# Reading 11-Sampling and Estimation

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## SAMPLING

Question | Answer |
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Definition of Simple Random Sample | A simple random sample is a subset of a larger population created in such a way that each element of the population has an equal probability of being selected to the subset. |

systematic sampling | every kth member until we have a sample of the desired size. |

Definition of Sampling Error. | Sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate. |

Definition of Sampling Distribution of a Statistic | The sampling distribution of a statistic is the distribution of all the distinct possible values that the statistic can assume when computed from samples of the same size randomly drawn from the same population. |

Definition of Stratified Random Sampling | the population is divided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum in sizes proportional to the relative size of each stratum in the population. These samples are then pooled to form a stratified random sample. |

Indexing | An investment strategy in which an investor constructs a portfolio to mirror the performance of a specified index |

time series | a sequence of returns collected at discrete and equally spaced intervals of time (such as a historical series of monthly stock returns) |

Cross-sectional data | data on some characteristic of individuals, groups, geographical regions, or companies at a single point in time. |

monetary policy | Actions taken by a nation’s central bank to affect aggregate output and prices through changes in bank reserves, reserve requirements, or its target interest rate |

## DISTRIBUTION OF THE SAMPLE MEAN

Question | Answer |
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Central Limit Theorem | Given a population described by any probability distribution having mean μ and finite variance σ2, the sampling distribution of the sample mean X, computed from samples of size n from this population will be approximately normal with mean μ (the population mean) and variance σ2/n (the population variance divided by n) when the sample size n is large. |

Definition of the Standard Error of the Sample Mean | sample mean X calculated from a sample generated by a population with standard deviation σ, the standard error of the sample mean is given by one of two expressions |

The distribution of the sample mean | will be approximately normal. |

The mean of the distribution of | will be equal to the mean of the population from which the samples are drawn. |

The variance of the distribution of | will be equal to the variance of the population divided by the sample size. |

## POINT AND INTERVAL ESTIMATES OF THE POPULATION MEAN

Question | Answer |
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estimators | formulas that we use to compute the sample mean and all the other sample statistics are examples of estimation formulas |

estimate. | particular value that we calculate from sample observations using an estimator |

point estimate of the population mean | the calculated value of the sample mean in a given sample, used as an estimate of the population mean |

Definition of Confidence Interval | A confidence interval is a range for which one can assert with a given probability 1 − α, called the degree of confidence, that it will contain the parameter it is intended to estimate. This interval is often referred to as the 100(1 − α)% confidence interval for the parameter. |

t-distribution | symmetrical probability distribution defined by a single parameter known as degrees of freedom (df). Each value for the number of degrees of freedom defines one distribution in this family of distributions. |

## MORE ON SAMPLING

Question | Answer |
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Data mining | overuse of the same or related data in ways that we shall describe shortly. Data-mining bias refers to the errors that arise from such misuse of data |

Out-of-sample test | A test of a strategy or model using a sample outside the time period on which the strategy or model was developed. |

Intergenerational data mining | using information developed by previous researchers using a dataset to guide current research using the same or a related dataset. |

look-ahead bias | uses information that was not available on the test date. For example, tests of trading rules that use stock market returns and accounting balance sheet data must account for look-ahead bias. |

Time-Period Bias. | A test design is subject to time-period bias if it is based on a time period that may make the results time-period specific |

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