefore, do not give us any reason to reject the claim that there is no relationship between drunk driving and gender. In terms of organization, the Inference unit consists of two main parts: Inference for One Variable and Inference for Relationships between Two Variables. The organization of each of these parts will be discussed further as we proceed through the unit. The next two topics in the inference unit will deal with inference for one variable.

Recall that in the Exploratory Data Analysis EDA unit, when we learned about summarizing the data obtained from one variable where we learned about examining distributions, we distinguished between two cases; categorical data and quantitative data. We will make a similar distinction here in the inference unit. In the EDA unit, the type of variable determined the displays and numerical measures we used to summarize the data.

In Inference, the type of variable of interest categorical or quantitative will determine what population parameter is of interest.

The following outlines describe some of the important points about the process of inferential statistics as well as compare and contrast how researchers and statisticians approach this process. Here is another restatement of the big picture of statistical inference as it pertains to the two simple examples we will discuss first. One issue for students is that the theoretical process of statistical inference is only a small part of the applied steps in a research project.

Previously, in our discussion of the role of biostatistics , we defined these steps to be:. Among researchers, the following represent some of the important questions to address when conducting a study. Then, we will see that we can u se the sampling distribution of a statistic to:.

Introduction to Probability Theory and Statistical Inference

In our discussion of sampling distributions , we discussed the variability of sample statistics ; here is a quick review of this general concept and a formal definition of the standard error of a statistic. In our discussion of sampling distributions, we looked at a situation involving a random sample of students taken from the population of all part-time students in the United States, for which the overall proportion of females is 0.

Here we have a categorical variable of interest, gender. In this case, the true standard error of p-hat will be 0. We also showed how we can use this information along with information about the center mean or expected value to calculate probabilities associated with particular values of p-hat.


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  • After verifying the sample size requirements are reasonable, we can use a normal distribution to approximate. Similarly, for a quantitative variable, we looked at an example of household size in the United States which has a mean of 2. The sampling distribution of x-bar has a mean which is the same as the population mean, 2. Again, this standard deviation of the sampling distribution of x-bar is more commonly called the standard error of x-bar , in this case 0. And we can use this information the center and spread of the sampling distribution to find probabilities involving particular values of x-bar.

    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference
    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference
    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference
    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference
    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference
    Introduction to the Theory of Statistical Inference Introduction to the Theory of Statistical Inference

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